From Peter.Gates at nottingham.ac.uk Tue Mar 1 22:02:21 2011 From: Peter.Gates at nottingham.ac.uk (Peter Gates) Date: Tue, 1 Mar 2011 22:02:21 +0000 Subject: [Maths-Education] Research and teacher practices for 'working class' underachievement in secondary mathematics In-Reply-To: <3AEB72CF0A9B2A4F865AB09B21803864936B4A@ict-exbe-vs5.lsbu.ac.uk> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu><4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <3AEB72CF0A9B2A4F865AB09B21803864936B4A@ict-exbe-vs5.lsbu.ac.uk> Message-ID: Given the important issues this is sparking off and the deep connection it has for some of us.... ...is anybody interested in putting together with me a DG for ICME-12 on Teaching mathematics to learners from disadvantaged backgrounds (or some similarly worded topic?) See details below... Peter. Dr Peter Gates Centre for Research in Mathematics Education School of Education University of Nottingham *************************************** ICME-12: 12th International Congress on Mathematical Education July 8-15, 2012, Seoul, Korea. A call for ICME-12 Discussion Groups Contrary to past ICME practice, Discussion Groups for ICME-12 will be created in response to a proposal submitted by a group of up to five persons representing a diverse region of the world. As their name suggests, Discussion Groups (DGs) are designed to gather Congress participants who are interested in discussing, in a genuinely interactive way, certain challenging, controversial or emerging issues and dilemmas of interest to an international or regional audience. The focus of DGs should be distinct from the subjects covered in the Topic Study Groups (TSG) (see TSG listing attached) but could discuss a specific issue in greater detail than that of a TSG. Each DG will be allocated two time slots of 90 minutes each during the Congress. A proposal should include -- Description of the background and expertise of the proposed organizers -- Detailed description of the topic including anticipated aims and a rationale for the topic -- Key questions and issues for the DG to consider -- A precise description of the anticipated structure that will be used to manage the discussion during the two sessions, taking into account there will be no oral presentations in a DG except introductions by the organizers of the group to provide the background and framework for the discussion. Application forms are available on the website (http://icme12.org). Members of the organizing team must conform to the ICME custom that a person may only play one major (TSG, DG, Survey Team, Panel, plenary and regular lecture) and one minor role (poster presentation & other forms of contribution to the scientific program) at ICME. Note that proposing a DG will be considered a major role. Proposals should be received by the International Program Committee (IPC) by June 30, 2011. Proposals will be reviewed in accordance to the relevance of the topic to an international audience, the diversity and expertise of the proposed organizing team, and the format proposed for the discussion. Proposers will be notified of acceptance by August 15, 2011. Tasks for Organizing Teams (OT) The OT will be expected to: * Set up and maintain the DG web page Before the congress, the discussion group organizing team will post their page at the ICME-12 web site (http://icme12.org ) including contributions that define, limit, and/or present basic premises, theoretical considerations, research findings, viewpoints and facts that should be accounted for if a fruitful discussion is to be attained. Prior to the congress, participants can send individual contributions to the organizers for consideration as additional background information and may raise questions or participate in an exchange of ideas through the web site. * Produce a progress report by December 30, 2011 * Submit a final version of the DG presentation to be included in the Final program booklet. The final version must be sent to the Local Organizing Committee by April 10th, 2012. This description for the Final Program booklet should be between one and two pages (700 to 1,400 words) with the following: a) Name of DG and composition of the organizing team b) General description of the program for this DG; that is the aims, scope, list of main questions it addresses, the rationale which guided the OT in arriving at the program, and so on. c) The program of the DG, that is, the manner in which the discussion is organized and distributed in the two sessions. * Organize and manage the DG sessions during the Congress * Produce a final report for the ICME-12 Proceedings Deadline summary: -- June 30, 2011 Proposal submission -- August 15, 2011 Notification of acceptance -- December 30, 2011 Progress report -- April 10, 2012 Final version of the DG program submitted to Local Organizing Committee An IPC liaison will be appointed for each DG. The role of the IPC liaison officer is to support and be an important resource on how a DG works. Another source for information and guidance in planning a DG are the websites of recent ICMEs (see http://icme11.org and http://www.icme10.dk ). Thank you for your willingness to contribute to the success of ICME-12. We are looking forward to an energetic exchange of ideas and information through the Discussion Groups. -----Original Message----- From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Lerman, Stephen Sent: Monday, February 28, 2011 7:20 AM To: Mathematics Education discussion forum Cc: phillip.kent at gmail.com Subject: [Maths-Education] Re: Research and teacher practices for 'working class' underachievement in secondary mathematics Dylan's contribution is very interesting and helpful. But I think it supports Basil Bernstein's argument. He was indicating the lack of linguistic resources that generally is found amongst children from working class and other disadvantaged backgrounds, and the ways that schooling reinforces that linguistic disadvantage, but in pointing out the causes he was also demonstrating that if schools can provide those resources on school entrance (small classes, informed teachers etc.) those children can acquire the resources needed. Dylan is showing us that Scandinavian schools provide those resources and it has some success. Steve Professor Stephen Lerman Department of Education London South Bank University 103 Borough Road LONDON SE1 0AA Tel: +44 (0)20 7815 7440 -----Original Message----- From: maths-education-bounces at lists.nottingham.ac.uk on behalf of dylanwiliam at mac.com Sent: Sun 2/27/2011 8:55 PM To: Mathematics Education discussion forum Cc: phillip.kent at gmail.com Subject: [Maths-Education] Re: Research and teacher practices for 'working class' underachievement in secondary mathematics *********************************************************************************************************** This message has been generated through the Mathematics Education email discussion list. Hitting the REPLY key sends a message to all list members. *********************************************************************************************************** While I agree that the link between socioeconomic disadvantage and educational achievement is not a new phenomenon, it is also worth noting that it is not universal. We will probably never stop affluent parents from securing educational advantages for their children, but there are countries that have managed to ensure that socioeconomic disadvantage does not lead to lower achievement. While in the US and the UK, the relationship between the income of parents and children is linear (and steeper in the US than the UK) in some countries, it is not. Notably in some Scandinavian countries, while the richest do best, the poorest do as well as average students. In fact the research on educational quality, whether in child care, primary school, or secondary schools, shows that high-quality education benefits low achievers more than higher achievers. In some studies, this effect has been so strong that the effect of quality teaching has completely overcome socio-economic disadvantage. So it may be that Basil Bernstein was wrong. Education _can_ perhaps compensate for society, provided it is of very high quality. I therefore see the challenge as political-how to get get the best teachers working with the students who need them most... Dylan Wiliam On 27 Feb 2011, at 17:59, Alan Rogerson wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > Dear Phillip, > > The link: > > http://www.independent.co.uk/news/education/education-news/social-class-determines-childs-success-934240.html > > makes depressing reading: eg > > Children's social class is still the most significant factor in determining their exam success in state schools, the Government's head of teacher training acknowledges today. In an interview with The Independent, Graham Holley, the chief executive of the Training and Development Agency, said: "The performance of a school and a child in it is highly linked to social class. If you turn the clock back on pupils in school today 15 years and predict their outcomes from where they were born, you can do it. We need to change that. It's not something this government has done. It's not something the last government has done. It's something that has been there since the Second World War and probably even before that." > > There is no "probably" (Graham was simply restricting his comments to his own experience) the right word is "inevitably". > > As you will recall, I told you of my experiences of working class culture growing up after WW2, and sadly and clearly the problem is still with us, and in no way is it restricted to mathematics! We are speaking here of the strength of exclusive social/cultural world-views derived from primary socialisation,... "give us a child until he is 11"..... etc. > > Best wishes, > Alan > > > > > On 18/02/2011 15:08, Phillip Kent wrote: >> *********************************************************************************************************** >> This message has been generated through the Mathematics Education email discussion list. >> Hitting the REPLY key sends a message to all list members. >> *********************************************************************************************************** >> Dear colleagues, >> >> I'd appreciate some pointers to research and guidance on dealing with >> the problem of 'working class' underachievement in maths in secondary >> school. I realise there is a huge literature on this, in terms of >> statistical analysis on the existence of the problem, sociological-type >> analysis of classroom behaviours (a la Bernstein, etc), and research on >> teachers' beliefs about 'ability' and so on. >> >> However, I'm specifically interested in any research/guidance about what >> is effective for maths teachers to do in practice in classrooms. There >> is a very familiar type of student who for 'social' reasons comes to >> construct for him or herself an identity as someone who 'can't do >> maths', which is not related to his or her actual mathematical >> potential. Then how should the teacher break through this identity to >> tap into the actual potential and interest? >> >> Perhaps I am wrong to see this as essentially a problem of 'class'. Any >> thoughts welcome. >> >> - Phillip >> > > > This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. > > This message has been checked for viruses but the contents of an attachment > may still contain software viruses which could damage your computer system: > you are advised to perform your own checks. Email communications with the > University of Nottingham may be monitored as permitted by UK legislation. > ============================================ Email has been scanned for spam and viruses by Altman Technologies' email management service - www.altman.co.uk/emailsystems/ Any queries regarding LSBU Email should be sent to ICTemail at lsbu.ac.uk or you can check our web site at www.lsbu.ac.uk/email/ for up to date information about this service. From support at geogebra.org Tue Mar 1 23:35:55 2011 From: support at geogebra.org (GeoGebra Support) Date: Wed, 2 Mar 2011 00:35:55 +0100 Subject: [Maths-Education] GeoGebra Conference 2011 in Austria Message-ID: Dear Colleagues, we would like to draw your attention to our upcoming International GeoGebra Conference in Hagenberg near Linz, Austria on 29-31 August 2011. Please see the preliminary conference website for more information: http://www.geogebra.org/en/wiki/index.php/GeoGebra_Conference_2011 At this conference GeoGebra 4 will be released which will include GeoGebraCAS (symbolic view), GeoGebraMobile (applet support on mobile phones and tablets), GeoGebraPrim (elementary school version), GeoGebraTube (online sharing platform), updated Spreadsheet/Statistics, and many other new features. It would be great if you could join us in Austria to share ideas and participate in the interesting working groups. We look forward to meeting you in Hagenberg. Best wishes, The GeoGebra Team ----------------------------------- GeoGebra Support Team http://www.geogebra.org http://www.geogebra.org/forum/ http://www.facebook.com/geogebra From alan at rogerson.pol.pl Wed Mar 2 13:48:50 2011 From: alan at rogerson.pol.pl (Alan Rogerson) Date: Wed, 02 Mar 2011 14:48:50 +0100 Subject: [Maths-Education] Very sad news In-Reply-To: References: Message-ID: <4D6E4AC2.2040602@rogerson.pol.pl> We have just received the news from Italy of the untimely death of Filippo Spagnolo, of the University of Palermo. He was a dear friend and colleague going back to our first meeting in 1979, and was the local organiser of our very successful Project Conference in Sicily in 2002. Filippo was a wonderful person, open-hearted, generous and full of energy and humour. He was a tireless worker in mathematics education at all levels and was especially helpful and encouraging to his many students at the University of Palermo. All of those who knew him will be saddened to hear of his death, and he will truly leave an empty place in our hearts and minds that no one else can fill. Alan Rogerson From s.maughan at nfer.ac.uk Fri Mar 4 11:29:51 2011 From: s.maughan at nfer.ac.uk (Maughan, Sarah) Date: Fri, 4 Mar 2011 11:29:51 +0000 Subject: [Maths-Education] ICT in mathematics In-Reply-To: <4D6B899E.9030005@rogerson.pol.pl> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> Message-ID: <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> This seemed to bounce back first time so I am trying again. Apologies if you receive it twice! Hi I am trying to find some evidence about whether ICT has a positive impact on attainment in mathematics and wonder if anyone has any good examples? If you look at syntheses of research they tend to find little or no positive impact, over and above good teaching. However, I believe there are some examples of where the findings are more positive, usually in terms of a particular kind of ICT in a particular context. Can anyone let me know which are the key research reports in this area? I am particularly interested in impact on attainment rather than motivation or engagement (even though ultimately this is likely to improve attainment), so ICT use that directly helps with understanding of particular concepts for example. Thanks for your help. Sarah Sarah Maughan Director of Research National Foundation for Educational Research The Mere, Upton Park, Slough, Berkshire? SL1 2DQ, UK Reg. No 900899 (England).? Reg Address as above. Tel +44(0) 1753 574123: direct line +44(0) 1753 637137 Fax +44(0) 1753 671708: Web http://www.nfer.ac.uk This e-mail is confidential to the addressee and may contain privileged information. If you are not the addressee you are not permitted to use or copy this e-mail or its attachments nor may you disclose the same to any third party. If this has been sent to you in error please notify us as soon as possible. The NFER reserves the right to intercept and read e-mails sent or received by our employees. If you do not wish for your communications to be subjected to such scrutiny, you should not communicate via this e-mail system. The Foundation endeavours to exclude viruses from our data but it is the obligation of the recipient to check any attachments for viruses. Opinions, conclusions and other information contained in this message that do not relate to the official business of the NFER, or are personal to the individual sender, shall not be understood as endorsed by the Foundation and no liability will be accepted. Any legally binding agreement resulting from its content must be made separately in a printed medium. From phillip.kent at gmail.com Fri Mar 4 12:49:48 2011 From: phillip.kent at gmail.com (Phillip Kent) Date: Fri, 04 Mar 2011 12:49:48 +0000 Subject: [Maths-Education] Maths-Art Seminar at LKL, 10th March : Mary Harris, 'Some mathematics within? What actually goes on in some traditional textiles crafts?' References: Message-ID: <1299242988.26700.21.camel@phillip-macbook-ubuntu> ** PLEASE CIRCULATE ** ALL WELCOME ** SOME MATHEMATICS WITHIN? WHAT ACTUALLY GOES ON IN SOME TRADITIONAL TEXTILES CRAFTS? An LKL Maths-Art seminar by Mary Harris Thursday 10 February 2011, 6.00 - 7.30pm Mary Harris has been an influential researcher on mathematical thinking and domestic textile crafts over many decades. In the 1980s, she developed the hugely successful exhibition COMMON THREADS which toured the UK for two years, and was re-developed as a touring exhibition for the British Council, which visited 23 countries between 1991 and 1994. (A summary of this experience was published in the 1997 book, "Common Threads: Women, mathematics and work".) This seminar returns to the original questions which inspired Common Threads. Most of us wear clothes most of the time and they and the fabrics they are made of are mostly made by women, either at home or in factories. Whilst researching women's work with textiles during the 1980s I found myself discovering undeniable mathematical thought going on in the very medium often taken as the mark of "brainless femininity". So I have spent a lot of time since then studying the kinds of mathematical thought which are involved in domestic work with textiles. In the Common Threads exhibition, low-status domestic textiles were labelled in the high-status language of mathematics. By co-incidence this happened just at a time when the relative failure in school mathematics of girls and some ethnic minority children had been recognised as a serious problem. I will begin the seminar with an incident which provoked me into taking a closer look at what actually goes on when weaving a kilim rug. I will then look at some knitted garments and how they were made. Current commercial instructions for hand-knitting, confusingly called "patterns", tend to be line by line physical descriptions of what a knitter does. This does not always reflect what a knitter actually thinks and such "patterns" often end up looking like uninviting sheets of algebra. I argue that there must be a better way, and invite you to find a general way of writing instructions for making a tam o' shanter. To enjoy this session there is absolutely no need whatsoever to be able to knit! DATE: Thursday 10th March TIME: 6.00 to 7.30pm PLACE: London Knowledge Lab, 23-29 Emerald St, London, WC1N 3QS [Travel information & maps at: http://bit.ly/LKL-MathsArt-venue ] FUTURE SEMINARS: April 14, Nick Sayers; May 12, Daniel White; June 9, special origami/maths-art meeting co-organised with the British Origami Society. LKL Maths-Art seminars are free to attend, and All are welcome. No reservation is required, but an email to lkl.maths.art at gmail.com is appreciated for planning purposes ----------------------------------- *Visit the website and seminar archive: http://www.lkl.ac.uk/events/maths-art *Join the email list for future seminar announcements: http://www.dcs.bbk.ac.uk/mailman/listinfo/lkl-maths-art ++++++ Dr Phillip Kent, Visiting Fellow, London Knowledge Lab p.kent at ioe.ac.uk phillip.kent at gmail.com www.phillipkent.net m: 07950 952034 ++++++ From phillip.kent at gmail.com Fri Mar 4 13:36:16 2011 From: phillip.kent at gmail.com (Phillip Kent) Date: Fri, 04 Mar 2011 13:36:16 +0000 Subject: [Maths-Education] Maths-Art Seminar at LKL, 10th March : Mary Harris, 'Some mathematics within? What actually goes on in some traditional textiles crafts?' References: Message-ID: <1299245776.26700.58.camel@phillip-macbook-ubuntu> ** PLEASE CIRCULATE ** ALL WELCOME ** ** SORRY FOLKS FOR INCORRECT DATE IN PREVIOUS MESSAGE!! IT IS 10TH MARCH ** SOME MATHEMATICS WITHIN? WHAT ACTUALLY GOES ON IN SOME TRADITIONAL TEXTILES CRAFTS? An LKL Maths-Art seminar by Mary Harris Thursday 10 March 2011, 6.00 - 7.30pm Mary Harris has been an influential researcher on mathematical thinking and domestic textile crafts over many decades. In the 1980s, she developed the hugely successful exhibition COMMON THREADS which toured the UK for two years, and was re-developed as a touring exhibition for the British Council, which visited 23 countries between 1991 and 1994. (A summary of this experience was published in the 1997 book, "Common Threads: Women, mathematics and work".) This seminar returns to the original questions which inspired Common Threads. Most of us wear clothes most of the time and they and the fabrics they are made of are mostly made by women, either at home or in factories. Whilst researching women's work with textiles during the 1980s I found myself discovering undeniable mathematical thought going on in the very medium often taken as the mark of "brainless femininity". So I have spent a lot of time since then studying the kinds of mathematical thought which are involved in domestic work with textiles. In the Common Threads exhibition, low-status domestic textiles were labelled in the high-status language of mathematics. By co-incidence this happened just at a time when the relative failure in school mathematics of girls and some ethnic minority children had been recognised as a serious problem. I will begin the seminar with an incident which provoked me into taking a closer look at what actually goes on when weaving a kilim rug. I will then look at some knitted garments and how they were made. Current commercial instructions for hand-knitting, confusingly called "patterns", tend to be line by line physical descriptions of what a knitter does. This does not always reflect what a knitter actually thinks and such "patterns" often end up looking like uninviting sheets of algebra. I argue that there must be a better way, and invite you to find a general way of writing instructions for making a tam o' shanter. To enjoy this session there is absolutely no need whatsoever to be able to knit! DATE: Thursday 10th March TIME: 6.00 to 7.30pm PLACE: London Knowledge Lab, 23-29 Emerald St, London, WC1N 3QS [Travel information & maps at: http://bit.ly/LKL-MathsArt-venue ] FUTURE SEMINARS: April 14, Nick Sayers; May 12, Daniel White; June 9, special origami/maths-art meeting co-organised with the British Origami Society. LKL Maths-Art seminars are free to attend, and All are welcome. No reservation is required, but an email to lkl.maths.art at gmail.com is appreciated for planning purposes ----------------------------------- *Visit the website and seminar archive: http://www.lkl.ac.uk/events/maths-art *Join the email list for future seminar announcements: http://www.dcs.bbk.ac.uk/mailman/listinfo/lkl-maths-art ++++++ Dr Phillip Kent, Visiting Fellow, London Knowledge Lab p.kent at ioe.ac.uk phillip.kent at gmail.com www.phillipkent.net m: 07950 952034 ++++++ From dylanwiliam at mac.com Fri Mar 4 13:53:31 2011 From: dylanwiliam at mac.com (dylanwiliam at mac.com) Date: Fri, 04 Mar 2011 13:53:31 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> Message-ID: Sarah One of the real success stories in the use of ICT to support learning in mathematics is Carnegie Learning's Cognitive Tutor for algebra. A summary of the research evidence can be found at: http://www.carnegielearning.com/research/reports/ Dylan On 4 Mar 2011, at 11:29, Maughan, Sarah wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > This seemed to bounce back first time so I am trying again. Apologies if you receive it twice! > > Hi > I am trying to find some evidence about whether ICT has a positive impact on attainment in mathematics and wonder if anyone has any good examples? If you look at syntheses of research they tend to find little or no positive impact, over and above good teaching. However, I believe there are some examples of where the findings are more positive, usually in terms of a particular kind of ICT in a particular context. Can anyone let me know which are the key research reports in this area? I am particularly interested in impact on attainment rather than motivation or engagement (even though ultimately this is likely to improve attainment), so ICT use that directly helps with understanding of particular concepts for example. > > Thanks for your help. > > Sarah > > Sarah Maughan > Director of Research > National Foundation for Educational Research > The Mere, Upton Park, Slough, Berkshire SL1 2DQ, UK > Reg. No 900899 (England). Reg Address as above. > Tel +44(0) 1753 574123: direct line +44(0) 1753 637137 > Fax +44(0) 1753 671708: > Web http://www.nfer.ac.uk > This e-mail is confidential to the addressee and may contain privileged information. If you are not the addressee you are not permitted to use or copy this e-mail or its attachments nor may you disclose the same to any third party. If this has been sent to you in error please notify us as soon as possible. The NFER reserves the right to intercept and read e-mails sent or received by our employees. If you do not wish for your communications to be subjected to such scrutiny, you should not communicate via this e-mail system. The Foundation endeavours to exclude viruses from our data but it is the obligation of the recipient to check any attachments for viruses. Opinions, conclusions and other information contained in this message that do not relate to the official business of the NFER, or are personal to the individual sender, shall not be understood as endorsed by the Foundation and no liability will be accepted. Any legally binding agreement resulting from its content must be made separately in a printed medium. > > > > This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. > > This message has been checked for viruses but the contents of an attachment > may still contain software viruses which could damage your computer system: > you are advised to perform your own checks. Email communications with the > University of Nottingham may be monitored as permitted by UK legislation. From debutler at argonet.co.uk Fri Mar 4 14:22:41 2011 From: debutler at argonet.co.uk (Douglas Butler (Argonet)) Date: Fri, 4 Mar 2011 14:22:41 -0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> Message-ID: <026601cbda77$9fb73ae0$df25b0a0$@argonet.co.uk> This is a thread that has troubled me for years - how to put some flesh on the assertion that ICT makes a difference in mathematics. I am both a creator and a user of mathematics software, and I need no convincing at all. But to get hard research evidence would presumably require setting up control groups of identical children doing the same courses with the same teachers, but without the technology. Surely this is impossible to achieve? Douglas == from Douglas Butler < debutler at argonet.co.uk > ==? Director, iCT TRAINING CENTRE (OUNDLE) PO Box 46, Oundle, Peterborough PE8 4EJ, UK T: +44 (0)1832 273444 F: 273529 M: +44 (0)7860 843462 www.tsm-resources.com? www.autograph-maths.com -----Original Message----- From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of dylanwiliam at mac.com Sent: 04 March 2011 13:54 To: Mathematics Education discussion forum Subject: [Maths-Education] Re: ICT in mathematics **************************************************************************** ******************************* This message has been generated through the Mathematics Education email discussion list. Hitting the REPLY key sends a message to all list members. **************************************************************************** ******************************* Sarah One of the real success stories in the use of ICT to support learning in mathematics is Carnegie Learning's Cognitive Tutor for algebra. A summary of the research evidence can be found at: http://www.carnegielearning.com/research/reports/ Dylan On 4 Mar 2011, at 11:29, Maughan, Sarah wrote: > ********************************************************************** > ************************************* > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > ********************************************************************** > ************************************* > This seemed to bounce back first time so I am trying again. Apologies if you receive it twice! > > Hi > I am trying to find some evidence about whether ICT has a positive impact on attainment in mathematics and wonder if anyone has any good examples? If you look at syntheses of research they tend to find little or no positive impact, over and above good teaching. However, I believe there are some examples of where the findings are more positive, usually in terms of a particular kind of ICT in a particular context. Can anyone let me know which are the key research reports in this area? I am particularly interested in impact on attainment rather than motivation or engagement (even though ultimately this is likely to improve attainment), so ICT use that directly helps with understanding of particular concepts for example. > > Thanks for your help. > > Sarah > > Sarah Maughan > Director of Research > National Foundation for Educational Research The Mere, Upton Park, > Slough, Berkshire SL1 2DQ, UK Reg. No 900899 (England). Reg Address > as above. > Tel +44(0) 1753 574123: direct line +44(0) 1753 637137 Fax +44(0) 1753 > 671708: > Web http://www.nfer.ac.uk > This e-mail is confidential to the addressee and may contain privileged information. If you are not the addressee you are not permitted to use or copy this e-mail or its attachments nor may you disclose the same to any third party. If this has been sent to you in error please notify us as soon as possible. The NFER reserves the right to intercept and read e-mails sent or received by our employees. If you do not wish for your communications to be subjected to such scrutiny, you should not communicate via this e-mail system. The Foundation endeavours to exclude viruses from our data but it is the obligation of the recipient to check any attachments for viruses. Opinions, conclusions and other information contained in this message that do not relate to the official business of the NFER, or are personal to the individual sender, shall not be understood as endorsed by the Foundation and no liability will be accepted. Any legally binding agreement resulting from its content must! be made separately in a printed medium. > > > > This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. > > This message has been checked for viruses but the contents of an > attachment may still contain software viruses which could damage your computer system: > you are advised to perform your own checks. Email communications with > the University of Nottingham may be monitored as permitted by UK legislation. From alan at rogerson.pol.pl Fri Mar 4 14:33:01 2011 From: alan at rogerson.pol.pl (Alan Rogerson) Date: Fri, 04 Mar 2011 15:33:01 +0100 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> Message-ID: <4D70F81D.1090100@rogerson.pol.pl> Dear Sarah, I am surprised that Dylan did not mention that the organisation below is a commercial publisher, whose primary objective must be, of course, to make money, not to do objective research nor to assist teachers or students in a philanthropic or educational way. The problem here with any of their own reported research would be: how objective is it? Please, please do not misunderstand me - there are many commercial companies doing work that we would regard as useful, and a symbiosis between commercial and educational bodies would seem to be inevitable in our society. But it behooves educationalists themselves to evaluate and assess the educational merits or otherwise of commercial products, this is simply a general statement of good practice, common sense even, it does not in any way impinge on the merits of commercial companies such as Carnegie. Have you tried Google, most questions similar to yours can be answered by several hours work sifting through the many pages there? There are as you surely know many, many programmes, software, projects, and so called virtual schools handling ICT, but very much less objective or educational research being done on them. I was, however, very impressed with the Nationally supported Educational work on ICT coordinated from Chichester University, when I visited them for a day several years ago. You might like to ask them? Having worked myself in the field of ICT (as it is now called) since about 1966 could I also especially draw to your attention the Virtual School for the Gifted, now defunct but at one time the world's only genuine interactive virtual school, with whom I worked for ten years as a teacher, the last two years as Manager or Coordinator. I believe it provided a very effective model for ICT learning and there was considerable anecdotal evidence of its success in helping children learn mathematics, and other subjects! Best wishes, Alan On 04/03/2011 14:53, dylanwiliam at mac.com wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > Sarah > > One of the real success stories in the use of ICT to support learning in mathematics is Carnegie Learning's Cognitive Tutor for algebra. > > A summary of the research evidence can be found at: > > http://www.carnegielearning.com/research/reports/ > > Dylan > > > On 4 Mar 2011, at 11:29, Maughan, Sarah wrote: > >> *********************************************************************************************************** >> This message has been generated through the Mathematics Education email discussion list. >> Hitting the REPLY key sends a message to all list members. >> *********************************************************************************************************** >> This seemed to bounce back first time so I am trying again. Apologies if you receive it twice! >> >> Hi >> I am trying to find some evidence about whether ICT has a positive impact on attainment in mathematics and wonder if anyone has any good examples? If you look at syntheses of research they tend to find little or no positive impact, over and above good teaching. However, I believe there are some examples of where the findings are more positive, usually in terms of a particular kind of ICT in a particular context. Can anyone let me know which are the key research reports in this area? I am particularly interested in impact on attainment rather than motivation or engagement (even though ultimately this is likely to improve attainment), so ICT use that directly helps with understanding of particular concepts for example. >> >> Thanks for your help. >> >> Sarah >> >> Sarah Maughan >> Director of Research >> National Foundation for Educational Research >> The Mere, Upton Park, Slough, Berkshire SL1 2DQ, UK >> Reg. No 900899 (England). Reg Address as above. >> Tel +44(0) 1753 574123: direct line +44(0) 1753 637137 >> Fax +44(0) 1753 671708: >> Web http://www.nfer.ac.uk >> This e-mail is confidential to the addressee and may contain privileged information. If you are not the addressee you are not permitted to use or copy this e-mail or its attachments nor may you disclose the same to any third party. If this has been sent to you in error please notify us as soon as possible. The NFER reserves the right to intercept and read e-mails sent or received by our employees. If you do not wish for your communications to be subjected to such scrutiny, you should not communicate via this e-mail system. The Foundation endeavours to exclude viruses from our data but it is the obligation of the recipient to check any attachments for viruses. Opinions, conclusions and other information contained in this message that do not relate to the official business of the NFER, or are personal to the individual sender, shall not be understood as endorsed by the Foundation and no liability will be accepted. Any legally binding agreement resulting from its content must > be made separately in a printed medium. >> >> >> This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. >> >> This message has been checked for viruses but the contents of an attachment >> may still contain software viruses which could damage your computer system: >> you are advised to perform your own checks. Email communications with the >> University of Nottingham may be monitored as permitted by UK legislation. > > From dylanwiliam at mac.com Fri Mar 4 14:52:40 2011 From: dylanwiliam at mac.com (dylanwiliam at mac.com) Date: Fri, 04 Mar 2011 14:52:40 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <4D70F81D.1090100@rogerson.pol.pl> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> <4D70F81D.1090100@rogerson.pol.pl> Message-ID: <605A41D4-D3EB-4F3D-9BB3-7A31D4BF4AF3@mac.com> Alan: Sarah asked specifically for studies that showed the impact of ICT on attainment, and the Cognitive Tutor is one of the best researched pieces of software for mathematics education. While Carnegie Learning is a commercial company that has taken over marketing and distribution of the products generated by the people who developed the Cognitive Tutor, the research itself is very solid (and much of it dates from before Carnegie Learning became involved). I agree that third party evaluations, such as those undertaken by Mathematica, would be better, and of course educationalists should evaluate the merits of the studies, but the fact that the research is now being used to support a commercial enterprise does not invalidate the original findings. Dylan On 4 Mar 2011, at 14:33, Alan Rogerson wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > Dear Sarah, > I am surprised that Dylan did not mention that the organisation below is a commercial publisher, whose primary objective must be, of course, to make money, not to do objective research nor to assist teachers or students in a philanthropic or educational way. The problem here with any of their own reported research would be: how objective is it? > Please, please do not misunderstand me - there are many commercial companies doing work that we would regard as useful, and a symbiosis between commercial and educational bodies would seem to be inevitable in our society. But it behooves educationalists themselves to evaluate and assess the educational merits or otherwise of commercial products, this is simply a general statement of good practice, common sense even, it does not in any way impinge on the merits of commercial companies such as Carnegie. > Have you tried Google, most questions similar to yours can be answered by several hours work sifting through the many pages there? There are as you surely know many, many programmes, software, projects, and so called virtual schools handling ICT, but very much less objective or educational research being done on them. I was, however, very impressed with the Nationally supported Educational work on ICT coordinated from Chichester University, when I visited them for a day several years ago. You might like to ask them? > Having worked myself in the field of ICT (as it is now called) since about 1966 could I also especially draw to your attention the Virtual School for the Gifted, now defunct but at one time the world's only genuine interactive virtual school, with whom I worked for ten years as a teacher, the last two years as Manager or Coordinator. I believe it provided a very effective model for ICT learning and there was considerable anecdotal evidence of its success in helping children learn mathematics, and other subjects! > Best wishes, > Alan > > > On 04/03/2011 14:53, dylanwiliam at mac.com wrote: >> *********************************************************************************************************** >> This message has been generated through the Mathematics Education email discussion list. >> Hitting the REPLY key sends a message to all list members. >> *********************************************************************************************************** >> Sarah >> >> One of the real success stories in the use of ICT to support learning in mathematics is Carnegie Learning's Cognitive Tutor for algebra. >> >> A summary of the research evidence can be found at: >> >> http://www.carnegielearning.com/research/reports/ >> >> Dylan >> >> >> On 4 Mar 2011, at 11:29, Maughan, Sarah wrote: >> >>> *********************************************************************************************************** >>> This message has been generated through the Mathematics Education email discussion list. >>> Hitting the REPLY key sends a message to all list members. >>> *********************************************************************************************************** >>> This seemed to bounce back first time so I am trying again. Apologies if you receive it twice! >>> >>> Hi >>> I am trying to find some evidence about whether ICT has a positive impact on attainment in mathematics and wonder if anyone has any good examples? If you look at syntheses of research they tend to find little or no positive impact, over and above good teaching. However, I believe there are some examples of where the findings are more positive, usually in terms of a particular kind of ICT in a particular context. Can anyone let me know which are the key research reports in this area? I am particularly interested in impact on attainment rather than motivation or engagement (even though ultimately this is likely to improve attainment), so ICT use that directly helps with understanding of particular concepts for example. >>> >>> Thanks for your help. >>> >>> Sarah >>> >>> Sarah Maughan >>> Director of Research >>> National Foundation for Educational Research >>> The Mere, Upton Park, Slough, Berkshire SL1 2DQ, UK >>> Reg. No 900899 (England). Reg Address as above. >>> Tel +44(0) 1753 574123: direct line +44(0) 1753 637137 >>> Fax +44(0) 1753 671708: >>> Web http://www.nfer.ac.uk >>> This e-mail is confidential to the addressee and may contain privileged information. If you are not the addressee you are not permitted to use or copy this e-mail or its attachments nor may you disclose the same to any third party. If this has been sent to you in error please notify us as soon as possible. The NFER reserves the right to intercept and read e-mails sent or received by our employees. If you do not wish for your communications to be subjected to such scrutiny, you should not communicate via this e-mail system. The Foundation endeavours to exclude viruses from our data but it is the obligation of the recipient to check any attachments for viruses. Opinions, conclusions and other information contained in this message that do not relate to the official business of the NFER, or are personal to the individual sender, shall not be understood as endorsed by the Foundation and no liability will be accepted. Any legally binding agreement resulting from its content must >> be made separately in a printed medium. >>> >>> >>> This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. >>> >>> This message has been checked for viruses but the contents of an attachment >>> may still contain software viruses which could damage your computer system: >>> you are advised to perform your own checks. Email communications with the >>> University of Nottingham may be monitored as permitted by UK legislation. >> >> > > From alan at rogerson.pol.pl Fri Mar 4 15:25:23 2011 From: alan at rogerson.pol.pl (Alan Rogerson) Date: Fri, 04 Mar 2011 16:25:23 +0100 Subject: [Maths-Education] Re: Maths-Education Digest, Vol 77, Issue 6 In-Reply-To: References: Message-ID: <4D710463.70108@rogerson.pol.pl> Dear Douglas, This is the perennial problem with all so-called objective research in mathematics education in as far as it concerns the actual classrooms. This is why I think more attention is now being given to participant-observer (as it is called in sociiology) styles of "research" where the researcher immediately assumes their presence changes the very situation they are looking at and hence tries to take this into account - a truism in sociology obviously (can we honestly imagine that real teachers and students will remain undisturbed when a "researcher" comes to visit them!?). You cannot step into the same classroom twice as it were! When we worked for some 8 years on the highly innovative SMP7-13 Individualised course in the 1970s (yes, indeed when dinosaurs roamed the earth) we did our best to "test" the new materials by having some 10,000 children (I think, of that order of magnitude anyway) in many testing schools, half the classes doing the new materials and half not. But as you say below, we knew immediately that this was not enough for any valid objective comparison, and never would be. Different teachers, different children, the Hawthorn effect, and its vice versa version presumably, and a host of other societal factors guaranteed that our results were only suggestive at best. It is surely our belief systems that drive us to produce creative and innovative programs, such as your Autograph, and these same belief systems support us in our needing no convincing that these new things DO work. But in addition we should be open-minded to experience and especially to constructive criticism. If this clearly shows there is a problem then the solution is to fix it in the next edition or upgrade and try it again? We were doing this continually with SMP - as you do with revisions and upgrades of Autograph. Surely reports of such educational feedback of this kind would help Sarah to evaluate whether or not certain things in ICT have worked better or not? Best wishes, Alan On 04/03/2011 15:32, maths-education-request at lists.nottingham.ac.uk wrote: > This is a thread that has troubled me for years - how to put some flesh on > the assertion that ICT makes a difference in mathematics. > > I am both a creator and a user of mathematics software, and I need no > convincing at all. > > But to get hard research evidence would presumably require setting up > control groups of identical children doing the same courses with the same > teachers, but without the technology. Surely this is impossible to achieve? > > Douglas > > == from Douglas Butler< debutler at argonet.co.uk > ==? > Director, iCT TRAINING CENTRE (OUNDLE) From jodie.hunter at plymouth.ac.uk Fri Mar 4 15:48:17 2011 From: jodie.hunter at plymouth.ac.uk (Jodie Hunter) Date: Fri, 4 Mar 2011 15:48:17 +0000 Subject: [Maths-Education] Early algebra references Message-ID: Hi I have been undertaking classroom based research in the area of early algebra with KS1 and KS2 children in the UK. I am interested in any references for research studies or reports in the area of early algebra with primary children in the UK or Europe - I am interested in work across a range of areas such as the links between arithmetic and algebra, functional reasoning and classroom practices which support children to engage in early algebraic reasoning. I have ample research reports and papers from the USA and would appreciate any suggestions for UK or European studies to widen my literature review. Thanks for your help. Jodie Hunter Lecturer in Mathematics Education University of Plymouth From Pam.Bye at ima.org.uk Fri Mar 4 15:49:03 2011 From: Pam.Bye at ima.org.uk (Pam Bye) Date: Fri, 4 Mar 2011 15:49:03 +0000 Subject: [Maths-Education] IMA Maths 2011 - 24 March Message-ID: IMA MATHEMATICS 2011 24 March 2011 Saddlers? Hall, Gutter Lane, London The IMA is holding a major one day conference on mathematics and its applications for the present day on 24 March 2011 at Saddlers' Hall, Gutter Lane, London. The aim of the conference is to bring together people with an interest in mathematics and its applications to consider current issues in the subject. The conference topics will cover research topics in mathematics; public understanding of mathematics and industrial applications of mathematics. These topics will be of interest to both mathematicians and those working with mathematicians as the presentations will address the impact of the work rather than emphasise its technical nature. The conference will give an opportunity for informal discussion between people who are interested in a variety of areas in mathematics. This conference is the next in the series following successful conferences held in Manchester in 2005 and London in 2007, 2008, 2009 and 2010. Registration form: http://www.ima.org.uk/Conferences/maths2011_application_form.doc Conference fees: IMA Member ? AMIMA ?16.00 IMA Member ? MIMA/FIMA/AFIMA ?27.00 IMA Member ? Student ?10.00 IMA Member ? Retired ?10.00 Non IMA member ?43.00 Student Non IMA member ?16.00 Programme: 10.00 Opening ? Mike Walker 10.05 Keynote speech ? Statistics in the retail financial services sector - David Hand 10.45 Industrial applications ? Heather Tewkesbury 11.25 Coffee 11.45 A quick tour of Mathematical Techniques Supporting Future Equipment Health Management ? Steve King, Rolls Royce 12.25 Tackling the mathematics potential and challenges ? Celia Hoyles 13.10 Lunch 14.10 Seeing the world with mathematical eyes ? Steve Humble 14.50 Bloodhound project 15.30 Tea 15.50 Mathematics in sport ? David Percy 16.30 IMA in 2011 ? Mike Walker 16.50 Reception Further information can be found at the conference website: http://www.ima.org.uk/Conferences/maths_2011.html For conference queries please contact conferences at ima.org.uk Pamela Bye Conference Support Officer The Institute of Mathematics and its Applications Tel: 01702 354020 Charity Registration number 1017777 ______________________________________________________________________ The Institute of Mathematics and its Applications is a not for profit organisation registered as a charity in the UK. This email has been scanned by the MessageLabs Email Security System before onward transmission. For more information please visit http://www.messagelabs.com/email ______________________________________________________________________ From alan at rogerson.pol.pl Fri Mar 4 16:10:11 2011 From: alan at rogerson.pol.pl (Alan Rogerson) Date: Fri, 04 Mar 2011 17:10:11 +0100 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <605A41D4-D3EB-4F3D-9BB3-7A31D4BF4AF3@mac.com> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> <4D70F81D.1090100@rogerson.pol.pl> <605A41D4-D3EB-4F3D-9BB3-7A31D4BF4AF3@mac.com> Message-ID: <4D710EE3.7050502@rogerson.pol.pl> Dear Dylan, What you say below does not in any way alter the fact that what you actually recommended to Sarah were reports on a webpage produced by a commercial company. That is the problem. You say something is "one of the best researched" but we need to know when and by whom? It is not the quantity of research that counts, rather its quality. Please note, I am not making any judgement about the actual research which you call "original" nor did I say that this research is some how invalidated by being used by a commercial company. Let's say for the sake of argument, that all this research could be validated, and also note that some of the reports on the Carnegie.inc webpage were (as we know) from Carnegie Mellon University itself, and may have even pre-dated the formation of Carnegie.inc, I do hope you can see that this does not change the problem? "Selective quotation" is still a real hazard, what company after all will quote research critical of its own products? We know only too well the much bigger and much more serious debate going on about so-called academic research being funded, or supported, (or of course suppressed!) by drug companies. Companies are in business to make money, so we can hardly use them, or the reports they quote, as objective exemplars of "research". The contrast is between reports which clearly have no such bias, and those which are at risk of being biassed. Surely we cannot say "third party evaluations... would be better", surely you mean essential? We know from basic statistics that biassed evidence, when we can not attach boundaries to the bias, , is, and must be, useless (not second best). We all know the story of the millions of telephone calls surveyed that failed to predict the next President of the USA....? Please also note that there is absolutely no bias (or specific accusations) against Carnegie.inc in particular here, it is a purely general point that is being made. The only remaining problem, and somewhat insoluble, is the one Douglas Butler has just mentioned. C'est la vie, c'est la ICT. Best wishes, Alan On 04/03/2011 15:52, dylanwiliam at mac.com wrote: > Alan: Sarah asked specifically for studies that showed the impact of ICT on attainment, and the Cognitive Tutor is one of the best researched pieces of software for mathematics education. While Carnegie Learning is a commercial company that has taken over marketing and distribution of the products generated by the people who developed the Cognitive Tutor, the research itself is very solid (and much of it dates from before Carnegie Learning became involved). I agree that third party evaluations, such as those undertaken by Mathematica, would be better, and of course educationalists should evaluate the merits of the studies, but the fact that the research is now being used to support a commercial enterprise does not invalidate the original findings. > > Dylan From dkirsh at lsu.edu Fri Mar 4 16:57:39 2011 From: dkirsh at lsu.edu (David H Kirshner) Date: Fri, 4 Mar 2011 10:57:39 -0600 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <4D710EE3.7050502@rogerson.pol.pl> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> <4D70F81D.1090100@rogerson.pol.pl><605A41D4-D3EB-4F3D-9BB3-7A31D4BF4AF3@mac.com> <4D710EE3.7050502@rogerson.pol.pl> Message-ID: <731CECC23FB8CA4E9127BD399744D1EC02F40343@email001.lsu.edu> I'm enjoying this thread. To be fair, Ken Koedinger, lead developer of the software, is a bona fide cognitive scientist who has published a variety of academic papers on the cognitive theory involved, in addition to publications on the effectiveness of the tutor. And even the latter publications have been in peer review academic journals. Still, it would be interesting to know if "independent" evaluations of the effectiveness have been undertaken and published. There is some software on the market now that seems to be effective in raising students' test scores in comparison with standard classroom instruction. For instance, at Northern Arizona University, the college algebra course is taught through an online facility that "promote[s] active and collaborative learning, address the diverse range of student learning styles and permit acceleration. It will use ALEKS, a comprehensive instructional software and course management system that individualizes assessment and learning. ALEKS is Web-based, allowing students to access course materials at anytime from anyplace, and can be customized to meet student and course needs. As a supplement to ALEKS, NAU will also use Thinkwell, a video-based mathematics software program that uses highlighted worked examples and video lectures for students who learn better in this mode." (http://www.thencat.org/PCR/R3/NAU/NAU_Abstract.htm) However, it is clear that the program's effectiveness primarily is related to its effective provision of practice problems and immediate feedback. In short, it promotes learning of skills through repetitive practice in the behaviorist tradition. I've looked at the Cognitive Tutor, and it's a more complex and ambitious project. The Tutor functions through a multidimensional model of expertise that it uses to update a student model, and thereby determine what kinds of problems and assistance would best benefit the student. It is not so straightforward an analysis as to whether what is being promoted is skills through practice (in a sophisticated way), or something more akin to what we would consider as mathematical concepts. The Cognitive Tutor is based on the ACT-series of acquisition models developed by John Anderson and company at Carnegie Melon--in fact, Ken was a student of his, and is now a frequent collaborator. The ambiguity of the Tutor in terms of its learning modalities is reflected also in the status of the ACT theories. Anderson (2005) would be a good source to begin to answer those questions, and Anderson (2007) includes an interesting discussion of the general issue of the kind of learning addressed in the ACT theories. David Kirshner Anderson, J. R. (2005). Human symbol manipulation within an integrated cognitive architecture. Cognitive Science, 29, 313-341. [algebraic symbol skills] Anderson, J. R. (2007). How can the human mind occur in the physical universe?. Oxford University Press. -----Original Message----- From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Alan Rogerson Sent: Friday, March 04, 2011 10:10 AM To: Mathematics Education discussion forum Subject: [Maths-Education] Re: ICT in mathematics ************************************************************************ *********************************** This message has been generated through the Mathematics Education email discussion list. Hitting the REPLY key sends a message to all list members. ************************************************************************ *********************************** Dear Dylan, What you say below does not in any way alter the fact that what you actually recommended to Sarah were reports on a webpage produced by a commercial company. That is the problem. You say something is "one of the best researched" but we need to know when and by whom? It is not the quantity of research that counts, rather its quality. Please note, I am not making any judgement about the actual research which you call "original" nor did I say that this research is some how invalidated by being used by a commercial company. Let's say for the sake of argument, that all this research could be validated, and also note that some of the reports on the Carnegie.inc webpage were (as we know) from Carnegie Mellon University itself, and may have even pre-dated the formation of Carnegie.inc, I do hope you can see that this does not change the problem? "Selective quotation" is still a real hazard, what company after all will quote research critical of its own products? We know only too well the much bigger and much more serious debate going on about so-called academic research being funded, or supported, (or of course suppressed!) by drug companies. Companies are in business to make money, so we can hardly use them, or the reports they quote, as objective exemplars of "research". The contrast is between reports which clearly have no such bias, and those which are at risk of being biassed. Surely we cannot say "third party evaluations... would be better", surely you mean essential? We know from basic statistics that biassed evidence, when we can not attach boundaries to the bias, , is, and must be, useless (not second best). We all know the story of the millions of telephone calls surveyed that failed to predict the next President of the USA....? Please also note that there is absolutely no bias (or specific accusations) against Carnegie.inc in particular here, it is a purely general point that is being made. The only remaining problem, and somewhat insoluble, is the one Douglas Butler has just mentioned. C'est la vie, c'est la ICT. Best wishes, Alan On 04/03/2011 15:52, dylanwiliam at mac.com wrote: > Alan: Sarah asked specifically for studies that showed the impact of ICT on attainment, and the Cognitive Tutor is one of the best researched pieces of software for mathematics education. While Carnegie Learning is a commercial company that has taken over marketing and distribution of the products generated by the people who developed the Cognitive Tutor, the research itself is very solid (and much of it dates from before Carnegie Learning became involved). I agree that third party evaluations, such as those undertaken by Mathematica, would be better, and of course educationalists should evaluate the merits of the studies, but the fact that the research is now being used to support a commercial enterprise does not invalidate the original findings. > > Dylan This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. This message has been checked for viruses but the contents of an attachment may still contain software viruses which could damage your computer system: you are advised to perform your own checks. Email communications with the University of Nottingham may be monitored as permitted by UK legislation. From Sinead.Breen at spd.dcu.ie Fri Mar 4 17:06:55 2011 From: Sinead.Breen at spd.dcu.ie (Sinead Breen) Date: Fri, 4 Mar 2011 17:06:55 -0000 Subject: [Maths-Education] First Announcement and Call for Papers - MEI4 Mathematics Teaching Matters In-Reply-To: <731CECC23FB8CA4E9127BD399744D1EC02F40343@email001.lsu.edu> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> <4D70F81D.1090100@rogerson.pol.pl><605A41D4-D3EB-4F3D-9BB3-7A31D4BF4AF3@mac.com> <4D710EE3.7050502@rogerson.pol.pl> <731CECC23FB8CA4E9127BD399744D1EC02F40343@email001.lsu.edu> Message-ID: <00be01cbda8e$908927b0$b19b7710$@Breen@spd.dcu.ie> Fourth Conference on Research in Mathematics Education MEI 4 Theme: Mathematics Teaching Matters St Patrick's College, Drumcondra, Dublin 9 Thursday 22nd and Friday 23rd September 2011 First Announcement and Call for Papers Confirmed Keynote Speakers . Dr Paul Andrews, University of Cambridge . Dr Therese Dooley, St Patrick's College . Dr Aki Murata, Stanford University . Professor Ron Tzur, University of Colorado Conference Goals The conference aims to bring together those interested in mathematics education to: . address current issues in relation to mathematics education both in Ireland and internationally; . review and discuss mathematics education research in Ireland in the light of international trends and practices; . consider ways of improving linkages and developing research collaborations with teachers and mathematics education communities. Call for Papers We invite submission of research reports or reviews, proposals for symposia and posters relating to work done in mathematics education across the educational spectrum. The conference proceedings will be published. Those interested in presenting at the conference should submit a paper by Friday April 29th 2011 to therese.dooley at spd.dcu.ie Submitted papers will be sent for peer review and, on the basis of reviews, will be accepted for presentation and publication, If revisions are necessary, the date for submission of final papers is June 30, 2011. A conference webpage and guidelines for submission of papers will be available at www.spd.dcu.ie/mei From alan at rogerson.pol.pl Fri Mar 4 19:07:01 2011 From: alan at rogerson.pol.pl (Alan Rogerson) Date: Fri, 04 Mar 2011 20:07:01 +0100 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <731CECC23FB8CA4E9127BD399744D1EC02F40343@email001.lsu.edu> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> <4D70F81D.1090100@rogerson.pol.pl><605A41D4-D3EB-4F3D-9BB3-7A31D4BF4AF3@mac.com> <4D710EE3.7050502@rogerson.pol.pl> <731CECC23FB8CA4E9127BD399744D1EC02F40343@email001.lsu.edu> Message-ID: <4D713855.90003@rogerson.pol.pl> Dear David, May I (again) try to clarify that there has been absolutely no negative criticism of the merit of the considerable body of work before and after the establishment of Carnegie.inc? There is no need therefore "to be fair" since what you, very helpfully, describe is all about the long and impressive history of the original work at Carnegie Mellon University (not Melon, but hey it's not an "l" of a difference). I agree very much, however, that "it would be interesting to know if "independent" evaluations of the effectiveness have been undertaken and published. " That was precisely my point, I don't know of any such work, and it would help us to evaluate this work of the creators, originators and eventually sellers of this material. It was very helpful to have your own impressions and evaluations. It was good to see too that your link below was to "The National Center for Academic Transformation (NCAT) is an independent, not-for-profit organization" so their evaluation of the work at Northern Arizona University looks truly independent except..oops,... it appears to be a direct quote from the NAU itself, about their own courses! The discussion of bias covers everything, not just commercial companies, in reality most if not all institutions would be positively biassed to their own way of doing things - so is there any chance of an independent evaluation here too?? Thanks for your personal evaluation of the Cognitive Tutor, which we can take to be independent and from experience - very helpful to Sarah who we hope is following this thread and taking notes (at least from you!). Over the years I have looked at a myriad of ICT programs, and would have to assess the majority as poor to very poor. It is therefore all the mor exciting and important when we find, and disseminate news about, those programs that are innovative and (from a subjective view of course) appear to work well and genuinely enhance the learning of our students. I am at this very moment evaluating at the request of the creators a very interesting and complex program called.. wait for it Statistics for the Terrified, which is still being trialled. If anyone on the list is interested in that area (and is we presume sufficiently terrified) please contact Jill at smorris at conceptstew.co.uk. This is I would say good (but not perfect, hence the trialling) ICT. Best wishes, and sorry if it's Friday, Alan On 04/03/2011 17:57, David H Kirshner wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > I'm enjoying this thread. > > To be fair, Ken Koedinger, lead developer of the software, is a bona > fide cognitive scientist who has published a variety of academic papers > on the cognitive theory involved, in addition to publications on the > effectiveness of the tutor. And even the latter publications have been > in peer review academic journals. Still, it would be interesting to know > if "independent" evaluations of the effectiveness have been undertaken > and published. > > There is some software on the market now that seems to be effective in > raising students' test scores in comparison with standard classroom > instruction. For instance, at Northern Arizona University, the college > algebra course is taught through an online facility that > > "promote[s] active and collaborative learning, address the diverse range > of student learning styles and permit acceleration. It will use ALEKS, a > comprehensive instructional software and course management system that > individualizes assessment and learning. ALEKS is Web-based, allowing > students to access course materials at anytime from anyplace, and can be > customized to meet student and course needs. As a supplement to ALEKS, > NAU will also use Thinkwell, a video-based mathematics software program > that uses highlighted worked examples and video lectures for students > who learn better in this mode." > (http://www.thencat.org/PCR/R3/NAU/NAU_Abstract.htm) > > However, it is clear that the program's effectiveness primarily is > related to its effective provision of practice problems and immediate > feedback. In short, it promotes learning of skills through repetitive > practice in the behaviorist tradition. > > I've looked at the Cognitive Tutor, and it's a more complex and > ambitious project. The Tutor functions through a multidimensional model > of expertise that it uses to update a student model, and thereby > determine what kinds of problems and assistance would best benefit the > student. It is not so straightforward an analysis as to whether what is > being promoted is skills through practice (in a sophisticated way), or > something more akin to what we would consider as mathematical concepts. > > The Cognitive Tutor is based on the ACT-series of acquisition models > developed by John Anderson and company at Carnegie Melon--in fact, Ken > was a student of his, and is now a frequent collaborator. The ambiguity > of the Tutor in terms of its learning modalities is reflected also in > the status of the ACT theories. Anderson (2005) would be a good source > to begin to answer those questions, and Anderson (2007) includes an > interesting discussion of the general issue of the kind of learning > addressed in the ACT theories. > > David Kirshner > > Anderson, J. R. (2005). Human symbol manipulation within an integrated > cognitive architecture. Cognitive Science, 29, 313-341. [algebraic > symbol skills] > Anderson, J. R. (2007). How can the human mind occur in the physical > universe?. Oxford University Press. > > > > > -----Original Message----- > From: maths-education-bounces at lists.nottingham.ac.uk > [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of > Alan Rogerson > Sent: Friday, March 04, 2011 10:10 AM > To: Mathematics Education discussion forum > Subject: [Maths-Education] Re: ICT in mathematics > > ************************************************************************ > *********************************** > This message has been generated through the Mathematics Education email > discussion list. > Hitting the REPLY key sends a message to all list members. > ************************************************************************ > *********************************** > Dear Dylan, > > What you say below does not in any way alter the fact that what you > actually recommended to Sarah were reports on a webpage produced by a > commercial company. That is the problem. You say something is "one of > the best researched" but we need to know when and by whom? It is not the > > quantity of research that counts, rather its quality. > > Please note, I am not making any judgement about the actual research > which you call "original" nor did I say that this research is some how > invalidated by being used by a commercial company. Let's say for the > sake of argument, that all this research could be validated, and also > note that some of the reports on the Carnegie.inc webpage were (as we > know) from Carnegie Mellon University itself, and may have even > pre-dated the formation of Carnegie.inc, I do hope you can see that this > > does not change the problem? "Selective quotation" is still a real > hazard, what company after all will quote research critical of its own > products? > > We know only too well the much bigger and much more serious debate going > > on about so-called academic research being funded, or supported, (or of > course suppressed!) by drug companies. Companies are in business to make > > money, so we can hardly use them, or the reports they quote, as > objective exemplars of "research". The contrast is between reports which > > clearly have no such bias, and those which are at risk of being biassed. > > Surely we cannot say "third party evaluations... would be better", > surely you mean essential? We know from basic statistics that biassed > evidence, when we can not attach boundaries to the bias, , is, and must > > be, useless (not second best). We all know the story of the millions of > telephone calls surveyed that failed to predict the next President of > the USA....? > > Please also note that there is absolutely no bias (or specific > accusations) against Carnegie.inc in particular here, it is a purely > general point that is being made. > > The only remaining problem, and somewhat insoluble, is the one Douglas > Butler has just mentioned. > > C'est la vie, c'est la ICT. > > Best wishes, > Alan > > > > > On 04/03/2011 15:52, dylanwiliam at mac.com wrote: >> Alan: Sarah asked specifically for studies that showed the impact of > ICT on attainment, and the Cognitive Tutor is one of the best researched > pieces of software for mathematics education. While Carnegie Learning > is a commercial company that has taken over marketing and distribution > of the products generated by the people who developed the Cognitive > Tutor, the research itself is very solid (and much of it dates from > before Carnegie Learning became involved). I agree that third party > evaluations, such as those undertaken by Mathematica, would be better, > and of course educationalists should evaluate the merits of the studies, > but the fact that the research is now being used to support a commercial > enterprise does not invalidate the original findings. >> Dylan > > This message and any attachment are intended solely for the addressee > and may contain confidential information. If you have received this > message in error, please send it back to me, and immediately delete it. > Please do not use, copy or disclose the information contained in this > message or in any attachment. Any views or opinions expressed by the > author of this email do not necessarily reflect the views of the > University of Nottingham. > > This message has been checked for viruses but the contents of an > attachment > may still contain software viruses which could damage your computer > system: > you are advised to perform your own checks. Email communications with > the > University of Nottingham may be monitored as permitted by UK > legislation. > > > From S.Trenholm at lboro.ac.uk Fri Mar 4 23:01:03 2011 From: S.Trenholm at lboro.ac.uk (Sven Trenholm) Date: Fri, 4 Mar 2011 23:01:03 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <731CECC23FB8CA4E9127BD399744D1EC02F40343@email001.lsu.edu> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> <4D70F81D.1090100@rogerson.pol.pl><605A41D4-D3EB-4F3D-9BB3-7A31D4BF4AF3@mac.com> <4D710EE3.7050502@rogerson.pol.pl>, <731CECC23FB8CA4E9127BD399744D1EC02F40343@email001.lsu.edu> Message-ID: <234B6B562A62654E93691A30A71B12CB2120043C9D@STAFFMBX-1.lunet.lboro.ac.uk> Re: NCAT New to this thread... I'm a PhD student at the Mathematics Education Center of Loughborough University (focused on mathematics e-learning in the higher education sector). In 2010 I arrived "off the boat" from upstate NY where I taught for over 10 years at the American junior college level. I've attended an NCAT workshop in the US and have followed their progress over the last decade. They have a sizeable focus on introductory level mathematics courses. Bill Gates recently put some of his money behind their work in "transforming" developmental mathematics offerings (which traditionally have failure rates around 40-60%). I am very interested in what they are doing given, on the surface, it appears to be successful for the specific introductory level large enrollment mathematics course context. Of course "success" may be well defined in terms of financial savings but not so well defined in terms of learning. In any case the movement (if you can call it that) appears to be picking up momentum. My question is this. After just over 10 years of work, the only peer-reviewed article, I am aware of, is a 2008 conference proceedings paper (citation below). For those familiar with NCAT, how much do you think this may be attributable, as I believe NCAT would attest, to the "inherent conservatism" in higher education (and perhaps the disciplinary culture of mathematics, in particular)? I don't necessarily believe that what they are doing is primarily instruction via repetitive practice... Sven Greenberg, W., & Williams, M. (2008). New pedagogical models for instruction in mathematics. Mathematical Modeling, Simulation, Visualization and e-Learning, 4, 361-371. Also, for those interested...(think tank paper) Miller, B. (2010). THE COURSE OF INNOVATION: Using technology to transform higher education. Education Sector Reports ________________________________________ From: maths-education-bounces at lists.nottingham.ac.uk [maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of David H Kirshner [dkirsh at lsu.edu] Sent: Friday, March 04, 2011 4:57 PM To: Mathematics Education discussion forum Subject: [Maths-Education] Re: ICT in mathematics *********************************************************************************************************** This message has been generated through the Mathematics Education email discussion list. Hitting the REPLY key sends a message to all list members. *********************************************************************************************************** I'm enjoying this thread. To be fair, Ken Koedinger, lead developer of the software, is a bona fide cognitive scientist who has published a variety of academic papers on the cognitive theory involved, in addition to publications on the effectiveness of the tutor. And even the latter publications have been in peer review academic journals. Still, it would be interesting to know if "independent" evaluations of the effectiveness have been undertaken and published. There is some software on the market now that seems to be effective in raising students' test scores in comparison with standard classroom instruction. For instance, at Northern Arizona University, the college algebra course is taught through an online facility that "promote[s] active and collaborative learning, address the diverse range of student learning styles and permit acceleration. It will use ALEKS, a comprehensive instructional software and course management system that individualizes assessment and learning. ALEKS is Web-based, allowing students to access course materials at anytime from anyplace, and can be customized to meet student and course needs. As a supplement to ALEKS, NAU will also use Thinkwell, a video-based mathematics software program that uses highlighted worked examples and video lectures for students who learn better in this mode." (http://www.thencat.org/PCR/R3/NAU/NAU_Abstract.htm) However, it is clear that the program's effectiveness primarily is related to its effective provision of practice problems and immediate feedback. In short, it promotes learning of skills through repetitive practice in the behaviorist tradition. I've looked at the Cognitive Tutor, and it's a more complex and ambitious project. The Tutor functions through a multidimensional model of expertise that it uses to update a student model, and thereby determine what kinds of problems and assistance would best benefit the student. It is not so straightforward an analysis as to whether what is being promoted is skills through practice (in a sophisticated way), or something more akin to what we would consider as mathematical concepts. The Cognitive Tutor is based on the ACT-series of acquisition models developed by John Anderson and company at Carnegie Melon--in fact, Ken was a student of his, and is now a frequent collaborator. The ambiguity of the Tutor in terms of its learning modalities is reflected also in the status of the ACT theories. Anderson (2005) would be a good source to begin to answer those questions, and Anderson (2007) includes an interesting discussion of the general issue of the kind of learning addressed in the ACT theories. David Kirshner Anderson, J. R. (2005). Human symbol manipulation within an integrated cognitive architecture. Cognitive Science, 29, 313-341. [algebraic symbol skills] Anderson, J. R. (2007). How can the human mind occur in the physical universe?. Oxford University Press. -----Original Message----- From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Alan Rogerson Sent: Friday, March 04, 2011 10:10 AM To: Mathematics Education discussion forum Subject: [Maths-Education] Re: ICT in mathematics ************************************************************************ *********************************** This message has been generated through the Mathematics Education email discussion list. Hitting the REPLY key sends a message to all list members. ************************************************************************ *********************************** Dear Dylan, What you say below does not in any way alter the fact that what you actually recommended to Sarah were reports on a webpage produced by a commercial company. That is the problem. You say something is "one of the best researched" but we need to know when and by whom? It is not the quantity of research that counts, rather its quality. Please note, I am not making any judgement about the actual research which you call "original" nor did I say that this research is some how invalidated by being used by a commercial company. Let's say for the sake of argument, that all this research could be validated, and also note that some of the reports on the Carnegie.inc webpage were (as we know) from Carnegie Mellon University itself, and may have even pre-dated the formation of Carnegie.inc, I do hope you can see that this does not change the problem? "Selective quotation" is still a real hazard, what company after all will quote research critical of its own products? We know only too well the much bigger and much more serious debate going on about so-called academic research being funded, or supported, (or of course suppressed!) by drug companies. Companies are in business to make money, so we can hardly use them, or the reports they quote, as objective exemplars of "research". The contrast is between reports which clearly have no such bias, and those which are at risk of being biassed. Surely we cannot say "third party evaluations... would be better", surely you mean essential? We know from basic statistics that biassed evidence, when we can not attach boundaries to the bias, , is, and must be, useless (not second best). We all know the story of the millions of telephone calls surveyed that failed to predict the next President of the USA....? Please also note that there is absolutely no bias (or specific accusations) against Carnegie.inc in particular here, it is a purely general point that is being made. The only remaining problem, and somewhat insoluble, is the one Douglas Butler has just mentioned. C'est la vie, c'est la ICT. Best wishes, Alan On 04/03/2011 15:52, dylanwiliam at mac.com wrote: > Alan: Sarah asked specifically for studies that showed the impact of ICT on attainment, and the Cognitive Tutor is one of the best researched pieces of software for mathematics education. While Carnegie Learning is a commercial company that has taken over marketing and distribution of the products generated by the people who developed the Cognitive Tutor, the research itself is very solid (and much of it dates from before Carnegie Learning became involved). I agree that third party evaluations, such as those undertaken by Mathematica, would be better, and of course educationalists should evaluate the merits of the studies, but the fact that the research is now being used to support a commercial enterprise does not invalidate the original findings. > > Dylan This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. This message has been checked for viruses but the contents of an attachment may still contain software viruses which could damage your computer system: you are advised to perform your own checks. Email communications with the University of Nottingham may be monitored as permitted by UK legislation. From alexandre.borovik at gmail.com Sat Mar 5 08:09:41 2011 From: alexandre.borovik at gmail.com (Alexandre Borovik) Date: Sat, 05 Mar 2011 08:09:41 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <234B6B562A62654E93691A30A71B12CB2120043C9D@STAFFMBX-1.lunet.lboro.ac.uk> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> <4D70F81D.1090100@rogerson.pol.pl><605A41D4-D3EB-4F3D-9BB3-7A31D4BF4AF3@mac.com> <4D710EE3.7050502@rogerson.pol.pl>, <731CECC23FB8CA4E9127BD399744D1EC02F40343@email001.lsu.edu> <234B6B562A62654E93691A30A71B12CB2120043C9D@STAFFMBX-1.lunet.lboro.ac.uk> Message-ID: <4D71EFC5.8050500@gmail.com> @Sven -- you are asking, in my opinion, the key question -- what is definition of "success" of mathematics teaching. I feel that discussants in this thread have no shared understanding of this key point, and this makes the "ICT in mathematics" thread truly engaging. Perhaps lack of shared criteria of "success" is a wider issue affecting the whole discourse on ICT in mathematics, and this perhaps explains shortage of proper academic papers assessing the ICT. Playing Devil's advocate, I wish to offer a questions. Would you agree that the whole idea of ICT in mathematics is self-defeating: if skills in carrying out certain types of tasks can be best taught by a computer, this is the best proof that these task are best done by a computer without human participation? Have a look at http://www.antiquark.com/sliderule/sim/n909es/virtual-n909-es.html -- it is fully functional interactive online slide rule. Without doubt, computers can be very efficient in teaching the use of slide rule. But why are we no longer using slider rules? Best wishes -- Alexandre On 04/03/2011 23:01, Sven Trenholm wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > Re: NCAT > New to this thread... I'm a PhD student at the Mathematics Education Center of Loughborough University (focused on mathematics e-learning in the higher education sector). In 2010 I arrived "off the boat" from upstate NY where I taught for over 10 years at the American junior college level. > > I've attended an NCAT workshop in the US and have followed their progress over the last decade. They have a sizeable focus on introductory level mathematics courses. Bill Gates recently put some of his money behind their work in "transforming" developmental mathematics offerings (which traditionally have failure rates around 40-60%). I am very interested in what they are doing given, on the surface, it appears to be successful for the specific introductory level large enrollment mathematics course context. Of course "success" may be well defined in terms of financial savings but not so well defined in terms of learning. In any case the movement (if you can call it that) appears to be picking up momentum. > > My question is this. After just over 10 years of work, the only peer-reviewed article, I am aware of, is a 2008 conference proceedings paper (citation below). For those familiar with NCAT, how much do you think this may be attributable, as I believe NCAT would attest, to the "inherent conservatism" in higher education (and perhaps the disciplinary culture of mathematics, in particular)? I don't necessarily believe that what they are doing is primarily instruction via repetitive practice... > > Sven > > > Greenberg, W.,& Williams, M. (2008). New pedagogical models for instruction in mathematics. Mathematical Modeling, Simulation, Visualization and e-Learning, 4, 361-371. > > Also, for those interested...(think tank paper) > Miller, B. (2010). THE COURSE OF INNOVATION: Using technology to transform higher education. Education Sector Reports > > > > > ________________________________________ > From: maths-education-bounces at lists.nottingham.ac.uk [maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of David H Kirshner [dkirsh at lsu.edu] > Sent: Friday, March 04, 2011 4:57 PM > To: Mathematics Education discussion forum > Subject: [Maths-Education] Re: ICT in mathematics > > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > I'm enjoying this thread. > > To be fair, Ken Koedinger, lead developer of the software, is a bona > fide cognitive scientist who has published a variety of academic papers > on the cognitive theory involved, in addition to publications on the > effectiveness of the tutor. And even the latter publications have been > in peer review academic journals. Still, it would be interesting to know > if "independent" evaluations of the effectiveness have been undertaken > and published. > > There is some software on the market now that seems to be effective in > raising students' test scores in comparison with standard classroom > instruction. For instance, at Northern Arizona University, the college > algebra course is taught through an online facility that > > "promote[s] active and collaborative learning, address the diverse range > of student learning styles and permit acceleration. It will use ALEKS, a > comprehensive instructional software and course management system that > individualizes assessment and learning. ALEKS is Web-based, allowing > students to access course materials at anytime from anyplace, and can be > customized to meet student and course needs. As a supplement to ALEKS, > NAU will also use Thinkwell, a video-based mathematics software program > that uses highlighted worked examples and video lectures for students > who learn better in this mode." > (http://www.thencat.org/PCR/R3/NAU/NAU_Abstract.htm) > > However, it is clear that the program's effectiveness primarily is > related to its effective provision of practice problems and immediate > feedback. In short, it promotes learning of skills through repetitive > practice in the behaviorist tradition. > > I've looked at the Cognitive Tutor, and it's a more complex and > ambitious project. The Tutor functions through a multidimensional model > of expertise that it uses to update a student model, and thereby > determine what kinds of problems and assistance would best benefit the > student. It is not so straightforward an analysis as to whether what is > being promoted is skills through practice (in a sophisticated way), or > something more akin to what we would consider as mathematical concepts. > > The Cognitive Tutor is based on the ACT-series of acquisition models > developed by John Anderson and company at Carnegie Melon--in fact, Ken > was a student of his, and is now a frequent collaborator. The ambiguity > of the Tutor in terms of its learning modalities is reflected also in > the status of the ACT theories. Anderson (2005) would be a good source > to begin to answer those questions, and Anderson (2007) includes an > interesting discussion of the general issue of the kind of learning > addressed in the ACT theories. > > David Kirshner > > Anderson, J. R. (2005). Human symbol manipulation within an integrated > cognitive architecture. Cognitive Science, 29, 313-341. [algebraic > symbol skills] > Anderson, J. R. (2007). How can the human mind occur in the physical > universe?. Oxford University Press. > > > > > -----Original Message----- > From: maths-education-bounces at lists.nottingham.ac.uk > [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of > Alan Rogerson > Sent: Friday, March 04, 2011 10:10 AM > To: Mathematics Education discussion forum > Subject: [Maths-Education] Re: ICT in mathematics > > ************************************************************************ > *********************************** > This message has been generated through the Mathematics Education email > discussion list. > Hitting the REPLY key sends a message to all list members. > ************************************************************************ > *********************************** > Dear Dylan, > > What you say below does not in any way alter the fact that what you > actually recommended to Sarah were reports on a webpage produced by a > commercial company. That is the problem. You say something is "one of > the best researched" but we need to know when and by whom? It is not the > > quantity of research that counts, rather its quality. > > Please note, I am not making any judgement about the actual research > which you call "original" nor did I say that this research is some how > invalidated by being used by a commercial company. Let's say for the > sake of argument, that all this research could be validated, and also > note that some of the reports on the Carnegie.inc webpage were (as we > know) from Carnegie Mellon University itself, and may have even > pre-dated the formation of Carnegie.inc, I do hope you can see that this > > does not change the problem? "Selective quotation" is still a real > hazard, what company after all will quote research critical of its own > products? > > We know only too well the much bigger and much more serious debate going > > on about so-called academic research being funded, or supported, (or of > course suppressed!) by drug companies. Companies are in business to make > > money, so we can hardly use them, or the reports they quote, as > objective exemplars of "research". The contrast is between reports which > > clearly have no such bias, and those which are at risk of being biassed. > > Surely we cannot say "third party evaluations... would be better", > surely you mean essential? We know from basic statistics that biassed > evidence, when we can not attach boundaries to the bias, , is, and must > > be, useless (not second best). We all know the story of the millions of > telephone calls surveyed that failed to predict the next President of > the USA....? > > Please also note that there is absolutely no bias (or specific > accusations) against Carnegie.inc in particular here, it is a purely > general point that is being made. > > The only remaining problem, and somewhat insoluble, is the one Douglas > Butler has just mentioned. > > C'est la vie, c'est la ICT. > > Best wishes, > Alan > > > > > On 04/03/2011 15:52, dylanwiliam at mac.com wrote: >> Alan: Sarah asked specifically for studies that showed the impact of > ICT on attainment, and the Cognitive Tutor is one of the best researched > pieces of software for mathematics education. While Carnegie Learning > is a commercial company that has taken over marketing and distribution > of the products generated by the people who developed the Cognitive > Tutor, the research itself is very solid (and much of it dates from > before Carnegie Learning became involved). I agree that third party > evaluations, such as those undertaken by Mathematica, would be better, > and of course educationalists should evaluate the merits of the studies, > but the fact that the research is now being used to support a commercial > enterprise does not invalidate the original findings. >> >> Dylan > > > This message and any attachment are intended solely for the addressee > and may contain confidential information. If you have received this > message in error, please send it back to me, and immediately delete it. > Please do not use, copy or disclose the information contained in this > message or in any attachment. Any views or opinions expressed by the > author of this email do not necessarily reflect the views of the > University of Nottingham. > > This message has been checked for viruses but the contents of an > attachment > may still contain software viruses which could damage your computer > system: > you are advised to perform your own checks. Email communications with > the > University of Nottingham may be monitored as permitted by UK > legislation. -- Professor Alexandre Borovik * University of Manchester Web: http://www.maths.manchester.ac.uk/~avb/ Wordpress: http://micromath.wordpress.com/ Academia: http://manchester.academia.edu/AlexandreBorovik From Peter.Gates at nottingham.ac.uk Sat Mar 5 15:40:38 2011 From: Peter.Gates at nottingham.ac.uk (Peter Gates) Date: Sat, 5 Mar 2011 15:40:38 +0000 Subject: [Maths-Education] Posting to the maths education list Message-ID: An HTML attachment was scrubbed... URL: From howard.tanner at smu.ac.uk Sat Mar 5 22:02:37 2011 From: howard.tanner at smu.ac.uk (Tanner, Howard) Date: Sat, 5 Mar 2011 22:02:37 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <240C36E18CADBE46962CC52E8839D67F5678BB@PLEIADES.sid.sihe.ac.uk> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> <4D70F81D.1090100@rogerson.pol.pl> <605A41D4-D3EB-4F3D-9BB3-7A31D4BF4AF3@mac.com> <4D710EE3.7050502@rogerson.pol.pl>, <240C36E18CADBE46962CC52E8839D67F5678BB@PLEIADES.sid.sihe.ac.uk> Message-ID: <240C36E18CADBE46962CC52E8839D67F4A2099@PLEIADES.sid.sihe.ac.uk> I have two points to make in relation to this thread: 1. The research reported / selected for reporting, on the Carnegie learning site lists the effect sizes reported in the trials. In most cases these are small (using Cohen's usual criteria for small, medium and big) and below d=0.4. Hattie (2009) reports that the average effect size for any intervention is 0.4 and demands effect sizes above this level for "innovations that work". The average effect size for "computer-assisted instruction" is reported as 0.31 - so nice try but no cigar! (Am I allowed to say that?) 2. I have a problem with classifying interventions as ICT or non-ICT as if that was the most important aspect of learning and teaching. Clearly there is a world of difference between a) computer aided learning in which a student works through a series of tasks as instructed by a computer; b) a good teacher using software such as Autograph, Geogebra or Cabri to support dialogic teaching that encourages debate around students' ideas and c) a poor teacher using the same software to tell students what the answer is. I don't think that there are easy technological fixes for educational problems. We need to focus on helping teachers to develop their own pedagogical subject knowledge and appreciate when the affordances of ICT might be useful. Hattie J (2009) Visible Learning; a synthesis of over 800 meta-analyses relating to achievement London; Routledge Dr Howard Tanner Reader in Education / Darllenydd Addysg Director of Centre for Research in Education / Cyfarwyddwr y Ganolfan Ymchwil mewn Addysg School of Education / Ysgol Addysg Swansea Metropolitan University / Prifysgol Fetropolitan Abertawe Townhill Road / Heol Townhill Swansea / Abertawe SA2 0UT Wales, UK / Cymru, y DU Phone / Ff?n: 01792 482019 Fax/Ffacs: 01792 482126 e-mail / e-bost: howard.tanner at smu.ac.uk -----Original Message----- From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Alan Rogerson Sent: 04 March 2011 16:10 To: Mathematics Education discussion forum Subject: [Maths-Education] Re: ICT in mathematics *********************************************************************************************************** This message has been generated through the Mathematics Education email discussion list. Hitting the REPLY key sends a message to all list members. *********************************************************************************************************** Dear Dylan, What you say below does not in any way alter the fact that what you actually recommended to Sarah were reports on a webpage produced by a commercial company. That is the problem. You say something is "one of the best researched" but we need to know when and by whom? It is not the quantity of research that counts, rather its quality. Please note, I am not making any judgement about the actual research which you call "original" nor did I say that this research is some how invalidated by being used by a commercial company. Let's say for the sake of argument, that all this research could be validated, and also note that some of the reports on the Carnegie.inc webpage were (as we know) from Carnegie Mellon University itself, and may have even pre-dated the formation of Carnegie.inc, I do hope you can see that this does not change the problem? "Selective quotation" is still a real hazard, what company after all will quote research critical of its own products? We know only too well the much bigger and much more serious debate going on about so-called academic research being funded, or supported, (or of course suppressed!) by drug companies. Companies are in business to make money, so we can hardly use them, or the reports they quote, as objective exemplars of "research". The contrast is between reports which clearly have no such bias, and those which are at risk of being biassed. Surely we cannot say "third party evaluations... would be better", surely you mean essential? We know from basic statistics that biassed evidence, when we can not attach boundaries to the bias, , is, and must be, useless (not second best). We all know the story of the millions of telephone calls surveyed that failed to predict the next President of the USA....? Please also note that there is absolutely no bias (or specific accusations) against Carnegie.inc in particular here, it is a purely general point that is being made. The only remaining problem, and somewhat insoluble, is the one Douglas Butler has just mentioned. C'est la vie, c'est la ICT. Best wishes, Alan On 04/03/2011 15:52, dylanwiliam at mac.com wrote: > Alan: Sarah asked specifically for studies that showed the impact of ICT on attainment, and the Cognitive Tutor is one of the best researched pieces of software for mathematics education. While Carnegie Learning is a commercial company that has taken over marketing and distribution of the products generated by the people who developed the Cognitive Tutor, the research itself is very solid (and much of it dates from before Carnegie Learning became involved). I agree that third party evaluations, such as those undertaken by Mathematica, would be better, and of course educationalists should evaluate the merits of the studies, but the fact that the research is now being used to support a commercial enterprise does not invalidate the original findings. > > Dylan This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. This message has been checked for viruses but the contents of an attachment may still contain software viruses which could damage your computer system: you are advised to perform your own checks. Email communications with the University of Nottingham may be monitored as permitted by UK legislation. From jhmason27 at googlemail.com Sun Mar 6 03:41:36 2011 From: jhmason27 at googlemail.com (John Mason) Date: Sun, 06 Mar 2011 03:41:36 +0000 Subject: [Maths-Education] ICT in mathematics In-Reply-To: <4D71EFC5.8050500@gmail.com> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> <4D70F81D.1090100@rogerson.pol.pl><605A41D4-D3EB-4F3D-9BB3-7A31D4BF4AF3@mac.com> <4D710EE3.7050502@rogerson.pol.pl>, <731CECC23FB8CA4E9127BD399744D1EC02F40343@email001.lsu.edu> <234B6B562A62654E93691A30A71B12CB2120043C9D@STAFFMBX-1.lunet.lboro.ac.uk> <4D71EFC5.8050500@gmail.com> Message-ID: <4D730270.20304@open.ac.uk> Replying to AlexandreB: I can use interactive graphing to enable students to experience the dual nature of a graph of a function: as an object and as the set of points [x, f(x)] where x varies over the domain. Combining two functions using 'cobweb' type diagrams, students can get a sense of what the composite of two functions looks like. Furthermore they make observations about apparent alignments that hold when the functions are changed, leading to appreciating more deeply things like the derivative of the composite, the conditions under which the derivative is zero, and hence relationships between local extrema for the composite in terms of the components. All this can best be done with interactive graphics (see http://mcs.open.ac.uk/jhm3/Applets%20&%20Animations/Applets%20&%20Animations.html item 2 'function studies') but it does not follow that these properties are best 'done' by computers without human intervention. Surely this applies to many uses of ICT for conceptual enrichment? JohnM On 5/3/11 08:09, Alexandre Borovik wrote: > *********************************************************************************************************** > > This message has been generated through the Mathematics Education > email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > > > @Sven -- you are asking, in my opinion, the key question -- what is > definition of "success" of mathematics teaching. I feel that > discussants in this thread have no shared understanding of this key > point, and this makes the "ICT in mathematics" thread truly engaging. > > Perhaps lack of shared criteria of "success" is a wider issue > affecting the whole discourse on ICT in mathematics, and this perhaps > explains shortage of proper academic papers assessing the ICT. > > Playing Devil's advocate, I wish to offer a questions. > > Would you agree that the whole idea of ICT in mathematics is > self-defeating: if skills in carrying out certain types of tasks can > be best taught by a computer, this is the best proof that these task > are best done by a computer without human participation? > > Have a look at > http://www.antiquark.com/sliderule/sim/n909es/virtual-n909-es.html -- > it is fully functional interactive online slide rule. > Without doubt, computers can be very efficient in teaching the use of > slide rule. But why are we no longer using slider rules? > > Best wishes -- Alexandre > > > On 04/03/2011 23:01, Sven Trenholm wrote: >> *********************************************************************************************************** >> >> This message has been generated through the Mathematics Education >> email discussion list. >> Hitting the REPLY key sends a message to all list members. >> *********************************************************************************************************** >> >> Re: NCAT >> New to this thread... I'm a PhD student at the Mathematics Education >> Center of Loughborough University (focused on mathematics e-learning >> in the higher education sector). In 2010 I arrived "off the boat" >> from upstate NY where I taught for over 10 years at the American >> junior college level. >> >> I've attended an NCAT workshop in the US and have followed their >> progress over the last decade. They have a sizeable focus on >> introductory level mathematics courses. Bill Gates recently put some >> of his money behind their work in "transforming" developmental >> mathematics offerings (which traditionally have failure rates around >> 40-60%). I am very interested in what they are doing given, on the >> surface, it appears to be successful for the specific introductory >> level large enrollment mathematics course context. Of course >> "success" may be well defined in terms of financial savings but not >> so well defined in terms of learning. In any case the movement (if >> you can call it that) appears to be picking up momentum. >> >> My question is this. After just over 10 years of work, the only >> peer-reviewed article, I am aware of, is a 2008 conference >> proceedings paper (citation below). For those familiar with NCAT, >> how much do you think this may be attributable, as I believe NCAT >> would attest, to the "inherent conservatism" in higher education (and >> perhaps the disciplinary culture of mathematics, in particular)? I >> don't necessarily believe that what they are doing is primarily >> instruction via repetitive practice... >> >> Sven >> >> >> Greenberg, W.,& Williams, M. (2008). New pedagogical models for >> instruction in mathematics. Mathematical Modeling, Simulation, >> Visualization and e-Learning, 4, 361-371. >> >> Also, for those interested...(think tank paper) >> Miller, B. (2010). THE COURSE OF INNOVATION: Using technology to >> transform higher education. Education Sector Reports >> >> >> >> >> ________________________________________ >> From: maths-education-bounces at lists.nottingham.ac.uk >> [maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of David H >> Kirshner [dkirsh at lsu.edu] >> Sent: Friday, March 04, 2011 4:57 PM >> To: Mathematics Education discussion forum >> Subject: [Maths-Education] Re: ICT in mathematics >> >> *********************************************************************************************************** >> >> This message has been generated through the Mathematics Education >> email discussion list. >> Hitting the REPLY key sends a message to all list members. >> *********************************************************************************************************** >> >> I'm enjoying this thread. >> >> To be fair, Ken Koedinger, lead developer of the software, is a bona >> fide cognitive scientist who has published a variety of academic papers >> on the cognitive theory involved, in addition to publications on the >> effectiveness of the tutor. And even the latter publications have been >> in peer review academic journals. Still, it would be interesting to know >> if "independent" evaluations of the effectiveness have been undertaken >> and published. >> >> There is some software on the market now that seems to be effective in >> raising students' test scores in comparison with standard classroom >> instruction. For instance, at Northern Arizona University, the college >> algebra course is taught through an online facility that >> >> "promote[s] active and collaborative learning, address the diverse range >> of student learning styles and permit acceleration. It will use ALEKS, a >> comprehensive instructional software and course management system that >> individualizes assessment and learning. ALEKS is Web-based, allowing >> students to access course materials at anytime from anyplace, and can be >> customized to meet student and course needs. As a supplement to ALEKS, >> NAU will also use Thinkwell, a video-based mathematics software program >> that uses highlighted worked examples and video lectures for students >> who learn better in this mode." >> (http://www.thencat.org/PCR/R3/NAU/NAU_Abstract.htm) >> >> However, it is clear that the program's effectiveness primarily is >> related to its effective provision of practice problems and immediate >> feedback. In short, it promotes learning of skills through repetitive >> practice in the behaviorist tradition. >> >> I've looked at the Cognitive Tutor, and it's a more complex and >> ambitious project. The Tutor functions through a multidimensional model >> of expertise that it uses to update a student model, and thereby >> determine what kinds of problems and assistance would best benefit the >> student. It is not so straightforward an analysis as to whether what is >> being promoted is skills through practice (in a sophisticated way), or >> something more akin to what we would consider as mathematical concepts. >> >> The Cognitive Tutor is based on the ACT-series of acquisition models >> developed by John Anderson and company at Carnegie Melon--in fact, Ken >> was a student of his, and is now a frequent collaborator. The ambiguity >> of the Tutor in terms of its learning modalities is reflected also in >> the status of the ACT theories. Anderson (2005) would be a good source >> to begin to answer those questions, and Anderson (2007) includes an >> interesting discussion of the general issue of the kind of learning >> addressed in the ACT theories. >> >> David Kirshner >> >> Anderson, J. R. (2005). Human symbol manipulation within an integrated >> cognitive architecture. Cognitive Science, 29, 313-341. [algebraic >> symbol skills] >> Anderson, J. R. (2007). How can the human mind occur in the physical >> universe?. Oxford University Press. >> >> >> >> >> -----Original Message----- >> From: maths-education-bounces at lists.nottingham.ac.uk >> [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of >> Alan Rogerson >> Sent: Friday, March 04, 2011 10:10 AM >> To: Mathematics Education discussion forum >> Subject: [Maths-Education] Re: ICT in mathematics >> >> ************************************************************************ >> *********************************** >> This message has been generated through the Mathematics Education email >> discussion list. >> Hitting the REPLY key sends a message to all list members. >> ************************************************************************ >> *********************************** >> Dear Dylan, >> >> What you say below does not in any way alter the fact that what you >> actually recommended to Sarah were reports on a webpage produced by a >> commercial company. That is the problem. You say something is "one of >> the best researched" but we need to know when and by whom? It is not the >> >> quantity of research that counts, rather its quality. >> >> Please note, I am not making any judgement about the actual research >> which you call "original" nor did I say that this research is some how >> invalidated by being used by a commercial company. Let's say for the >> sake of argument, that all this research could be validated, and also >> note that some of the reports on the Carnegie.inc webpage were (as we >> know) from Carnegie Mellon University itself, and may have even >> pre-dated the formation of Carnegie.inc, I do hope you can see that this >> >> does not change the problem? "Selective quotation" is still a real >> hazard, what company after all will quote research critical of its own >> products? >> >> We know only too well the much bigger and much more serious debate going >> >> on about so-called academic research being funded, or supported, (or of >> course suppressed!) by drug companies. Companies are in business to make >> >> money, so we can hardly use them, or the reports they quote, as >> objective exemplars of "research". The contrast is between reports which >> >> clearly have no such bias, and those which are at risk of being biassed. >> >> Surely we cannot say "third party evaluations... would be better", >> surely you mean essential? We know from basic statistics that biassed >> evidence, when we can not attach boundaries to the bias, , is, and must >> >> be, useless (not second best). We all know the story of the millions of >> telephone calls surveyed that failed to predict the next President of >> the USA....? >> >> Please also note that there is absolutely no bias (or specific >> accusations) against Carnegie.inc in particular here, it is a purely >> general point that is being made. >> >> The only remaining problem, and somewhat insoluble, is the one Douglas >> Butler has just mentioned. >> >> C'est la vie, c'est la ICT. >> >> Best wishes, >> Alan >> >> >> >> >> On 04/03/2011 15:52, dylanwiliam at mac.com wrote: >>> Alan: Sarah asked specifically for studies that showed the impact of >> ICT on attainment, and the Cognitive Tutor is one of the best researched >> pieces of software for mathematics education. While Carnegie Learning >> is a commercial company that has taken over marketing and distribution >> of the products generated by the people who developed the Cognitive >> Tutor, the research itself is very solid (and much of it dates from >> before Carnegie Learning became involved). I agree that third party >> evaluations, such as those undertaken by Mathematica, would be better, >> and of course educationalists should evaluate the merits of the studies, >> but the fact that the research is now being used to support a commercial >> enterprise does not invalidate the original findings. >>> >>> Dylan >> >> >> This message and any attachment are intended solely for the addressee >> and may contain confidential information. If you have received this >> message in error, please send it back to me, and immediately delete it. >> Please do not use, copy or disclose the information contained in this >> message or in any attachment. Any views or opinions expressed by the >> author of this email do not necessarily reflect the views of the >> University of Nottingham. >> >> This message has been checked for viruses but the contents of an >> attachment >> may still contain software viruses which could damage your computer >> system: >> you are advised to perform your own checks. Email communications with >> the >> University of Nottingham may be monitored as permitted by UK >> legislation. > From tandiclausenmay at gmail.com Sun Mar 6 07:12:09 2011 From: tandiclausenmay at gmail.com (Tandi Clausen-May) Date: Sun, 6 Mar 2011 07:12:09 -0000 Subject: [Maths-Education] Re: ICT in mathematics Message-ID: <8B1E41E4B39E4374A2BC3034C3717750@homet4dz4d6xu0> How 'successful' any teaching is judged to be depends on how that 'success' is measured. The way in which learning is usually measured in our formal education system is with a test. If a test question is Use appropriate dynamic geometry (Geogebra, Cabri, Sketchpad, Autograph, whatever) to construct a polygon with given properties then the learners will probably do better in the test if they have spent time working with dynamic geometry. If the test question is Use compasses and a straight edge to construct a polygon with given properties then they probably won't. Previous experience with dynamic geometry will probably have little, if any, impact on their 'success'. I have yet to see a GCSE question like the former, but questions like the latter are de rigueur. Yours, Tandi Tandi Clausen-May Independent Consultant Mathematics curriculum and assessment Special education Tel: 01628 776 204 From dylanwiliam at mac.com Sun Mar 6 07:36:59 2011 From: dylanwiliam at mac.com (dylanwiliam at mac.com) Date: Sun, 06 Mar 2011 07:36:59 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <240C36E18CADBE46962CC52E8839D67F4A2099@PLEIADES.sid.sihe.ac.uk> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> <4D70F81D.1090100@rogerson.pol.pl> <605A41D4-D3EB-4F3D-9BB3-7A31D4BF4AF3@mac.com> <4D710EE3.7050502@rogerson.pol.pl> <240C36E18CADBE46962CC52E8839D67F5678BB@PLEIADES.sid.sihe.ac.uk> <240C36E18CADBE46962CC52E8839D67F4A2099@PLEIADES.sid.sihe.ac.uk> Message-ID: Jacob Cohen's views about the interpretation of effect sizes are widely accepted but it is important to note that they were based on experiences in psychology, rather than education. In psychology, an effect size of 0.2 might be small, but in education it is huge. This is because the average increase in achievement in mathematics (and most other subjects) is 0.4 standard deviations per year. An effect size of 0.2 therefore represents a 50% increase in the rate of learning?a very dramatic effect that, if it could be replicated across just one year group in England, would have a net present value equivalent to around three times the national debt. This 0.4 figure is what Hattie was quoting. He was basically saying that ordinary teaching will give you 0.4 standard deviations per year, so all interventions should be measured against this baseline. The figures quoted in most of the Carnegie studies are against comparison groups over the same period, so the 0.4 has already been subtracted. The other thing to say about Hattie's "Visible Learning" project is that the use of meta-analysis in such situations is problematic. First, measures of educational outcomes differ in their sensitivity to instruction, so apparently similar measures would give different effect sizes for the same intervention. Second, the calculation of effect sizes uses the standard deviation of the control and treatment groups as a divisor. Where the groups are sub-group of the whole population, this divisor will be smaller, and so the effect size will be larger. This partly explains why interventions for students with special educational needs appear to provide larger effects (See Fuchs & Fuchs, 1986), but more importantly means that where studies are not conducting on representative samples of the whole population, average effect sizes are difficult, if not impossible, to interpret. Most readers of this thread will have had enough about this already, but for those that want to read more about effect sizes in education, and sensitivity to instruction, I have written more about this in: Wiliam, D. (2010). Standardized testing and school accountability. Educational Psychologist, 45(2), 107-122. Regarding Howard's second point, it is important to note that the Cognitive Tutor was designed to do just one thing: teach procedural aspects of algebra to ninth grade students in the United States. In many countries, these particular aspects of algebra are not regarded as particularly important, but in the US, this is a substantial proportion (perhaps 50%) of what students do in ninth grade mathematics. In terms of these very limited goals, Cognitive Tutor does a good job (by my estimate, it is better than 90% of teachers). Of course we should work to increase teachers' pedagogical content knowledge, but while we do this I think we need to worry about the students who are being taught right now. I would love to get to a point where every teacher is better than Cognitive Tutor, but while we are getting there, we need also to think about the short term. Dylan Wiliam On 5 Mar 2011, at 22:02, Tanner, Howard wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > I have two points to make in relation to this thread: > > 1. The research reported / selected for reporting, on the Carnegie learning site lists the effect sizes reported in the trials. In most cases these are small (using Cohen's usual criteria for small, medium and big) and below d=0.4. Hattie (2009) reports that the average effect size for any intervention is 0.4 and demands effect sizes above this level for "innovations that work". The average effect size for "computer-assisted instruction" is reported as 0.31 - so nice try but no cigar! (Am I allowed to say that?) > > 2. I have a problem with classifying interventions as ICT or non-ICT as if that was the most important aspect of learning and teaching. > > Clearly there is a world of difference between > a) computer aided learning in which a student works through a series of tasks as instructed by a computer; > b) a good teacher using software such as Autograph, Geogebra or Cabri to support dialogic teaching that encourages debate around students' ideas and > c) a poor teacher using the same software to tell students what the answer is. > > I don't think that there are easy technological fixes for educational problems. We need to focus on helping teachers to develop their own pedagogical subject knowledge and appreciate when the affordances of ICT might be useful. > > > Hattie J (2009) Visible Learning; a synthesis of over 800 meta-analyses relating to achievement London; Routledge > > > Dr Howard Tanner > Reader in Education / Darllenydd Addysg > > Director of Centre for Research in Education / Cyfarwyddwr y Ganolfan Ymchwil mewn Addysg > School of Education / Ysgol Addysg > Swansea Metropolitan University / Prifysgol Fetropolitan Abertawe > Townhill Road / Heol Townhill > Swansea / Abertawe SA2 0UT > Wales, UK / Cymru, y DU > > Phone / Ff?n: 01792 482019 > Fax/Ffacs: 01792 482126 > e-mail / e-bost: howard.tanner at smu.ac.uk > > -----Original Message----- > From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Alan Rogerson > Sent: 04 March 2011 16:10 > To: Mathematics Education discussion forum > Subject: [Maths-Education] Re: ICT in mathematics > > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > Dear Dylan, > > What you say below does not in any way alter the fact that what you > actually recommended to Sarah were reports on a webpage produced by a > commercial company. That is the problem. You say something is "one of > the best researched" but we need to know when and by whom? It is not the > quantity of research that counts, rather its quality. > > Please note, I am not making any judgement about the actual research > which you call "original" nor did I say that this research is some how > invalidated by being used by a commercial company. Let's say for the > sake of argument, that all this research could be validated, and also > note that some of the reports on the Carnegie.inc webpage were (as we > know) from Carnegie Mellon University itself, and may have even > pre-dated the formation of Carnegie.inc, I do hope you can see that this > does not change the problem? "Selective quotation" is still a real > hazard, what company after all will quote research critical of its own > products? > > We know only too well the much bigger and much more serious debate going > on about so-called academic research being funded, or supported, (or of > course suppressed!) by drug companies. Companies are in business to make > money, so we can hardly use them, or the reports they quote, as > objective exemplars of "research". The contrast is between reports which > clearly have no such bias, and those which are at risk of being biassed. > Surely we cannot say "third party evaluations... would be better", > surely you mean essential? We know from basic statistics that biassed > evidence, when we can not attach boundaries to the bias, , is, and must > be, useless (not second best). We all know the story of the millions of > telephone calls surveyed that failed to predict the next President of > the USA....? > > Please also note that there is absolutely no bias (or specific > accusations) against Carnegie.inc in particular here, it is a purely > general point that is being made. > > The only remaining problem, and somewhat insoluble, is the one Douglas > Butler has just mentioned. > > C'est la vie, c'est la ICT. > > Best wishes, > Alan > > > > > On 04/03/2011 15:52, dylanwiliam at mac.com wrote: >> Alan: Sarah asked specifically for studies that showed the impact of ICT on attainment, and the Cognitive Tutor is one of the best researched pieces of software for mathematics education. While Carnegie Learning is a commercial company that has taken over marketing and distribution of the products generated by the people who developed the Cognitive Tutor, the research itself is very solid (and much of it dates from before Carnegie Learning became involved). I agree that third party evaluations, such as those undertaken by Mathematica, would be better, and of course educationalists should evaluate the merits of the studies, but the fact that the research is now being used to support a commercial enterprise does not invalidate the original findings. >> >> Dylan > > > This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. > > This message has been checked for viruses but the contents of an attachment > may still contain software viruses which could damage your computer system: > you are advised to perform your own checks. Email communications with the > University of Nottingham may be monitored as permitted by UK legislation. From alexandre.borovik at gmail.com Sun Mar 6 08:37:09 2011 From: alexandre.borovik at gmail.com (Alexandre Borovik) Date: Sun, 06 Mar 2011 08:37:09 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <8B1E41E4B39E4374A2BC3034C3717750@homet4dz4d6xu0> References: <8B1E41E4B39E4374A2BC3034C3717750@homet4dz4d6xu0> Message-ID: <4D7347B5.5050003@gmail.com> On 06/03/2011 07:12, Tandi Clausen-May wrote: > How 'successful' any teaching is judged to be depends on how that 'success' > is measured. > > The way in which learning is usually measured in our formal education system > is with a test. I am new to this discussion and perhaps I have to make an attempt at making my question a bit more precise: I asked "What is "success" of mathematics teaching?" I would suggest to define "success" first, and only then discuss how it could be measured. Physicists do not answer the question "what is electric current" by saying "it is measured by an ammeter". My observations and experience (admit tedly, in university mathematics teaching) suggest that the ease of use of Computer Aided Assessment encourages "teaching to test". Wouldn't you agree that "teaching to test" is a cancer of mathematical education? Alexandre. -- Professor Alexandre Borovik * University of Manchester Web: http://www.maths.manchester.ac.uk/~avb/ Wordpress: http://micromath.wordpress.com/ Academia: http://manchester.academia.edu/AlexandreBorovik From alexandre.borovik at gmail.com Sun Mar 6 10:26:01 2011 From: alexandre.borovik at gmail.com (Alexandre Borovik) Date: Sun, 06 Mar 2011 10:26:01 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <4D730270.20304@open.ac.uk> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> <4D70F81D.1090100@rogerson.pol.pl><605A41D4-D3EB-4F3D-9BB3-7A31D4BF4AF3@mac.com> <4D710EE3.7050502@rogerson.pol.pl>, <731CECC23FB8CA4E9127BD399744D1EC02F40343@email001.lsu.edu> <234B6B562A62654E93691A30A71B12CB2120043C9D@STAFFMBX-1.lunet.lboro.ac.uk> <4D71EFC5.8050500@gmail.com> <4D730270.20304@open.ac.uk> Message-ID: <4D736139.6040808@gmail.com> Dear John, On 06/03/2011 03:41, John Mason wrote: > I can use interactive graphing to enable students to experience the dual > nature of a graph of a function: as an object and as the set of points > [x, f(x)] where x varies over the domain. Combining two functions using > 'cobweb' type diagrams, students can get a sense of what the composite > of two functions looks like. [....] > Surely this > applies to many uses of ICT for conceptual enrichment? I wholeheartedly agree with you -- of course it does; I am not a Luddite; I started to teach entirely computer-based, computer-assessed courses at least 15 years ago; a detailed explanation of my views on ICT in (university level) mathematics teaching can be found in http://www.maths.manchester.ac.uk/~avb/pdf/Mathematics_and_IT.pdf But I would like to play the Devil's advocate role one step further and suggest that the use of ICT in school mathematics may help students to pass school exams -- and damage their chances of understanding university level mathematics. The "dual" nature of function mentioned by you is a wonderful example of a multi-layer structure of mathematical concepts. There is a more abstract layer of duality in the concept of function, the point-function duality, when a point x is seen as a functional evaluated at the function f. This duality is prominent in functional analysis or algebraic geometry, and, at the level of applications, in computer programming or, say, mathematical economics (in the latter it takes the form of the price/output duality of linear optimisation---among many other manifestations). Does experience of interactive graphing helps, at later stages of mathematical education, to understand this duality? Or hinders it, by tying the concept of function to concrete visual images? I dare to conjecture that this is a general principle of pedagogy of mathematics: a next level of abstraction is better understood by students if the previous one has been learned by them by direct mental manipulations not mediated by use of technology. For example, my favorite approach to graphs and composites of functions is to invite students to play with the absolute value of the absolute value function y = |x|, using just a pencil and squared paper. When you take f(x) = ||x|-1|, a graph of the composite f(f(x)) is easy to draw -- and, moreover, sketching of a graph of an iterated function like f(f(f(...f(x)...))) where the symbol f is repeated, say, 100 times, becomes an accessible exercise. The sketch of 100th iteration cannot be actually drawn -- only crudely sketched; but it is not difficult, however, to explain *verbally* how the graph looks like (and hand-waving is quite useful here, too). We have the all-important feeding of a visual image back into the realm of "verbal" thinking and locomotor intuition. I had seen Mathematica programme (for Apple computers) first time in 1990 or 1991, under curious circumstances: I taught a standard calculus course at University of California, and my teaching assistant, a very clever graduate student, was unable to change order of integration in a double integral without graphing first, with the help of Mathematica, the area of integration -- this was why she introduced me to Mathematica. And this allows me to produce an example illustrating my conjecture: If you wish to teach students to evaluate double integrals as an end in itself, then the use of interactive graphing is of course OK. (But why bother if computers calculate integrals better than humans?) But if you wish to use change of order of integration as a propaedeutics for introduction of Lebesgue integral, then it is best done by hand. Learning mathematics is about growing connections in the brain. And I love a simile from the boxing world: allowing a cut brow to slowly heal itself in a natural way is considered to be safer for future fights than application of stitches. Best wishes -- Alexandre -- Professor Alexandre Borovik * University of Manchester Web: http://www.maths.manchester.ac.uk/~avb/ Wordpress: http://micromath.wordpress.com/ Academia: http://manchester.academia.edu/AlexandreBorovik From lefouque at gmail.com Mon Mar 7 06:11:24 2011 From: lefouque at gmail.com (Ng Foo Keong) Date: Mon, 7 Mar 2011 14:11:24 +0800 Subject: [Maths-Education] Re: Maths-Education Digest, Vol 77, Issue 5 In-Reply-To: References: Message-ID: ... (cont'd from previous post) having said that, i am very impressed by Sugata Mitra's hole-in-the-wall computers for kids. maybe it's better to just let the kids learn themselves and teach one another? From lefouque at gmail.com Mon Mar 7 06:05:37 2011 From: lefouque at gmail.com (Ng Foo Keong) Date: Mon, 7 Mar 2011 14:05:37 +0800 Subject: [Maths-Education] Re: Maths-Education Digest, Vol 77, Issue 5 In-Reply-To: References: Message-ID: dear all, i'd like us to distinguish between the potential of ICT and what has actually been achieved in our evaluations of the effectiveness of ICT. for various reasons, the latter far pales compared to the former. a lot of effort by various parties (government, school leaders, teachers, business entities, technologists, support staff, students, parents ... etc.) needs be aligned to a _common_ goal in order to achieve success. Ng, Foo Keong Independent Educational Consultant (ICT and AR) On 4 March 2011 20:00, wrote: > Send Maths-Education mailing list submissions to > maths-education at lists.nottingham.ac.uk > > To subscribe or unsubscribe via the World Wide Web, visit > http://lists.nottingham.ac.uk/mailman/listinfo/maths-education > or, via email, send a message with subject or body 'help' to > maths-education-request at lists.nottingham.ac.uk > > You can reach the person managing the list at > maths-education-owner at lists.nottingham.ac.uk > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of Maths-Education digest..." > > > ************************************************* > This is the regular digest of all messages sent out on the discussion list > Maths-Education. > ************************************************* > > > Today's Topics: > > 1. ICT in mathematics (Maughan, Sarah) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Fri, 4 Mar 2011 11:29:51 +0000 > From: "Maughan, Sarah" > To: Mathematics Education discussion forum > > Subject: [Maths-Education] ICT in mathematics > Message-ID: > < > 7B94FE5A0830AB4EAAEC80941357684822C3CC07C5 at MILECCR.ntnfer2.nfer.ac.uk> > > Content-Type: text/plain; charset="iso-8859-1" > > This seemed to bounce back first time so I am trying again. Apologies if > you receive it twice! > > Hi > I am trying to find some evidence about whether ICT has a positive impact > on attainment in mathematics and wonder if anyone has any good examples? If > you look at syntheses of research they tend to find little or no positive > impact, over and above good teaching. However, I believe there are some > examples of where the findings are more positive, usually in terms of a > particular kind of ICT in a particular context. Can anyone let me know > which are the key research reports in this area? I am particularly > interested in impact on attainment rather than motivation or engagement > (even though ultimately this is likely to improve attainment), so ICT use > that directly helps with understanding of particular concepts for example. > > Thanks for your help. > > Sarah > > Sarah Maughan > Director of Research > National Foundation for Educational Research > The Mere, Upton Park, Slough, Berkshire? SL1 2DQ, UK > Reg. No 900899 (England).? Reg Address as above. > Tel +44(0) 1753 574123: direct line +44(0) 1753 637137 > Fax +44(0) 1753 671708: > Web http://www.nfer.ac.uk > This e-mail is confidential to the addressee and may contain privileged > information. If you are not the addressee you are not permitted to use or > copy this e-mail or its attachments nor may you disclose the same to any > third party. If this has been sent to you in error please notify us as soon > as possible. The NFER reserves the right to intercept and read e-mails sent > or received by our employees. If you do not wish for your communications to > be subjected to such scrutiny, you should not communicate via this e-mail > system. The Foundation endeavours to exclude viruses from our data but it is > the obligation of the recipient to check any attachments for viruses. > Opinions, conclusions and other information contained in this message that > do not relate to the official business of the NFER, or are personal to the > individual sender, shall not be understood as endorsed by the Foundation and > no liability will be accepted. Any legally binding agreement resulting from > its content must be made separately in a printed medium. > > > > > > ------------------------------ > > _______________________________________________ > Maths-Education mailing list > Maths-Education at lists.nottingham.ac.uk > http://lists.nottingham.ac.uk/mailman/listinfo/maths-education > > > End of Maths-Education Digest, Vol 77, Issue 5 > ********************************************** > > This message and any attachment are intended solely for the addressee and > may contain confidential information. If you have received this message in > error, please send it back to me, and immediately delete it. Please do not > use, copy or disclose the information contained in this message or in any > attachment. Any views or opinions expressed by the author of this email do > not necessarily reflect the views of the University of Nottingham. > > This message has been checked for viruses but the contents of an attachment > may still contain software viruses which could damage your computer system: > you are advised to perform your own checks. Email communications with the > University of Nottingham may be monitored as permitted by UK legislation. > > -- Ng Foo Keong (Personal) mobile: +065 9636 3163 From alexandre.borovik at gmail.com Mon Mar 7 06:46:36 2011 From: alexandre.borovik at gmail.com (Alexandre Borovik) Date: Mon, 07 Mar 2011 06:46:36 +0000 Subject: [Maths-Education] Re: Maths-Education Digest, Vol 77, Issue 5 In-Reply-To: References: Message-ID: <4D747F4C.5020506@gmail.com> On 07/03/2011 06:05, Ng Foo Keong wrote: > i'd like us to distinguish between the potential of ICT and what has > actually been achieved in our evaluations of the effectiveness of ICT. This goes against the conventional wisdom which can be traced not just centuries, millenia back in time: "The proof of the pudding is in the eating" (14th century, according to Oxford Dictionary), "Rhodes is here, here is where you jump!" (Aesop). Alexandre Borovik -- Professor Alexandre Borovik * University of Manchester Web: http://www.maths.manchester.ac.uk/~avb/ Wordpress: http://micromath.wordpress.com/ Academia: http://manchester.academia.edu/AlexandreBorovik From matt.dickenson at londongt.org Mon Mar 7 08:56:31 2011 From: matt.dickenson at londongt.org (Matt Dickenson) Date: Mon, 7 Mar 2011 08:56:31 -0000 Subject: [Maths-Education] Re: Research and teacher practices for 'working class' underachievement in secondary mathematics In-Reply-To: <3AEB72CF0A9B2A4F865AB09B21803864936B4A@ict-exbe-vs5.lsbu.ac.uk> Message-ID: Hi All We (London G&T) have done quite a bit of work on academic literacy with schools in challenging (and less challenging) settings, much of which has arisen developed from an explicit focus on teaching and learning for advanced bilingual learners. Without an explicit focus on language, even high achieving mathematicians and those for whom language no longer seems to be an issue (conversationally fluent etc) are likely to underachieve, or will struggle to maintain their mathematical development beyond Key Stage 4. But this is not just an issue for learners of English as an additional language. Formal English might as well be regarded as an additional language for many children with English as their first language. It is not just linguistic resources that the students need; there are often huge gaps in cultural capital and experience, which can prevent them from engaging with challenge in learning. It is also often the case that the working class underachiever previous postings have referred to will tend not see language as a resource for learning, whereas EAL learners mostly will. Teachers have a tendency to think that learners with a OEdeficit? tend to need support and this has been very much in keeping with/reinforced by the language used by the National Strategies and others. But often in providing this support there is a tendency to negate the purpose of the challenge in the learning. There is also a tendency to use the word support in the absence of an understanding of what is really meant. Disadvantaged learners may need support in accessing challenge in their learning, but critically they don?t need the challenge to be simplified out of it and to be spoon-fed pre-digested chunks in a way that enables them to consume more, but digest less. They don?t need teachers who see learning as avoiding or practising out mistakes. Students need structures to be able to understand how to deal with language and to enable them to develop a variety of ways to think mathematically and this is support that teachers can give. But, it is readily apparent that maths teachers won?t necessarily regard themselves as teachers of language and that many lack an understanding of how formal language works, or how it can be explicitly developed through ordinary classroom learning. Language is acquired in context ? mathematical language needs to be taught in the context of mathematical thinking. Would be happy to share some ideas from the work that we have done in this area if colleagues are interested. Best wishes Matt Matt Dickenson Equalities & Achievement Director London Gifted & Talented 91 Berwick St, LONDON W1F 0BP Fax: 020 7287 6970 07817 552806 www.londongt.org The REAL Project ? Realising Equality & Achievement for Learners www.realproject.org.uk -- On 28/02/2011 07:19, "Lerman, Stephen" wrote: > Dylan's contribution is very interesting and helpful. But I think it supports > Basil Bernstein's argument. He was indicating the lack of linguistic resources > that generally is found amongst children from working class and other > disadvantaged backgrounds, and the ways that schooling reinforces that > linguistic disadvantage, but in pointing out the causes he was also > demonstrating that if schools can provide those resources on school entrance > (small classes, informed teachers etc.) those children can acquire the > resources needed. Dylan is showing us that Scandinavian schools provide those > resources and it has some success. > > Steve > > Professor Stephen Lerman > Department of Education > London South Bank University > 103 Borough Road > LONDON SE1 0AA > Tel: +44 (0)20 7815 7440 > > > > -----Original Message----- > From: maths-education-bounces at lists.nottingham.ac.uk on behalf of > dylanwiliam at mac.com > Sent: Sun 2/27/2011 8:55 PM > To: Mathematics Education discussion forum > Cc: phillip.kent at gmail.com > Subject: [Maths-Education] Re: Research and teacher practices for 'working > class' underachievement in secondary mathematics > > > ****************************************************************************** > ***************************** > This message has been generated through the Mathematics Education email > discussion list. > Hitting the REPLY key sends a message to all list members. > ****************************************************************************** > ***************************** > > While I agree that the link between socioeconomic disadvantage and educational > achievement is not a new phenomenon, it is also worth noting that it is not > universal. We will probably never stop affluent parents from securing > educational advantages for their children, but there are countries that have > managed to ensure that socioeconomic disadvantage does not lead to lower > achievement. While in the US and the UK, the relationship between the income > of parents and children is linear (and steeper in the US than the UK) in some > countries, it is not. Notably in some Scandinavian countries, while the > richest do best, the poorest do as well as average students. In fact the > research on educational quality, whether in child care, primary school, or > secondary schools, shows that high-quality education benefits low achievers > more than higher achievers. In some studies, this effect has been so strong > that the effect of quality teaching has completely overcome socio-economic > disadvantage. So it may be that Basil Bernstein was wrong. Education _can_ > perhaps compensate for society, provided it is of very high quality. I > therefore see the challenge as political-how to get get the best teachers > working with the students who need them most... > > Dylan Wiliam > > > On 27 Feb 2011, at 17:59, Alan Rogerson wrote: > >> > >> ***************************************************************************** >> ****************************** >> > This message has been generated through the Mathematics Education email >> discussion list. >> > Hitting the REPLY key sends a message to all list members. >> > >> ***************************************************************************** >> ****************************** >> > Dear Phillip, >> > >> > The link: >> > >> > >> http://www.independent.co.uk/news/education/education-news/social-class-deter >> mines-childs-success-934240.html >> > >> > makes depressing reading: eg >> > >> > Children's social class is still the most significant factor in determining >> their exam success in state schools, the Government's head of teacher >> training acknowledges today. In an interview with The Independent, Graham >> Holley, the chief executive of the Training and Development Agency, said: >> "The performance of a school and a child in it is highly linked to social >> class. If you turn the clock back on pupils in school today 15 years and >> predict their outcomes from where they were born, you can do it. We need to >> change that. It's not something this government has done. It's not something >> the last government has done. It's something that has been there since the >> Second World War and probably even before that." > >> > >> > There is no "probably" (Graham was simply restricting his comments to his >> own experience) the right word is "inevitably". > >> > >> > As you will recall, I told you of my experiences of working class culture >> growing up after WW2, and sadly and clearly the problem is still with us, and >> in no way is it restricted to mathematics! We are speaking here of the >> strength of exclusive social/cultural world-views derived from primary >> socialisation,... "give us a child until he is 11"..... etc. > >> > >> > Best wishes, >> > Alan >> > >> > >> > >> > >> > On 18/02/2011 15:08, Phillip Kent wrote: >>> >> >>> **************************************************************************** >>> ******************************* >>> >> This message has been generated through the Mathematics Education email >>> discussion list. >>> >> Hitting the REPLY key sends a message to all list members. >>> >> >>> **************************************************************************** >>> ******************************* >>> >> Dear colleagues, >>> >> >>> >> I'd appreciate some pointers to research and guidance on dealing with >>> >> the problem of 'working class' underachievement in maths in secondary >>> >> school. I realise there is a huge literature on this, in terms of >>> >> statistical analysis on the existence of the problem, sociological-type >>> >> analysis of classroom behaviours (a la Bernstein, etc), and research on >>> >> teachers' beliefs about 'ability' and so on. >>> >> >>> >> However, I'm specifically interested in any research/guidance about what >>> >> is effective for maths teachers to do in practice in classrooms. There >>> >> is a very familiar type of student who for 'social' reasons comes to >>> >> construct for him or herself an identity as someone who 'can't do >>> >> maths', which is not related to his or her actual mathematical >>> >> potential. Then how should the teacher break through this identity to >>> >> tap into the actual potential and interest? >>> >> >>> >> Perhaps I am wrong to see this as essentially a problem of 'class'. Any >>> >> thoughts welcome. >>> >> >>> >> - Phillip >>> >> >> > >> > >> > This message and any attachment are intended solely for the addressee and >> may contain confidential information. If you have received this message in >> error, please send it back to me, and immediately delete it. Please do not >> use, copy or disclose the information contained in this message or in any >> attachment. Any views or opinions expressed by the author of this email do >> not necessarily reflect the views of the University of Nottingham. > >> > >> > This message has been checked for viruses but the contents of an attachment >> > may still contain software viruses which could damage your computer system: >> > you are advised to perform your own checks. Email communications with the >> > University of Nottingham may be monitored as permitted by UK legislation. >> > > > > ============================================ > Email has been scanned for spam and viruses by Altman Technologies' email > management service - www.altman.co.uk/emailsystems/ > > Any queries regarding LSBU Email should be sent to ICTemail at lsbu.ac.uk or > you can check our web site at www.lsbu.ac.uk/email/ for up to date information > about this service. > > From alan at rogerson.pol.pl Mon Mar 7 16:08:56 2011 From: alan at rogerson.pol.pl (Alan Rogerson) Date: Mon, 07 Mar 2011 17:08:56 +0100 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <026601cbda77$9fb73ae0$df25b0a0$@argonet.co.uk> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> <026601cbda77$9fb73ae0$df25b0a0$@argonet.co.uk> Message-ID: <4D750318.1050909@rogerson.pol.pl> By a strange coincidence a colleague emailed me today about something else but his work is very relevant to your question below Douglas, : http://driyekekpolor.blogspot.com/ I haven't looked at the full study and analysis, but others who wish to may like to email him at driyekekpolor at gmail.com Best wishes, Alan On 04/03/2011 15:22, Douglas Butler (Argonet) wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > This is a thread that has troubled me for years - how to put some flesh on > the assertion that ICT makes a difference in mathematics. > > I am both a creator and a user of mathematics software, and I need no > convincing at all. > > But to get hard research evidence would presumably require setting up > control groups of identical children doing the same courses with the same > teachers, but without the technology. Surely this is impossible to achieve? > > Douglas > > == from Douglas Butler< debutler at argonet.co.uk> == > Director, iCT TRAINING CENTRE (OUNDLE) > PO Box 46, Oundle, Peterborough PE8 4EJ, UK > T: +44 (0)1832 273444 F: 273529 M: +44 (0)7860 843462 > www.tsm-resources.com www.autograph-maths.com From S.Trenholm at lboro.ac.uk Mon Mar 7 16:15:55 2011 From: S.Trenholm at lboro.ac.uk (Sven Trenholm) Date: Mon, 7 Mar 2011 16:15:55 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <4D71EFC5.8050500@gmail.com> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> <4D70F81D.1090100@rogerson.pol.pl><605A41D4-D3EB-4F3D-9BB3-7A31D4BF4AF3@mac.com> <4D710EE3.7050502@rogerson.pol.pl>, <731CECC23FB8CA4E9127BD399744D1EC02F40343@email001.lsu.edu> <234B6B562A62654E93691A30A71B12CB2120043C9D@STAFFMBX-1.lunet.lboro.ac.uk>, <4D71EFC5.8050500@gmail.com> Message-ID: <234B6B562A62654E93691A30A71B12CB2120043CA4@STAFFMBX-1.lunet.lboro.ac.uk> Re: Would you agree that the whole idea of ICT in mathematics is self-defeating: if skills in carrying out certain types of tasks can be best taught by a computer, this is the best proof that these task are best done by a computer without human participation? One thought...How much is the wider issue in this discussion the professionalization of higher education? We seem to be engaged in a Tayloristic quest for efficiency where it is unclear whether we are developing human beings or human capital? Teaching by a computer without human participation would seem to be adept at developing the latter but not the former? Sven ________________________________________ From: maths-education-bounces at lists.nottingham.ac.uk [maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Alexandre Borovik [alexandre.borovik at gmail.com] Sent: Saturday, March 05, 2011 8:09 AM To: Mathematics Education discussion forum Subject: [Maths-Education] Re: ICT in mathematics *********************************************************************************************************** This message has been generated through the Mathematics Education email discussion list. Hitting the REPLY key sends a message to all list members. *********************************************************************************************************** @Sven -- you are asking, in my opinion, the key question -- what is definition of "success" of mathematics teaching. I feel that discussants in this thread have no shared understanding of this key point, and this makes the "ICT in mathematics" thread truly engaging. Perhaps lack of shared criteria of "success" is a wider issue affecting the whole discourse on ICT in mathematics, and this perhaps explains shortage of proper academic papers assessing the ICT. Playing Devil's advocate, I wish to offer a questions. Would you agree that the whole idea of ICT in mathematics is self-defeating: if skills in carrying out certain types of tasks can be best taught by a computer, this is the best proof that these task are best done by a computer without human participation? Have a look at http://www.antiquark.com/sliderule/sim/n909es/virtual-n909-es.html -- it is fully functional interactive online slide rule. Without doubt, computers can be very efficient in teaching the use of slide rule. But why are we no longer using slider rules? Best wishes -- Alexandre On 04/03/2011 23:01, Sven Trenholm wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > Re: NCAT > New to this thread... I'm a PhD student at the Mathematics Education Center of Loughborough University (focused on mathematics e-learning in the higher education sector). In 2010 I arrived "off the boat" from upstate NY where I taught for over 10 years at the American junior college level. > > I've attended an NCAT workshop in the US and have followed their progress over the last decade. They have a sizeable focus on introductory level mathematics courses. Bill Gates recently put some of his money behind their work in "transforming" developmental mathematics offerings (which traditionally have failure rates around 40-60%). I am very interested in what they are doing given, on the surface, it appears to be successful for the specific introductory level large enrollment mathematics course context. Of course "success" may be well defined in terms of financial savings but not so well defined in terms of learning. In any case the movement (if you can call it that) appears to be picking up momentum. > > My question is this. After just over 10 years of work, the only peer-reviewed article, I am aware of, is a 2008 conference proceedings paper (citation below). For those familiar with NCAT, how much do you think this may be attributable, as I believe NCAT would attest, to the "inherent conservatism" in higher education (and perhaps the disciplinary culture of mathematics, in particular)? I don't necessarily believe that what they are doing is primarily instruction via repetitive practice... > > Sven > > > Greenberg, W.,& Williams, M. (2008). New pedagogical models for instruction in mathematics. Mathematical Modeling, Simulation, Visualization and e-Learning, 4, 361-371. > > Also, for those interested...(think tank paper) > Miller, B. (2010). THE COURSE OF INNOVATION: Using technology to transform higher education. Education Sector Reports > > > > > ________________________________________ > From: maths-education-bounces at lists.nottingham.ac.uk [maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of David H Kirshner [dkirsh at lsu.edu] > Sent: Friday, March 04, 2011 4:57 PM > To: Mathematics Education discussion forum > Subject: [Maths-Education] Re: ICT in mathematics > > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > I'm enjoying this thread. > > To be fair, Ken Koedinger, lead developer of the software, is a bona > fide cognitive scientist who has published a variety of academic papers > on the cognitive theory involved, in addition to publications on the > effectiveness of the tutor. And even the latter publications have been > in peer review academic journals. Still, it would be interesting to know > if "independent" evaluations of the effectiveness have been undertaken > and published. > > There is some software on the market now that seems to be effective in > raising students' test scores in comparison with standard classroom > instruction. For instance, at Northern Arizona University, the college > algebra course is taught through an online facility that > > "promote[s] active and collaborative learning, address the diverse range > of student learning styles and permit acceleration. It will use ALEKS, a > comprehensive instructional software and course management system that > individualizes assessment and learning. ALEKS is Web-based, allowing > students to access course materials at anytime from anyplace, and can be > customized to meet student and course needs. As a supplement to ALEKS, > NAU will also use Thinkwell, a video-based mathematics software program > that uses highlighted worked examples and video lectures for students > who learn better in this mode." > (http://www.thencat.org/PCR/R3/NAU/NAU_Abstract.htm) > > However, it is clear that the program's effectiveness primarily is > related to its effective provision of practice problems and immediate > feedback. In short, it promotes learning of skills through repetitive > practice in the behaviorist tradition. > > I've looked at the Cognitive Tutor, and it's a more complex and > ambitious project. The Tutor functions through a multidimensional model > of expertise that it uses to update a student model, and thereby > determine what kinds of problems and assistance would best benefit the > student. It is not so straightforward an analysis as to whether what is > being promoted is skills through practice (in a sophisticated way), or > something more akin to what we would consider as mathematical concepts. > > The Cognitive Tutor is based on the ACT-series of acquisition models > developed by John Anderson and company at Carnegie Melon--in fact, Ken > was a student of his, and is now a frequent collaborator. The ambiguity > of the Tutor in terms of its learning modalities is reflected also in > the status of the ACT theories. Anderson (2005) would be a good source > to begin to answer those questions, and Anderson (2007) includes an > interesting discussion of the general issue of the kind of learning > addressed in the ACT theories. > > David Kirshner > > Anderson, J. R. (2005). Human symbol manipulation within an integrated > cognitive architecture. Cognitive Science, 29, 313-341. [algebraic > symbol skills] > Anderson, J. R. (2007). How can the human mind occur in the physical > universe?. Oxford University Press. > > > > > -----Original Message----- > From: maths-education-bounces at lists.nottingham.ac.uk > [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of > Alan Rogerson > Sent: Friday, March 04, 2011 10:10 AM > To: Mathematics Education discussion forum > Subject: [Maths-Education] Re: ICT in mathematics > > ************************************************************************ > *********************************** > This message has been generated through the Mathematics Education email > discussion list. > Hitting the REPLY key sends a message to all list members. > ************************************************************************ > *********************************** > Dear Dylan, > > What you say below does not in any way alter the fact that what you > actually recommended to Sarah were reports on a webpage produced by a > commercial company. That is the problem. You say something is "one of > the best researched" but we need to know when and by whom? It is not the > > quantity of research that counts, rather its quality. > > Please note, I am not making any judgement about the actual research > which you call "original" nor did I say that this research is some how > invalidated by being used by a commercial company. Let's say for the > sake of argument, that all this research could be validated, and also > note that some of the reports on the Carnegie.inc webpage were (as we > know) from Carnegie Mellon University itself, and may have even > pre-dated the formation of Carnegie.inc, I do hope you can see that this > > does not change the problem? "Selective quotation" is still a real > hazard, what company after all will quote research critical of its own > products? > > We know only too well the much bigger and much more serious debate going > > on about so-called academic research being funded, or supported, (or of > course suppressed!) by drug companies. Companies are in business to make > > money, so we can hardly use them, or the reports they quote, as > objective exemplars of "research". The contrast is between reports which > > clearly have no such bias, and those which are at risk of being biassed. > > Surely we cannot say "third party evaluations... would be better", > surely you mean essential? We know from basic statistics that biassed > evidence, when we can not attach boundaries to the bias, , is, and must > > be, useless (not second best). We all know the story of the millions of > telephone calls surveyed that failed to predict the next President of > the USA....? > > Please also note that there is absolutely no bias (or specific > accusations) against Carnegie.inc in particular here, it is a purely > general point that is being made. > > The only remaining problem, and somewhat insoluble, is the one Douglas > Butler has just mentioned. > > C'est la vie, c'est la ICT. > > Best wishes, > Alan > > > > > On 04/03/2011 15:52, dylanwiliam at mac.com wrote: >> Alan: Sarah asked specifically for studies that showed the impact of > ICT on attainment, and the Cognitive Tutor is one of the best researched > pieces of software for mathematics education. While Carnegie Learning > is a commercial company that has taken over marketing and distribution > of the products generated by the people who developed the Cognitive > Tutor, the research itself is very solid (and much of it dates from > before Carnegie Learning became involved). I agree that third party > evaluations, such as those undertaken by Mathematica, would be better, > and of course educationalists should evaluate the merits of the studies, > but the fact that the research is now being used to support a commercial > enterprise does not invalidate the original findings. >> >> Dylan > > > This message and any attachment are intended solely for the addressee > and may contain confidential information. If you have received this > message in error, please send it back to me, and immediately delete it. > Please do not use, copy or disclose the information contained in this > message or in any attachment. Any views or opinions expressed by the > author of this email do not necessarily reflect the views of the > University of Nottingham. > > This message has been checked for viruses but the contents of an > attachment > may still contain software viruses which could damage your computer > system: > you are advised to perform your own checks. Email communications with > the > University of Nottingham may be monitored as permitted by UK > legislation. -- Professor Alexandre Borovik * University of Manchester Web: http://www.maths.manchester.ac.uk/~avb/ Wordpress: http://micromath.wordpress.com/ Academia: http://manchester.academia.edu/AlexandreBorovik From d.j.miller at educ.keele.ac.uk Mon Mar 7 16:37:07 2011 From: d.j.miller at educ.keele.ac.uk (Dave Miller) Date: Mon, 7 Mar 2011 16:37:07 -0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <234B6B562A62654E93691A30A71B12CB2120043CA4@STAFFMBX-1.lunet.lboro.ac.uk> References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> <4D70F81D.1090100@rogerson.pol.pl><605A41D4-D3EB-4F3D-9BB3-7A31D4BF4AF3@mac.com> <4D710EE3.7050502@rogerson.pol.pl>, <731CECC23FB8CA4E9127BD399744D1EC02F40343@email001.lsu.edu> <234B6B562A62654E93691A30A71B12CB2120043C9D@STAFFMBX-1.lunet.lboro.ac.uk>, <4D71EFC5.8050500@gmail.com> <234B6B562A62654E93691A30A71B12CB2120043CA4@STAFFMBX-1.lunet.lboro.ac.uk> Message-ID: <017e01cbdce5$e61ef0c0$b25cd240$@j.miller@educ.keele.ac.uk> ICT in mathematics: Our report Mathematics and digital technologies: New beginnings is found at: bit.ly/ncetmdtreport https://www.ncetm.org.uk/files/3399662/NCETMDigitTechReport2010.pdf We looked to separate out the use of digital technologies by teachers of mathematics (which may happen a lot) - depending on what you call 'use' and that of how pupils use digital technologies in mathematics (which 'on average' does not happen that often in England). It makes recommendations and has suggestions for software etc that pupils should use. Dave ________________________________ Check out our new IWB offerings on www.iwbmathstraining.co.uk Check our new Mathematics Development Programme for Teachers at: www.keele.ac.uk/mathsed/mdpt/ Check our IWB research page at: http://www.keele.ac.uk/education/research/interactivewhiteboard/ For IWB 'At the board, on the desk, in the head' go to: www.ncetm.org.uk/mathemapedia/BoardDeskHead ________________________________ Dave Miller School of Public Policy and Professional Practice Senior Lecturer in Mathematics Education Keele University Keele Staffordshire ST5 5BG UK eda19 at educ.keele.ac.uk -----Original Message----- From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Sven Trenholm Sent: 07 March 2011 16:16 To: Mathematics Education discussion forum Subject: [Maths-Education] Re: ICT in mathematics **************************************************************************** ******************************* This message has been generated through the Mathematics Education email discussion list. Hitting the REPLY key sends a message to all list members. **************************************************************************** ******************************* Re: Would you agree that the whole idea of ICT in mathematics is self-defeating: if skills in carrying out certain types of tasks can be best taught by a computer, this is the best proof that these task are best done by a computer without human participation? One thought...How much is the wider issue in this discussion the professionalization of higher education? We seem to be engaged in a Tayloristic quest for efficiency where it is unclear whether we are developing human beings or human capital? Teaching by a computer without human participation would seem to be adept at developing the latter but not the former? Sven ________________________________________ From: maths-education-bounces at lists.nottingham.ac.uk [maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Alexandre Borovik [alexandre.borovik at gmail.com] Sent: Saturday, March 05, 2011 8:09 AM To: Mathematics Education discussion forum Subject: [Maths-Education] Re: ICT in mathematics **************************************************************************** ******************************* This message has been generated through the Mathematics Education email discussion list. Hitting the REPLY key sends a message to all list members. **************************************************************************** ******************************* @Sven -- you are asking, in my opinion, the key question -- what is definition of "success" of mathematics teaching. I feel that discussants in this thread have no shared understanding of this key point, and this makes the "ICT in mathematics" thread truly engaging. Perhaps lack of shared criteria of "success" is a wider issue affecting the whole discourse on ICT in mathematics, and this perhaps explains shortage of proper academic papers assessing the ICT. Playing Devil's advocate, I wish to offer a questions. Would you agree that the whole idea of ICT in mathematics is self-defeating: if skills in carrying out certain types of tasks can be best taught by a computer, this is the best proof that these task are best done by a computer without human participation? Have a look at http://www.antiquark.com/sliderule/sim/n909es/virtual-n909-es.html -- it is fully functional interactive online slide rule. Without doubt, computers can be very efficient in teaching the use of slide rule. But why are we no longer using slider rules? Best wishes -- Alexandre On 04/03/2011 23:01, Sven Trenholm wrote: > **************************************************************************** ******************************* > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > **************************************************************************** ******************************* > Re: NCAT > New to this thread... I'm a PhD student at the Mathematics Education Center of Loughborough University (focused on mathematics e-learning in the higher education sector). In 2010 I arrived "off the boat" from upstate NY where I taught for over 10 years at the American junior college level. > > I've attended an NCAT workshop in the US and have followed their progress over the last decade. They have a sizeable focus on introductory level mathematics courses. Bill Gates recently put some of his money behind their work in "transforming" developmental mathematics offerings (which traditionally have failure rates around 40-60%). I am very interested in what they are doing given, on the surface, it appears to be successful for the specific introductory level large enrollment mathematics course context. Of course "success" may be well defined in terms of financial savings but not so well defined in terms of learning. In any case the movement (if you can call it that) appears to be picking up momentum. > > My question is this. After just over 10 years of work, the only peer-reviewed article, I am aware of, is a 2008 conference proceedings paper (citation below). For those familiar with NCAT, how much do you think this may be attributable, as I believe NCAT would attest, to the "inherent conservatism" in higher education (and perhaps the disciplinary culture of mathematics, in particular)? I don't necessarily believe that what they are doing is primarily instruction via repetitive practice... > > Sven > > > Greenberg, W.,& Williams, M. (2008). New pedagogical models for instruction in mathematics. Mathematical Modeling, Simulation, Visualization and e-Learning, 4, 361-371. > > Also, for those interested...(think tank paper) > Miller, B. (2010). THE COURSE OF INNOVATION: Using technology to transform higher education. Education Sector Reports > > > > > ________________________________________ > From: maths-education-bounces at lists.nottingham.ac.uk [maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of David H Kirshner [dkirsh at lsu.edu] > Sent: Friday, March 04, 2011 4:57 PM > To: Mathematics Education discussion forum > Subject: [Maths-Education] Re: ICT in mathematics > > **************************************************************************** ******************************* > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > **************************************************************************** ******************************* > I'm enjoying this thread. > > To be fair, Ken Koedinger, lead developer of the software, is a bona > fide cognitive scientist who has published a variety of academic papers > on the cognitive theory involved, in addition to publications on the > effectiveness of the tutor. And even the latter publications have been > in peer review academic journals. Still, it would be interesting to know > if "independent" evaluations of the effectiveness have been undertaken > and published. > > There is some software on the market now that seems to be effective in > raising students' test scores in comparison with standard classroom > instruction. For instance, at Northern Arizona University, the college > algebra course is taught through an online facility that > > "promote[s] active and collaborative learning, address the diverse range > of student learning styles and permit acceleration. It will use ALEKS, a > comprehensive instructional software and course management system that > individualizes assessment and learning. ALEKS is Web-based, allowing > students to access course materials at anytime from anyplace, and can be > customized to meet student and course needs. As a supplement to ALEKS, > NAU will also use Thinkwell, a video-based mathematics software program > that uses highlighted worked examples and video lectures for students > who learn better in this mode." > (http://www.thencat.org/PCR/R3/NAU/NAU_Abstract.htm) > > However, it is clear that the program's effectiveness primarily is > related to its effective provision of practice problems and immediate > feedback. In short, it promotes learning of skills through repetitive > practice in the behaviorist tradition. > > I've looked at the Cognitive Tutor, and it's a more complex and > ambitious project. The Tutor functions through a multidimensional model > of expertise that it uses to update a student model, and thereby > determine what kinds of problems and assistance would best benefit the > student. It is not so straightforward an analysis as to whether what is > being promoted is skills through practice (in a sophisticated way), or > something more akin to what we would consider as mathematical concepts. > > The Cognitive Tutor is based on the ACT-series of acquisition models > developed by John Anderson and company at Carnegie Melon--in fact, Ken > was a student of his, and is now a frequent collaborator. The ambiguity > of the Tutor in terms of its learning modalities is reflected also in > the status of the ACT theories. Anderson (2005) would be a good source > to begin to answer those questions, and Anderson (2007) includes an > interesting discussion of the general issue of the kind of learning > addressed in the ACT theories. > > David Kirshner > > Anderson, J. R. (2005). Human symbol manipulation within an integrated > cognitive architecture. Cognitive Science, 29, 313-341. [algebraic > symbol skills] > Anderson, J. R. (2007). How can the human mind occur in the physical > universe?. Oxford University Press. > > > > > -----Original Message----- > From: maths-education-bounces at lists.nottingham.ac.uk > [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of > Alan Rogerson > Sent: Friday, March 04, 2011 10:10 AM > To: Mathematics Education discussion forum > Subject: [Maths-Education] Re: ICT in mathematics > > ************************************************************************ > *********************************** > This message has been generated through the Mathematics Education email > discussion list. > Hitting the REPLY key sends a message to all list members. > ************************************************************************ > *********************************** > Dear Dylan, > > What you say below does not in any way alter the fact that what you > actually recommended to Sarah were reports on a webpage produced by a > commercial company. That is the problem. You say something is "one of > the best researched" but we need to know when and by whom? It is not the > > quantity of research that counts, rather its quality. > > Please note, I am not making any judgement about the actual research > which you call "original" nor did I say that this research is some how > invalidated by being used by a commercial company. Let's say for the > sake of argument, that all this research could be validated, and also > note that some of the reports on the Carnegie.inc webpage were (as we > know) from Carnegie Mellon University itself, and may have even > pre-dated the formation of Carnegie.inc, I do hope you can see that this > > does not change the problem? "Selective quotation" is still a real > hazard, what company after all will quote research critical of its own > products? > > We know only too well the much bigger and much more serious debate going > > on about so-called academic research being funded, or supported, (or of > course suppressed!) by drug companies. Companies are in business to make > > money, so we can hardly use them, or the reports they quote, as > objective exemplars of "research". The contrast is between reports which > > clearly have no such bias, and those which are at risk of being biassed. > > Surely we cannot say "third party evaluations... would be better", > surely you mean essential? We know from basic statistics that biassed > evidence, when we can not attach boundaries to the bias, , is, and must > > be, useless (not second best). We all know the story of the millions of > telephone calls surveyed that failed to predict the next President of > the USA....? > > Please also note that there is absolutely no bias (or specific > accusations) against Carnegie.inc in particular here, it is a purely > general point that is being made. > > The only remaining problem, and somewhat insoluble, is the one Douglas > Butler has just mentioned. > > C'est la vie, c'est la ICT. > > Best wishes, > Alan > > > > > On 04/03/2011 15:52, dylanwiliam at mac.com wrote: >> Alan: Sarah asked specifically for studies that showed the impact of > ICT on attainment, and the Cognitive Tutor is one of the best researched > pieces of software for mathematics education. While Carnegie Learning > is a commercial company that has taken over marketing and distribution > of the products generated by the people who developed the Cognitive > Tutor, the research itself is very solid (and much of it dates from > before Carnegie Learning became involved). I agree that third party > evaluations, such as those undertaken by Mathematica, would be better, > and of course educationalists should evaluate the merits of the studies, > but the fact that the research is now being used to support a commercial > enterprise does not invalidate the original findings. >> >> Dylan > > > This message and any attachment are intended solely for the addressee > and may contain confidential information. If you have received this > message in error, please send it back to me, and immediately delete it. > Please do not use, copy or disclose the information contained in this > message or in any attachment. Any views or opinions expressed by the > author of this email do not necessarily reflect the views of the > University of Nottingham. > > This message has been checked for viruses but the contents of an > attachment > may still contain software viruses which could damage your computer > system: > you are advised to perform your own checks. Email communications with > the > University of Nottingham may be monitored as permitted by UK > legislation. -- Professor Alexandre Borovik * University of Manchester Web: http://www.maths.manchester.ac.uk/~avb/ Wordpress: http://micromath.wordpress.com/ Academia: http://manchester.academia.edu/AlexandreBorovik From howard.tanner at smu.ac.uk Mon Mar 7 18:41:59 2011 From: howard.tanner at smu.ac.uk (Tanner, Howard) Date: Mon, 7 Mar 2011 18:41:59 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: References: <1298038099.4207.16.camel@phillip-macbook-ubuntu> <4D6A9112.90506@rogerson.pol.pl> <3A445E6D-A2E1-45C2-8B56-60053C931C7A@mac.com> <4D6B899E.9030005@rogerson.pol.pl> <7B94FE5A0830AB4EAAEC80941357684822C3CC07C5@MILECCR.ntnfer2.nfer.ac.uk> <4D70F81D.1090100@rogerson.pol.pl> <605A41D4-D3EB-4F3D-9BB3-7A31D4BF4AF3@mac.com> <4D710EE3.7050502@rogerson.pol.pl> <240C36E18CADBE46962CC52E8839D67F5678BB@PLEIADES.sid.sihe.ac.uk> <240C36E18CADBE46962CC52E8839D67F4A2099@PLEIADES.sid.sihe.ac.uk> Message-ID: <240C36E18CADBE46962CC52E8839D67F01570771@PLEIADES.sid.sihe.ac.uk> This is a very interesting and useful thread, which is raising some interesting issues for me. I do not claim to be an expert on or advocate for meta-analyses, so First with regard to effect size. I do not think I was misrepresenting Hattie. I quote here from his inaugural address: "An effect-size of .31 would not, according to Cohen (1977), be perceptible to the naked observational eye, and would be approximately equivalent to the difference between the height of a 5'11" and a 6'0" person." Now I agree with Dylan that I can see an effect size of 0.2, but it is very small and I have been much happier when innovations that I have been involved in have reached the 0.4 benchmark above controls. However, Hattie claims "Most innovations that are introduced in schools improve achievement by about .4 of a standard deviation. This is the benchmark figure and provides a 'standard' from which to judge effects." "The typical effect does not mean that merely placing a teacher in front of a class would lead to an improvement of .4 standard deviations. Some deliberate attempt to change, improve, plan, modify, or innovate is involved." http://www.education.auckland.ac.nz/webdav/site/education/shared/hattie/docs/influences-on-student-learning.pdf Hattie is not referring to the baseline rate of progress within a system, but to the average effect of INNOVATIONS in education. He is comparing innovations with each other and suggesting that some innovations are more effective than others. Now there are obviously methodological issues associated with meta-analyses, such as the possible tendency for negative or null results not to be published, which would raise the bar. There are also meta-studies that ignore context or which lump together a range of disparate innovations under the same theme. However, Hattie's core point is about investing in the innovations that have the biggest effect. (Although I'm not sure that I want to promise that investing in such innovations would clear the National Debt). With regard to the second point, I feel on stronger ground. The limited aims of the Cognitive Tutor in teaching procedural knowledge have a degree of validity in that there are probably many teachers in the UK as well as the USA who see mathematics in this limited way. But surely we don't wish to accept this status quo but to improve matters? Surely we don't want to work to take teachers out of the system, but to help them to understand how the affordances of ICT can provide opportunities for creativity, experimentation, discussion, argumentation and justification? Effective education requires effect teachers. We need a highly skilled, highly qualified, creative and reflective teaching profession that chooses to use technology to develop higher level mathematical thinking. There are no shortcuts. Howard Tanner PS I would like to read the paper referenced, but my library won't let me access it until November 2011. -----Original Message----- From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of dylanwiliam at mac.com Sent: 06 March 2011 07:37 To: Mathematics Education discussion forum Subject: [Maths-Education] Re: ICT in mathematics *********************************************************************************************************** This message has been generated through the Mathematics Education email discussion list. Hitting the REPLY key sends a message to all list members. *********************************************************************************************************** Jacob Cohen's views about the interpretation of effect sizes are widely accepted but it is important to note that they were based on experiences in psychology, rather than education. In psychology, an effect size of 0.2 might be small, but in education it is huge. This is because the average increase in achievement in mathematics (and most other subjects) is 0.4 standard deviations per year. An effect size of 0.2 therefore represents a 50% increase in the rate of learning-a very dramatic effect that, if it could be replicated across just one year group in England, would have a net present value equivalent to around three times the national debt. This 0.4 figure is what Hattie was quoting. He was basically saying that ordinary teaching will give you 0.4 standard deviations per year, so all interventions should be measured against this baseline. The figures quoted in most of the Carnegie studies are against comparison groups over the same period, so the 0.4 has already been subtracted. The other thing to say about Hattie's "Visible Learning" project is that the use of meta-analysis in such situations is problematic. First, measures of educational outcomes differ in their sensitivity to instruction, so apparently similar measures would give different effect sizes for the same intervention. Second, the calculation of effect sizes uses the standard deviation of the control and treatment groups as a divisor. Where the groups are sub-group of the whole population, this divisor will be smaller, and so the effect size will be larger. This partly explains why interventions for students with special educational needs appear to provide larger effects (See Fuchs & Fuchs, 1986), but more importantly means that where studies are not conducting on representative samples of the whole population, average effect sizes are difficult, if not impossible, to interpret. Most readers of this thread will have had enough about this already, but for those that want to read more about effect sizes in education, and sensitivity to instruction, I have written more about this in: Wiliam, D. (2010). Standardized testing and school accountability. Educational Psychologist, 45(2), 107-122. Regarding Howard's second point, it is important to note that the Cognitive Tutor was designed to do just one thing: teach procedural aspects of algebra to ninth grade students in the United States. In many countries, these particular aspects of algebra are not regarded as particularly important, but in the US, this is a substantial proportion (perhaps 50%) of what students do in ninth grade mathematics. In terms of these very limited goals, Cognitive Tutor does a good job (by my estimate, it is better than 90% of teachers). Of course we should work to increase teachers' pedagogical content knowledge, but while we do this I think we need to worry about the students who are being taught right now. I would love to get to a point where every teacher is better than Cognitive Tutor, but while we are getting there, we need also to think about the short term. Dylan Wiliam On 5 Mar 2011, at 22:02, Tanner, Howard wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > I have two points to make in relation to this thread: > > 1. The research reported / selected for reporting, on the Carnegie learning site lists the effect sizes reported in the trials. In most cases these are small (using Cohen's usual criteria for small, medium and big) and below d=0.4. Hattie (2009) reports that the average effect size for any intervention is 0.4 and demands effect sizes above this level for "innovations that work". The average effect size for "computer-assisted instruction" is reported as 0.31 - so nice try but no cigar! (Am I allowed to say that?) > > 2. I have a problem with classifying interventions as ICT or non-ICT as if that was the most important aspect of learning and teaching. > > Clearly there is a world of difference between > a) computer aided learning in which a student works through a series of tasks as instructed by a computer; > b) a good teacher using software such as Autograph, Geogebra or Cabri to support dialogic teaching that encourages debate around students' ideas and > c) a poor teacher using the same software to tell students what the answer is. > > I don't think that there are easy technological fixes for educational problems. We need to focus on helping teachers to develop their own pedagogical subject knowledge and appreciate when the affordances of ICT might be useful. > > > Hattie J (2009) Visible Learning; a synthesis of over 800 meta-analyses relating to achievement London; Routledge > > > Dr Howard Tanner > Reader in Education / Darllenydd Addysg > > Director of Centre for Research in Education / Cyfarwyddwr y Ganolfan Ymchwil mewn Addysg > School of Education / Ysgol Addysg > Swansea Metropolitan University / Prifysgol Fetropolitan Abertawe > Townhill Road / Heol Townhill > Swansea / Abertawe SA2 0UT > Wales, UK / Cymru, y DU > > Phone / Ff?n: 01792 482019 > Fax/Ffacs: 01792 482126 > e-mail / e-bost: howard.tanner at smu.ac.uk > > -----Original Message----- > From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Alan Rogerson > Sent: 04 March 2011 16:10 > To: Mathematics Education discussion forum > Subject: [Maths-Education] Re: ICT in mathematics > > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > Dear Dylan, > > What you say below does not in any way alter the fact that what you > actually recommended to Sarah were reports on a webpage produced by a > commercial company. That is the problem. You say something is "one of > the best researched" but we need to know when and by whom? It is not the > quantity of research that counts, rather its quality. > > Please note, I am not making any judgement about the actual research > which you call "original" nor did I say that this research is some how > invalidated by being used by a commercial company. Let's say for the > sake of argument, that all this research could be validated, and also > note that some of the reports on the Carnegie.inc webpage were (as we > know) from Carnegie Mellon University itself, and may have even > pre-dated the formation of Carnegie.inc, I do hope you can see that this > does not change the problem? "Selective quotation" is still a real > hazard, what company after all will quote research critical of its own > products? > > We know only too well the much bigger and much more serious debate going > on about so-called academic research being funded, or supported, (or of > course suppressed!) by drug companies. Companies are in business to make > money, so we can hardly use them, or the reports they quote, as > objective exemplars of "research". The contrast is between reports which > clearly have no such bias, and those which are at risk of being biassed. > Surely we cannot say "third party evaluations... would be better", > surely you mean essential? We know from basic statistics that biassed > evidence, when we can not attach boundaries to the bias, , is, and must > be, useless (not second best). We all know the story of the millions of > telephone calls surveyed that failed to predict the next President of > the USA....? > > Please also note that there is absolutely no bias (or specific > accusations) against Carnegie.inc in particular here, it is a purely > general point that is being made. > > The only remaining problem, and somewhat insoluble, is the one Douglas > Butler has just mentioned. > > C'est la vie, c'est la ICT. > > Best wishes, > Alan > > > > > On 04/03/2011 15:52, dylanwiliam at mac.com wrote: >> Alan: Sarah asked specifically for studies that showed the impact of ICT on attainment, and the Cognitive Tutor is one of the best researched pieces of software for mathematics education. While Carnegie Learning is a commercial company that has taken over marketing and distribution of the products generated by the people who developed the Cognitive Tutor, the research itself is very solid (and much of it dates from before Carnegie Learning became involved). I agree that third party evaluations, such as those undertaken by Mathematica, would be better, and of course educationalists should evaluate the merits of the studies, but the fact that the research is now being used to support a commercial enterprise does not invalidate the original findings. >> >> Dylan > > > This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. > > This message has been checked for viruses but the contents of an attachment > may still contain software viruses which could damage your computer system: > you are advised to perform your own checks. Email communications with the > University of Nottingham may be monitored as permitted by UK legislation. From alexandre.borovik at gmail.com Tue Mar 8 06:01:49 2011 From: alexandre.borovik at gmail.com (Alexandre Borovik) Date: Tue, 08 Mar 2011 06:01:49 +0000 Subject: [Maths-Education] Re: Research and teacher practices for 'working class' underachievement in secondary mathematics In-Reply-To: References: Message-ID: <4D75C64D.9040305@gmail.com> Matt Dickenson's message branches out to an interesting new theme: the role of language in mathematics education. British Logic Colloquium (http://www.cs.bham.ac.uk/~exr/blc/) is seeking support for a possible joint submission to National Curriculum Review. As Matt Dickenson's contribution suggests, it could be of interests to this mail group; here is the text. ================================================================= The Importance of English Grammar Joint Submission of Evidence to the National Curriculum Review The British Logic Colloquium and [the name of your organisation here] welcome the White Paper "The Importance of Teaching" and its emphasis on core subjects, in particular the recognition of the effective teaching of English as a bedrock of good education in this country. Our concern is an important but neglected area of English as a school subject: grammar. Grammar is a precondition of logic in any language, the foundation of systematic reasoning. This connection is obvious at later stages of education, especially in mathematics, computer science and law, but also in every discipline or profession that involves clearly defined rules, such as natural science and finance. The ability to understand and use principles of grammar to analyse the meaning of complex texts and express thought precisely in speech and writing is one of the most important skills for students to acquire in their school education. Mastery of grammar helps us navigate the increasingly complex information world in which we all live in the 21st century. Every dialect has its own grammar. What students need to acquire is sufficient grasp of general concepts and principles of grammar to enable them to understand how sentences of English work, how their parts fit together to express the meaning they do. We have found in practice that students who have never been explicitly taught formal grammar are at a disadvantage when they have to assess reasoning to exact standards, because they lack the intellectual resources to reflect critically on the language in which it is stated. We leave it to specialists to decide the optimal scope and methods for English grammar teaching in schools. The aim of this statement is to raise the profile of the issue. ==================================================================== Alexandre Borovik -- Professor Alexandre Borovik * University of Manchester Web: http://www.maths.manchester.ac.uk/~avb/ Wordpress: http://micromath.wordpress.com/ Academia: http://manchester.academia.edu/AlexandreBorovik On 07/03/2011 08:56, Matt Dickenson wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > Hi All > > We (London G&T) have done quite a bit of work on academic literacy with > schools in challenging (and less challenging) settings, much of which has > arisen developed from an explicit focus on teaching and learning for > advanced bilingual learners. > Without an explicit focus on language, even high achieving mathematicians > and those for whom language no longer seems to be an issue (conversationally > fluent etc) are likely to underachieve, or will struggle to maintain their > mathematical development beyond Key Stage 4. > > But this is not just an issue for learners of English as an additional > language. Formal English might as well be regarded as an additional language > for many children with English as their first language. > > It is not just linguistic resources that the students need; there are often > huge gaps in cultural capital and experience, which can prevent them from > engaging with challenge in learning. It is also often the case that the > working class underachiever previous postings have referred to will tend not > see language as a resource for learning, whereas EAL learners mostly will. > > Teachers have a tendency to think that learners with a OEdeficit? tend to > need support and this has been very much in keeping with/reinforced by the > language used by the National Strategies and others. But often in providing > this support there is a tendency to negate the purpose of the challenge in > the learning. > > There is also a tendency to use the word support in the absence of an > understanding of what is really meant. Disadvantaged learners may need > support in accessing challenge in their learning, but critically they don?t > need the challenge to be simplified out of it and to be spoon-fed > pre-digested chunks in a way that enables them to consume more, but digest > less. They don?t need teachers who see learning as avoiding or practising > out mistakes. > > Students need structures to be able to understand how to deal with language > and to enable them to develop a variety of ways to think mathematically and > this is support that teachers can give. But, it is readily apparent that > maths teachers won?t necessarily regard themselves as teachers of language > and that many lack an understanding of how formal language works, or how it > can be explicitly developed through ordinary classroom learning. Language is > acquired in context ? mathematical language needs to be taught in the > context of mathematical thinking. > > Would be happy to share some ideas from the work that we have done in this > area if colleagues are interested. > > Best wishes > > Matt > > > Matt Dickenson > Equalities& Achievement Director > > London Gifted& Talented > 91 Berwick St, LONDON W1F 0BP > Fax: 020 7287 6970 > > 07817 552806 > > www.londongt.org > > The REAL Project ? Realising Equality& Achievement for Learners > www.realproject.org.uk > -- > > > > On 28/02/2011 07:19, "Lerman, Stephen" wrote: > >> Dylan's contribution is very interesting and helpful. But I think it supports >> Basil Bernstein's argument. He was indicating the lack of linguistic resources >> that generally is found amongst children from working class and other >> disadvantaged backgrounds, and the ways that schooling reinforces that >> linguistic disadvantage, but in pointing out the causes he was also >> demonstrating that if schools can provide those resources on school entrance >> (small classes, informed teachers etc.) those children can acquire the >> resources needed. Dylan is showing us that Scandinavian schools provide those >> resources and it has some success. >> >> Steve >> >> Professor Stephen Lerman >> Department of Education >> London South Bank University >> 103 Borough Road >> LONDON SE1 0AA >> Tel: +44 (0)20 7815 7440 >> >> >> >> -----Original Message----- >> From: maths-education-bounces at lists.nottingham.ac.uk on behalf of >> dylanwiliam at mac.com >> Sent: Sun 2/27/2011 8:55 PM >> To: Mathematics Education discussion forum >> Cc: phillip.kent at gmail.com >> Subject: [Maths-Education] Re: Research and teacher practices for 'working >> class' underachievement in secondary mathematics >> >> >> ****************************************************************************** >> ***************************** >> This message has been generated through the Mathematics Education email >> discussion list. >> Hitting the REPLY key sends a message to all list members. >> ****************************************************************************** >> ***************************** >> >> While I agree that the link between socioeconomic disadvantage and educational >> achievement is not a new phenomenon, it is also worth noting that it is not >> universal. We will probably never stop affluent parents from securing >> educational advantages for their children, but there are countries that have >> managed to ensure that socioeconomic disadvantage does not lead to lower >> achievement. While in the US and the UK, the relationship between the income >> of parents and children is linear (and steeper in the US than the UK) in some >> countries, it is not. Notably in some Scandinavian countries, while the >> richest do best, the poorest do as well as average students. In fact the >> research on educational quality, whether in child care, primary school, or >> secondary schools, shows that high-quality education benefits low achievers >> more than higher achievers. In some studies, this effect has been so strong >> that the effect of quality teaching has completely overcome socio-economic >> disadvantage. So it may be that Basil Bernstein was wrong. Education _can_ >> perhaps compensate for society, provided it is of very high quality. I >> therefore see the challenge as political-how to get get the best teachers >> working with the students who need them most... >> >> Dylan Wiliam >> >> >> On 27 Feb 2011, at 17:59, Alan Rogerson wrote: >> >>>> >>> ***************************************************************************** >>> ****************************** >>>> This message has been generated through the Mathematics Education email >>> discussion list. >>>> Hitting the REPLY key sends a message to all list members. >>>> >>> ***************************************************************************** >>> ****************************** >>>> Dear Phillip, >>>> >>>> The link: >>>> >>>> >>> http://www.independent.co.uk/news/education/education-news/social-class-deter >>> mines-childs-success-934240.html >>>> >>>> makes depressing reading: eg >>>> >>>> Children's social class is still the most significant factor in determining >>> their exam success in state schools, the Government's head of teacher >>> training acknowledges today. In an interview with The Independent, Graham >>> Holley, the chief executive of the Training and Development Agency, said: >>> "The performance of a school and a child in it is highly linked to social >>> class. If you turn the clock back on pupils in school today 15 years and >>> predict their outcomes from where they were born, you can do it. We need to >>> change that. It's not something this government has done. It's not something >>> the last government has done. It's something that has been there since the >>> Second World War and probably even before that." >> >>>> >>>> There is no "probably" (Graham was simply restricting his comments to his >>> own experience) the right word is "inevitably". >> >>>> >>>> As you will recall, I told you of my experiences of working class culture >>> growing up after WW2, and sadly and clearly the problem is still with us, and >>> in no way is it restricted to mathematics! We are speaking here of the >>> strength of exclusive social/cultural world-views derived from primary >>> socialisation,... "give us a child until he is 11"..... etc. >> >>>> >>>> Best wishes, >>>> Alan >>>> >>>> >>>> >>>> >>>> On 18/02/2011 15:08, Phillip Kent wrote: >>>>>> >>>> **************************************************************************** >>>> ******************************* >>>>>> This message has been generated through the Mathematics Education email >>>> discussion list. >>>>>> Hitting the REPLY key sends a message to all list members. >>>>>> >>>> **************************************************************************** >>>> ******************************* >>>>>> Dear colleagues, >>>>>> >>>>>> I'd appreciate some pointers to research and guidance on dealing with >>>>>> the problem of 'working class' underachievement in maths in secondary >>>>>> school. I realise there is a huge literature on this, in terms of >>>>>> statistical analysis on the existence of the problem, sociological-type >>>>>> analysis of classroom behaviours (a la Bernstein, etc), and research on >>>>>> teachers' beliefs about 'ability' and so on. >>>>>> >>>>>> However, I'm specifically interested in any research/guidance about what >>>>>> is effective for maths teachers to do in practice in classrooms. There >>>>>> is a very familiar type of student who for 'social' reasons comes to >>>>>> construct for him or herself an identity as someone who 'can't do >>>>>> maths', which is not related to his or her actual mathematical >>>>>> potential. Then how should the teacher break through this identity to >>>>>> tap into the actual potential and interest? >>>>>> >>>>>> Perhaps I am wrong to see this as essentially a problem of 'class'. Any >>>>>> thoughts welcome. >>>>>> >>>>>> - Phillip >>>>>> >>>> >>>> >>>> This message and any attachment are intended solely for the addressee and >>> may contain confidential information. If you have received this message in >>> error, please send it back to me, and immediately delete it. Please do not >>> use, copy or disclose the information contained in this message or in any >>> attachment. Any views or opinions expressed by the author of this email do >>> not necessarily reflect the views of the University of Nottingham. >> >>>> >>>> This message has been checked for viruses but the contents of an attachment >>>> may still contain software viruses which could damage your computer system: >>>> you are advised to perform your own checks. Email communications with the >>>> University of Nottingham may be monitored as permitted by UK legislation. >>>> >> >> >> ============================================ >> Email has been scanned for spam and viruses by Altman Technologies' email >> management service - www.altman.co.uk/emailsystems/ >> >> Any queries regarding LSBU Email should be sent to ICTemail at lsbu.ac.uk or >> you can check our web site at www.lsbu.ac.uk/email/ for up to date information >> about this service. >> >> > From tandiclausenmay at gmail.com Tue Mar 8 14:36:35 2011 From: tandiclausenmay at gmail.com (Tandi Clausen-May) Date: Tue, 8 Mar 2011 14:36:35 -0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <4D7347B5.5050003@gmail.com> References: <8B1E41E4B39E4374A2BC3034C3717750@homet4dz4d6xu0> <4D7347B5.5050003@gmail.com> Message-ID: Sarah Maugham asked for 'evidence about whether ICT has a positive impact on attainment in mathematics'. Alexandre Borovik wrote 'I would suggest to define "success" first, and only then discuss how it could be measured'. This is a suggestion that everyone, from an Early Years/Foundation teacher to (I assume) a university teacher, would support. But that does not change the sorry fact that the way in which attainment is usually measured in schools is with a test - and written key stage test and GCSE questions are not designed to assess what pupils learn using mathematics tool software. If the assessment required pupils to use Geogebra or Autograph to do some mathematics then they would probably be more successful if they had learnt some mathematics using these tools, so ICT would have 'a positive impact on attainment in mathematics'. But the assessments do not require this, so the evidence is hard to find. Tandi Tandi Clausen-May Independent Consultant Mathematics curriculum and assessment Special education From a.m.brown at mmu.ac.uk Tue Mar 8 15:52:43 2011 From: a.m.brown at mmu.ac.uk (Tony Brown) Date: Tue, 8 Mar 2011 15:52:43 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: References: <8B1E41E4B39E4374A2BC3034C3717750@homet4dz4d6xu0> <4D7347B5.5050003@gmail.com> Message-ID: Another way to go would be to ask the question of what has been secured as majority practice within a given regulative or assessment regime, and which aspects of that practice are supported by research as being good. The difficulty of targeting research at finding models of good practice generated in local sites is that subsequent dissemination is so often elusive, with the given supply of teachers, and the current states of affairs in schools. Tony On 8 Mar 2011, at 14:36, Tandi Clausen-May wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > Sarah Maugham asked for 'evidence about whether ICT has a positive impact on > attainment in mathematics'. > Alexandre Borovik wrote 'I would suggest to define "success" first, and > only then discuss how it could be measured'. > > This is a suggestion that everyone, from an Early Years/Foundation teacher > to (I assume) a university teacher, would support. But that does not change > the sorry fact that the way in which attainment is usually measured in > schools is with a test - and written key stage test and GCSE questions are > not designed to assess what pupils learn using mathematics tool software. > If the assessment required pupils to use Geogebra or Autograph to do some > mathematics then they would probably be more successful if they had learnt > some mathematics using these tools, so ICT would have 'a positive impact on > attainment in mathematics'. But the assessments do not require this, so the > evidence is hard to find. > Tandi > Professor Tony Brown Institute of Education Manchester Metropolitan University 799 Wilmslow Road Didsbury Manchester M20 2RR 0161 434 6355 a.m.brown at mmu.ac.uk Webpage: http://www.esri.mmu.ac.uk/resstaff/profile.php?name=Tony&%20surname=Brown New book: Tony Brown and Olwen McNamara, Becoming a mathematics teacher: identity and identifications, Dordrecht: Springer http://springerlink.com/content/978-94-007-0553-1/#section=855457&page=1 http://www.mmu.ac.uk/emaildisclaimer From alexandre.borovik at gmail.com Wed Mar 9 08:59:15 2011 From: alexandre.borovik at gmail.com (Alexandre Borovik) Date: Wed, 09 Mar 2011 08:59:15 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: References: <8B1E41E4B39E4374A2BC3034C3717750@homet4dz4d6xu0> <4D7347B5.5050003@gmail.com> Message-ID: <4D774163.3080409@gmail.com> On 08/03/2011 14:36, Tandi Clausen-May wrote: > If the assessment required pupils to use Geogebra or Autograph to do some > mathematics then they would probably be more successful if they had learnt > some mathematics using these tools, so ICT would have 'a positive impact on > attainment in mathematics'. But the assessments do not require this, so the > evidence is hard to find. I dare to suggest that if a student needs particular software (say, Autograph) to answer a mathematical question, this means that he or she has learnt Autograph, not mathematics. Also, why not accept that if "the evidence is hard to find" then perhaps it does not exist? IMHO, the ability to do and to communicate mathematics should not depend on the medium of communication. If it is dependent than something is wrong it the way students are taught. Alexandre -- Professor Alexandre Borovik * University of Manchester Web: http://www.maths.manchester.ac.uk/~avb/ Wordpress: http://micromath.wordpress.com/ Academia: http://manchester.academia.edu/AlexandreBorovik From C.Morgan at ioe.ac.uk Wed Mar 9 09:07:18 2011 From: C.Morgan at ioe.ac.uk (Candia Morgan) Date: Wed, 9 Mar 2011 09:07:18 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <4D774163.3080409@gmail.com> References: <8B1E41E4B39E4374A2BC3034C3717750@homet4dz4d6xu0> <4D7347B5.5050003@gmail.com> <4D774163.3080409@gmail.com> Message-ID: <124417FE-BBBB-496E-B8EF-8E216D2AF229@ioe.ac.uk> Or if someone needs pencil and paper to solve a problem they have learnt using pencil and paper not mathematics? Different media allow different forms of mathematical activity and thinking. Conventions and power (including assessments) determine which of the possible forms are valued. Sent from my iPhone On 9 Mar 2011, at 09:03, "Alexandre Borovik" wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > > > On 08/03/2011 14:36, Tandi Clausen-May wrote: >> If the assessment required pupils to use Geogebra or Autograph to do some >> mathematics then they would probably be more successful if they had learnt >> some mathematics using these tools, so ICT would have 'a positive impact on >> attainment in mathematics'. But the assessments do not require this, so the >> evidence is hard to find. > > I dare to suggest that if a student needs particular software (say, > Autograph) to answer a mathematical question, this means that he or she > has learnt Autograph, not mathematics. Also, why not accept that if "the > evidence is hard to find" then perhaps it does not exist? > > IMHO, the ability to do and to communicate mathematics should not depend > on the medium of communication. If it is dependent than something is > wrong it the way students are taught. > > Alexandre > > -- > Professor Alexandre Borovik * University of Manchester > Web: http://www.maths.manchester.ac.uk/~avb/ > Wordpress: http://micromath.wordpress.com/ > Academia: http://manchester.academia.edu/AlexandreBorovik > > > This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. > > This message has been checked for viruses but the contents of an attachment > may still contain software viruses which could damage your computer system: > you are advised to perform your own checks. Email communications with the > University of Nottingham may be monitored as permitted by UK legislation. > From dylanwiliam at mac.com Wed Mar 9 09:08:03 2011 From: dylanwiliam at mac.com (dylanwiliam at mac.com) Date: Wed, 09 Mar 2011 09:08:03 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <4D774163.3080409@gmail.com> References: <8B1E41E4B39E4374A2BC3034C3717750@homet4dz4d6xu0> <4D7347B5.5050003@gmail.com> <4D774163.3080409@gmail.com> Message-ID: <1B3B180B-260C-4835-9F02-629B2FB786B0@mac.com> Of course this is the age old problem of "transfer" in psychology. What is undoubtedly true but rarely acknowledged explicitly is that as teachers we never care about our students' ability to do what we have taught them. If I teach students to add two fractions, I do not care about whether they can add those two fractions?of course they can; I have just shown them how to do it. What I care about is whether they can add a different pair of fractions. From a situated learning perspective, it seems to me that the issue is the extent to which students become attuned to the constraints and affordances present in the learning environment, and whether those constraints and affordances are present in other environments in which the student is likely to find herself. Dylan Wiliam On 9 Mar 2011, at 08:59, Alexandre Borovik wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > > > On 08/03/2011 14:36, Tandi Clausen-May wrote: >> If the assessment required pupils to use Geogebra or Autograph to do some >> mathematics then they would probably be more successful if they had learnt >> some mathematics using these tools, so ICT would have 'a positive impact on >> attainment in mathematics'. But the assessments do not require this, so the >> evidence is hard to find. > > I dare to suggest that if a student needs particular software (say, Autograph) to answer a mathematical question, this means that he or she has learnt Autograph, not mathematics. Also, why not accept that if "the evidence is hard to find" then perhaps it does not exist? > > IMHO, the ability to do and to communicate mathematics should not depend on the medium of communication. If it is dependent than something is wrong it the way students are taught. > > Alexandre > > -- > Professor Alexandre Borovik * University of Manchester > Web: http://www.maths.manchester.ac.uk/~avb/ > Wordpress: http://micromath.wordpress.com/ > Academia: http://manchester.academia.edu/AlexandreBorovik > > > This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. > > This message has been checked for viruses but the contents of an attachment > may still contain software viruses which could damage your computer system: > you are advised to perform your own checks. Email communications with the > University of Nottingham may be monitored as permitted by UK legislation. > From dkirsh at lsu.edu Wed Mar 9 09:56:48 2011 From: dkirsh at lsu.edu (David H Kirshner) Date: Wed, 9 Mar 2011 03:56:48 -0600 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <1B3B180B-260C-4835-9F02-629B2FB786B0@mac.com> References: <8B1E41E4B39E4374A2BC3034C3717750@homet4dz4d6xu0><4D7347B5.5050003@gmail.com><4D774163.3080409@gmail.com> <1B3B180B-260C-4835-9F02-629B2FB786B0@mac.com> Message-ID: <731CECC23FB8CA4E9127BD399744D1EC02F405D6@email001.lsu.edu> But Alexandre's position: > IMHO, the ability to do and to communicate mathematics should not depend on the medium of communication. If it is dependent than something is wrong it the way students are taught. goes well beyond a concern for transfer. Alexandre's idealism denies the material constitution of knowledge, arguing instead for an utterly abstract and a-contextual form of knowledge. I might subscribe to that vision as well, except for the fact that my own construal of mathematics is regularly revealed as limited and context bound whenever the framing is shifted even slightly. An excellent testing ground is Stephen Brown and Marion Walter's (1990) The Art of Problem Posing. Their "what if not" method just shatters my illusions of decontextual knowledge for even simple mathematics, the so-called abstract representations revealing themselves, yet again, as nothing more than another concrete symbol system. The tradition of critique of idealism is strongly represented in the pragmatist philosophy of James, Dewey, and Mead, especially as incorporating Charles Peirce's tripartite semiotic system in which the sign involves an interplay of the representamen (the physical signifier), the object (that which is signified), and the interpretant (the effect produced by the sign). David Kirshner -----Original Message----- From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of dylanwiliam at mac.com Sent: Wednesday, March 09, 2011 3:08 AM To: Mathematics Education discussion forum Subject: [Maths-Education] Re: ICT in mathematics ************************************************************************ *********************************** This message has been generated through the Mathematics Education email discussion list. Hitting the REPLY key sends a message to all list members. ************************************************************************ *********************************** Of course this is the age old problem of "transfer" in psychology. What is undoubtedly true but rarely acknowledged explicitly is that as teachers we never care about our students' ability to do what we have taught them. If I teach students to add two fractions, I do not care about whether they can add those two fractions-of course they can; I have just shown them how to do it. What I care about is whether they can add a different pair of fractions. From a situated learning perspective, it seems to me that the issue is the extent to which students become attuned to the constraints and affordances present in the learning environment, and whether those constraints and affordances are present in other environments in which the student is likely to find herself. Dylan Wiliam On 9 Mar 2011, at 08:59, Alexandre Borovik wrote: > ************************************************************************ *********************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > ************************************************************************ *********************************** > > > On 08/03/2011 14:36, Tandi Clausen-May wrote: >> If the assessment required pupils to use Geogebra or Autograph to do some >> mathematics then they would probably be more successful if they had learnt >> some mathematics using these tools, so ICT would have 'a positive impact on >> attainment in mathematics'. But the assessments do not require this, so the >> evidence is hard to find. > > I dare to suggest that if a student needs particular software (say, Autograph) to answer a mathematical question, this means that he or she has learnt Autograph, not mathematics. Also, why not accept that if "the evidence is hard to find" then perhaps it does not exist? > > IMHO, the ability to do and to communicate mathematics should not depend on the medium of communication. If it is dependent than something is wrong it the way students are taught. > > Alexandre > > -- > Professor Alexandre Borovik * University of Manchester > Web: http://www.maths.manchester.ac.uk/~avb/ > Wordpress: http://micromath.wordpress.com/ > Academia: http://manchester.academia.edu/AlexandreBorovik > > > This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. > > This message has been checked for viruses but the contents of an attachment > may still contain software viruses which could damage your computer system: > you are advised to perform your own checks. Email communications with the > University of Nottingham may be monitored as permitted by UK legislation. > From alexandre.borovik at gmail.com Wed Mar 9 10:00:31 2011 From: alexandre.borovik at gmail.com (Alexandre Borovik) Date: Wed, 09 Mar 2011 10:00:31 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <124417FE-BBBB-496E-B8EF-8E216D2AF229@ioe.ac.uk> References: <8B1E41E4B39E4374A2BC3034C3717750@homet4dz4d6xu0> <4D7347B5.5050003@gmail.com> <4D774163.3080409@gmail.com> <124417FE-BBBB-496E-B8EF-8E216D2AF229@ioe.ac.uk> Message-ID: <4D774FBF.1080705@gmail.com> On 09/03/2011 09:07, Candia Morgan wrote: > Or if someone needs pencil and paper to solve a problem > they have learnt using pencil and paper not mathematics? > Different media allow different forms of mathematical > activity and thinking. Conventions and power > (including assessments) determine which of the > possible forms are valued. There is a natural hierarchy of human modes of communication. In mathematics, the most important is the most ancient, voice. Chalk on a blackboard, penicil on paper are just assistive tools for human speech. It is worth noting that, despite all the technological progress, teachers are still using speech in teaching, but (at least university teachers in this country) do not teach their students to talk about mathematics. It is perfectly possible to get a good university degree without ever opening mouth. This is one of the main flaws obstructing the cycle of reproduction of mathematics in this country. (The situation is different on teh continent, where many countries still stick to the tradition of public oral examinations). Alexandre -- Professor Alexandre Borovik * University of Manchester Web: http://www.maths.manchester.ac.uk/~avb/ Wordpress: http://micromath.wordpress.com/ Academia: http://manchester.academia.edu/AlexandreBorovik From M.S.Boylan at shu.ac.uk Wed Mar 9 10:01:28 2011 From: M.S.Boylan at shu.ac.uk (Boylan, Mark S) Date: Wed, 9 Mar 2011 10:01:28 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <124417FE-BBBB-496E-B8EF-8E216D2AF229@ioe.ac.uk> References: <8B1E41E4B39E4374A2BC3034C3717750@homet4dz4d6xu0> <4D7347B5.5050003@gmail.com> <4D774163.3080409@gmail.com> <124417FE-BBBB-496E-B8EF-8E216D2AF229@ioe.ac.uk> Message-ID: <2577DA3CF7A58A4DB5F12B771753999AADF7FB15@HOLLYHOCK.hallam.shu.ac.uk> I am reminded of a situation that arose when I was working as part of a team on a project. Someone in the team had been assigned to find mean averages from a frequency table and use a spreadsheet to produce charts from this. I noticed that the data presented on the charts were given to an inappropriate degree of accuracy so I checked the spreadsheet seeking to make slight modification to address this. I found that all of the data in the spreadsheet was disconnected. None of the cells were linked. No formula functions had been used. However the averages were 'correct' - although presented to more decimal places than could be justified by the initial data. When I (gently) discussed this with the team member responsible for the charts it emerged that they had calculated the averages from the frequency tables with pencil and paper and calculator. They had then manually entered the data into the spreadsheet. This had taken them many hours to do - a process that could have been done much more quickly if they had previously had the opportunity to learn about the mathematical power of the spreadsheet . No doubt they had achieved the required grade C in GCSE (UK school exam taken at 16) and presumably answered the question on averages and frequency tables correctly. Were they being let down by the curriculum and assessment regime in relation to mathematics and ICT - I would say so. I am sure that colleagues have examples of their own that illustrate the multiple ways that the ability to do and communicate mathematics cannot be separated from the tools used and the medium of communication. Mark Boylan -----Original Message----- From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Candia Morgan Sent: 09 March 2011 09:07 To: Mathematics Education discussion forum Cc: maths-education at lists.nottingham.ac.uk Subject: [Maths-Education] Re: ICT in mathematics *********************************************************************************************************** This message has been generated through the Mathematics Education email discussion list. Hitting the REPLY key sends a message to all list members. *********************************************************************************************************** Or if someone needs pencil and paper to solve a problem they have learnt using pencil and paper not mathematics? Different media allow different forms of mathematical activity and thinking. Conventions and power (including assessments) determine which of the possible forms are valued. Sent from my iPhone On 9 Mar 2011, at 09:03, "Alexandre Borovik" wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > > > On 08/03/2011 14:36, Tandi Clausen-May wrote: >> If the assessment required pupils to use Geogebra or Autograph to do some >> mathematics then they would probably be more successful if they had learnt >> some mathematics using these tools, so ICT would have 'a positive impact on >> attainment in mathematics'. But the assessments do not require this, so the >> evidence is hard to find. > > I dare to suggest that if a student needs particular software (say, > Autograph) to answer a mathematical question, this means that he or she > has learnt Autograph, not mathematics. Also, why not accept that if "the > evidence is hard to find" then perhaps it does not exist? > > IMHO, the ability to do and to communicate mathematics should not depend > on the medium of communication. If it is dependent than something is > wrong it the way students are taught. > > Alexandre > > -- > Professor Alexandre Borovik * University of Manchester > Web: http://www.maths.manchester.ac.uk/~avb/ > Wordpress: http://micromath.wordpress.com/ > Academia: http://manchester.academia.edu/AlexandreBorovik > > > This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. > > This message has been checked for viruses but the contents of an attachment > may still contain software viruses which could damage your computer system: > you are advised to perform your own checks. Email communications with the > University of Nottingham may be monitored as permitted by UK legislation. > From dietmar.kuchemann at kcl.ac.uk Wed Mar 9 10:13:41 2011 From: dietmar.kuchemann at kcl.ac.uk (Kuchemann, Dietmar) Date: Wed, 9 Mar 2011 10:13:41 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <4D774FBF.1080705@gmail.com> Message-ID: Some of the comments in this thread have been thoughtful and interesting, but some are dogmatic born of ignorance. Is there a way of filtering out the latter? Dietmar On 09/03/2011 10:00, "Alexandre Borovik" wrote: *********************************************************************************************************** This message has been generated through the Mathematics Education email discussion list. Hitting the REPLY key sends a message to all list members. *********************************************************************************************************** On 09/03/2011 09:07, Candia Morgan wrote: > Or if someone needs pencil and paper to solve a problem > they have learnt using pencil and paper not mathematics? > Different media allow different forms of mathematical > activity and thinking. Conventions and power > (including assessments) determine which of the > possible forms are valued. There is a natural hierarchy of human modes of communication. In mathematics, the most important is the most ancient, voice. Chalk on a blackboard, penicil on paper are just assistive tools for human speech. It is worth noting that, despite all the technological progress, teachers are still using speech in teaching, but (at least university teachers in this country) do not teach their students to talk about mathematics. It is perfectly possible to get a good university degree without ever opening mouth. This is one of the main flaws obstructing the cycle of reproduction of mathematics in this country. (The situation is different on teh continent, where many countries still stick to the tradition of public oral examinations). Alexandre -- Professor Alexandre Borovik * University of Manchester Web: http://www.maths.manchester.ac.uk/~avb/ Wordpress: http://micromath.wordpress.com/ Academia: http://manchester.academia.edu/AlexandreBorovik This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. This message has been checked for viruses but the contents of an attachment may still contain software viruses which could damage your computer system: you are advised to perform your own checks. Email communications with the University of Nottingham may be monitored as permitted by UK legislation. -- From johnbibbyjohnbibby at gmail.com Wed Mar 9 10:21:43 2011 From: johnbibbyjohnbibby at gmail.com (John Bibby) Date: Wed, 9 Mar 2011 10:21:43 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: References: <4D774FBF.1080705@gmail.com> Message-ID: I'm not sure I agree with Alexandre about examinations, but I do agree about the importance of "Mathematical Oracy" i.e. speaking and listening to conversations about mathematics. This is part of Mathematicking. The spoken discourse is different from the written discourse (and there are different forms of both). Tied up with this is the key pedagogic point that learners learn more from each other than they do from the 'teacher' - if they are allowed to chat about their mathematical enquiry. A good classroom is a noisy classroom! (Sorry Dietmar if this is a "dogmatic born of ignorance". You ask foir a filter. You have one! - it is called the delete key.) JOHN BIBBY On 9 March 2011 10:13, Kuchemann, Dietmar wrote: > > *********************************************************************************************************** > This message has been generated through the Mathematics Education email > discussion list. > Hitting the REPLY key sends a message to all list members. > > *********************************************************************************************************** > Some of the comments in this thread have been thoughtful and interesting, > but some are dogmatic born of ignorance. Is there a way of filtering out the > latter? > Dietmar > > > On 09/03/2011 10:00, "Alexandre Borovik" > wrote: > > > *********************************************************************************************************** > This message has been generated through the Mathematics Education email > discussion list. > Hitting the REPLY key sends a message to all list members. > > *********************************************************************************************************** > > On 09/03/2011 09:07, Candia Morgan wrote: > > Or if someone needs pencil and paper to solve a problem > > they have learnt using pencil and paper not mathematics? > > Different media allow different forms of mathematical > > activity and thinking. Conventions and power > > (including assessments) determine which of the > > possible forms are valued. > > There is a natural hierarchy of human modes of communication. In > mathematics, the most important is the most ancient, voice. Chalk on a > blackboard, penicil on paper are just assistive tools for human speech. > > It is worth noting that, despite all the technological progress, > teachers are still using speech in teaching, but (at least university > teachers in this country) do not teach their students to talk about > mathematics. It is perfectly possible to get a good university degree > without ever opening mouth. This is one of the main flaws obstructing > the cycle of reproduction of mathematics in this country. (The situation > is different on teh continent, where many countries still stick to the > tradition of public oral examinations). > > Alexandre > -- > Professor Alexandre Borovik * University of Manchester > Web: http://www.maths.manchester.ac.uk/~avb/ > Wordpress: http://micromath.wordpress.com/ > Academia: http://manchester.academia.edu/AlexandreBorovik > > > This message and any attachment are intended solely for the addressee and > may contain confidential information. If you have received this message in > error, please send it back to me, and immediately delete it. Please do not > use, copy or disclose the information contained in this message or in any > attachment. Any views or opinions expressed by the author of this email do > not necessarily reflect the views of the University of Nottingham. > > This message has been checked for viruses but the contents of an attachment > may still contain software viruses which could damage your computer system: > you are advised to perform your own checks. Email communications with the > University of Nottingham may be monitored as permitted by UK legislation. > > > > > -- > > From howard.tanner at smu.ac.uk Wed Mar 9 11:42:28 2011 From: howard.tanner at smu.ac.uk (Tanner, Howard) Date: Wed, 9 Mar 2011 11:42:28 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: References: <4D774FBF.1080705@gmail.com> Message-ID: <240C36E18CADBE46962CC52E8839D67F0176A823@PLEIADES.sid.sihe.ac.uk> I agree with many of the comments in this interesting thread. I would love to have a curriculum and assessment regime in mathematics that demonstrated how problems could be mathematised using the widest possible range of tools and an assessment regime that demanded the same. Sadly, cost, practicality and reliability issues have often prevented us from achieving this. Using GCSE results to create league tables to evaluate the performance of schools has led to an emphasis on systems with high reliability at the expense of validity, for example leading to the end of coursework assessments that afforded the use of non-traditional approaches. However, the high cost of examinations may be leading us to a point at which the paper and pencil test might be replaced by on-line assessment. There may be a choice in the near future between on line assessments that are simple digital multiple choice tests and wider reaching assessments that require the use of digital mathematical tools such as Geogebra or autograph. I hope that there is room for the latter. Howard Tanner -----Original Message----- From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of John Bibby Sent: 09 March 2011 10:22 To: Mathematics Education discussion forum Subject: [Maths-Education] Re: ICT in mathematics *********************************************************************************************************** This message has been generated through the Mathematics Education email discussion list. Hitting the REPLY key sends a message to all list members. *********************************************************************************************************** I'm not sure I agree with Alexandre about examinations, but I do agree about the importance of "Mathematical Oracy" i.e. speaking and listening to conversations about mathematics. This is part of Mathematicking. The spoken discourse is different from the written discourse (and there are different forms of both). Tied up with this is the key pedagogic point that learners learn more from each other than they do from the 'teacher' - if they are allowed to chat about their mathematical enquiry. A good classroom is a noisy classroom! (Sorry Dietmar if this is a "dogmatic born of ignorance". You ask foir a filter. You have one! - it is called the delete key.) JOHN BIBBY On 9 March 2011 10:13, Kuchemann, Dietmar wrote: > > *********************************************************************************************************** > This message has been generated through the Mathematics Education email > discussion list. > Hitting the REPLY key sends a message to all list members. > > *********************************************************************************************************** > Some of the comments in this thread have been thoughtful and interesting, > but some are dogmatic born of ignorance. Is there a way of filtering out the > latter? > Dietmar > > > On 09/03/2011 10:00, "Alexandre Borovik" > wrote: > > > *********************************************************************************************************** > This message has been generated through the Mathematics Education email > discussion list. > Hitting the REPLY key sends a message to all list members. > > *********************************************************************************************************** > > On 09/03/2011 09:07, Candia Morgan wrote: > > Or if someone needs pencil and paper to solve a problem > > they have learnt using pencil and paper not mathematics? > > Different media allow different forms of mathematical > > activity and thinking. Conventions and power > > (including assessments) determine which of the > > possible forms are valued. > > There is a natural hierarchy of human modes of communication. In > mathematics, the most important is the most ancient, voice. Chalk on a > blackboard, penicil on paper are just assistive tools for human speech. > > It is worth noting that, despite all the technological progress, > teachers are still using speech in teaching, but (at least university > teachers in this country) do not teach their students to talk about > mathematics. It is perfectly possible to get a good university degree > without ever opening mouth. This is one of the main flaws obstructing > the cycle of reproduction of mathematics in this country. (The situation > is different on teh continent, where many countries still stick to the > tradition of public oral examinations). > > Alexandre > -- > Professor Alexandre Borovik * University of Manchester > Web: http://www.maths.manchester.ac.uk/~avb/ > Wordpress: http://micromath.wordpress.com/ > Academia: http://manchester.academia.edu/AlexandreBorovik > > > This message and any attachment are intended solely for the addressee and > may contain confidential information. If you have received this message in > error, please send it back to me, and immediately delete it. Please do not > use, copy or disclose the information contained in this message or in any > attachment. Any views or opinions expressed by the author of this email do > not necessarily reflect the views of the University of Nottingham. > > This message has been checked for viruses but the contents of an attachment > may still contain software viruses which could damage your computer system: > you are advised to perform your own checks. Email communications with the > University of Nottingham may be monitored as permitted by UK legislation. > > > > > -- > > From whiteley at mathstat.yorku.ca Wed Mar 9 13:38:05 2011 From: whiteley at mathstat.yorku.ca (Walter Whiteley) Date: Wed, 9 Mar 2011 08:38:05 -0500 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <4D774FBF.1080705@gmail.com> References: <8B1E41E4B39E4374A2BC3034C3717750@homet4dz4d6xu0> <4D7347B5.5050003@gmail.com> <4D774163.3080409@gmail.com> <124417FE-BBBB-496E-B8EF-8E216D2AF229@ioe.ac.uk> <4D774FBF.1080705@gmail.com> Message-ID: <7C55AA8D-DD68-4661-AD32-FBD43F1C089E@mathstat.yorku.ca> I have been following the thread as it evolves. I hope the following is still relevant. My point of view starts as a practicing mathematician (applied geometer) but includes some research and writing on visual and kinesthetic reasoning in mathematics and mathematics education, including early childhood. ICT is an integral part of the modern practice of mathematics, both by current mathematicians and by those who use mathematics in other disciplines. I use some versions of ICT very regularly in my mathematical practices. In particular, it is central to my collaborations with people outside mathematics (structural engineers, mechanical engineers, biochemists, biophysicists, material scientists, computational geometers, ... ) To not use the powerful visualization, data processing, and other affordances is to leave students unprepared for future use of mathematics, or even to engage with current uses of mathematics. Let me give a couple of examples: 1. As I also think of statistics as one of the mathematical sciences, I do not know anyone who argues statistics should be learned, and applied, without major support of technology. (These days that is R at the higher levels, often Excel at the lower levels.) Major advances in data visualization are also relevant, and students need to learn to extract information from, modify and critique, and sometimes create appropriate visualizations of statistical situations to reason and communicate. I don't know anyone who regrets the loss of statistical tables! I don't know who would work with these visualizations without ICT. 2. In geometry (and some other areas) it is possible, even desirable that key communication and reasoning be done visually (either externally supported or internally). Key reasoning is embedded in a sequence of diagrams (with transformations). In line with the theories of Sfaard - thinking is an internalization of the visual communication among peers and with experts. Now - dynamic software such as GSP (what is licensed for all students here) permits some valuable changes in the external visual forms, and in the resulting reasoning. It also supports development of constrained mental visualization, including transformations. Initially, I found the software made visible to my students what I was already 'seeing' in my mind. Now what is in my mind has also been modified. I regularly encounter students who are handicapped in their mathematical practice by their inability to extract information from and to communicate with themselves and others via visual forms (sometimes 3-D). For example, I have encountered a number of students/teachers who 'hit a wall' in their first course of multi- variable calculus and their inability to 'see' the shapes being described. This grew from a number of prior years (senior secondary school) where learning to visualize and reason spatially was considered unimportant. ICT can play a valuable role in supporting spatial reasoning, and words (and gestures) often refer back to prior visual abilities and experiences. Of course, physical manipulatives can also play an important role in spatial communication, and in reasoning. (I have a cupboard of them for my undergraduate and in-service geometry classes. Students use them, and GSP, for in class work, for assignments, for presentations.) These are the ways that young children have learned spatial reasoning (starting in their 3-D world). That pencil and paper has reduced us to 2-D for too much of the elementary curriculum is an artifact of old technology we can overcome. ICT is part of that. I am generally concerned about references to a 'hierarchy' of tools and of communication. I worry about descriptions which place visual reasoning and communication 'down' the hierarchy (as in van Hiele hierarchy). There is now a recognition that these visual forms live (and thrive) at all levels of the reasoning hierarchy, and need the same kinds of teaching / learning support as verbal reasoning, and symbolic reasoning (which has its own key visual components - think visual patterns in matrices). My claims and my concerns are informed by observing that my work (and my teaching) continues to become more centered on visual reasoning, including ICT supports, as my work evolves. This is true for collaborating with other researchers, for supporting research students, for working with in-service teachers, for teaching math undergrads, and for preparing pre-service teachers. Walter Whiteley Mathematics and Statistics, York University Graduate Programs in Mathematics, in Education, in Computer Science, and in Interdisciplinary Studies. http://www.math.yorku.ca/~whiteley/ On 9-Mar-11, at 5:00 AM, Alexandre Borovik wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education > email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > > On 09/03/2011 09:07, Candia Morgan wrote: > > Or if someone needs pencil and paper to solve a problem > > they have learnt using pencil and paper not mathematics? > > Different media allow different forms of mathematical > > activity and thinking. Conventions and power > > (including assessments) determine which of the > > possible forms are valued. > > There is a natural hierarchy of human modes of communication. In > mathematics, the most important is the most ancient, voice. Chalk > on a blackboard, penicil on paper are just assistive tools for human > speech. > > It is worth noting that, despite all the technological progress, > teachers are still using speech in teaching, but (at least > university teachers in this country) do not teach their students to > talk about mathematics. It is perfectly possible to get a good > university degree without ever opening mouth. This is one of the > main flaws obstructing the cycle of reproduction of mathematics in > this country. (The situation is different on teh continent, where > many countries still stick to the tradition of public oral > examinations). > > Alexandre > -- > Professor Alexandre Borovik * University of Manchester > Web: http://www.maths.manchester.ac.uk/~avb/ > Wordpress: http://micromath.wordpress.com/ > Academia: http://manchester.academia.edu/AlexandreBorovik > > > This message and any attachment are intended solely for the > addressee and may contain confidential information. If you have > received this message in error, please send it back to me, and > immediately delete it. Please do not use, copy or disclose the > information contained in this message or in any attachment. Any > views or opinions expressed by the author of this email do not > necessarily reflect the views of the University of Nottingham. > > This message has been checked for viruses but the contents of an > attachment > may still contain software viruses which could damage your computer > system: > you are advised to perform your own checks. Email communications > with the > University of Nottingham may be monitored as permitted by UK > legislation. From Hugh.Burkhardt at nottingham.ac.uk Wed Mar 9 15:53:24 2011 From: Hugh.Burkhardt at nottingham.ac.uk (Hugh Burkhardt) Date: Wed, 9 Mar 2011 15:53:24 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <240C36E18CADBE46962CC52E8839D67F0176A823@PLEIADES.sid.sihe.ac.uk> References: <4D774FBF.1080705@gmail.com> <240C36E18CADBE46962CC52E8839D67F0176A823@PLEIADES.sid.sihe.ac.uk> Message-ID: <7C2686A4-F686-4298-91CF-F4955928D3C2@nottingham.ac.uk> Interesting stuff. People may like to look at Section 4 (starting p 12) of http://www.mathshell.org/papers/pdf/ISDDE_PARCC_Feb11.pdf which looks at computer-based assessment in mathematics (currently proposed by the two US multi-state assessment consortia that are seeking to implement the new Common Core State Standards) It concludes that, while computers are indispensable for some aspects of assessment, they do not offer: a natural working medium for students working on non-routine mathematics problems established methods of scoring complex non-text responses (except by scanning and human scoring) The section concludes with the statement: "To summarize: given the basic principles that assessment should image desired instruction, because of WYTIWG[1], and that desired instruction has to be attainable in ordinary circumstances, a corollary is that computer use in assessment should image desired computer use in instruction." The paper also discusses why, given all the wonderful maths software of so many kinds developed over the last 30+ years, the school maths classroom is the only place where computers do not play a major part in doing maths. The complex set of reasons includes levels of provision that vary with a time scale that is much shorter than the decade or so needed to develop a "computer-assisted mathematics curriculum"** with examinations to match. We need a much more flexible model of change to close this credibility gap in school maths. Alternative modules might provide a way forward. Hugh ** INterestingly, a comprehensive middle school curriculum with a similar title was developed at the University of Minnesota in the 1960s by David C Johnson (later at Kings), Larry Hatfield and others. The students programmed maths in BASIC over a line to the university mainframe. Tom Kieran showed that this approach provided a "semi-concrete" bridge that got twice as many students through to fluency with normal algebra as the standard comparison curriculum. [1] ?What You Test Is What You Get? Burkhardt, H. 1987, The Dynamics of Curriculum Change in Developments in School Mathematics Worldwide, Wirszup, I & Streit, R. (Eds.) Chicago: University of Chicago School Mathematics Project. On 9 Mar 2011, at 11:42, Tanner, Howard wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > I agree with many of the comments in this interesting thread. I would love to have a curriculum and assessment regime in mathematics that demonstrated how problems could be mathematised using the widest possible range of tools and an assessment regime that demanded the same. > > Sadly, cost, practicality and reliability issues have often prevented us from achieving this. Using GCSE results to create league tables to evaluate the performance of schools has led to an emphasis on systems with high reliability at the expense of validity, for example leading to the end of coursework assessments that afforded the use of non-traditional approaches. > > However, the high cost of examinations may be leading us to a point at which the paper and pencil test might be replaced by on-line assessment. There may be a choice in the near future between on line assessments that are simple digital multiple choice tests and wider reaching assessments that require the use of digital mathematical tools such as Geogebra or autograph. I hope that there is room for the latter. > > Howard Tanner > > -----Original Message----- > From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of John Bibby > Sent: 09 March 2011 10:22 > To: Mathematics Education discussion forum > Subject: [Maths-Education] Re: ICT in mathematics > > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > I'm not sure I agree with Alexandre about examinations, but I do agree about > the importance of "Mathematical Oracy" i.e. speaking and listening to > conversations about mathematics. This is part of Mathematicking. > > The spoken discourse is different from the written discourse (and there are > different forms of both). > > Tied up with this is the key pedagogic point that learners learn more from > each other than they do from the 'teacher' - if they are allowed to chat > about their mathematical enquiry. > > A good classroom is a noisy classroom! > > (Sorry Dietmar if this is a "dogmatic born of ignorance". You ask foir a > filter. You have one! - it is called the delete key.) > > JOHN BIBBY > > On 9 March 2011 10:13, Kuchemann, Dietmar wrote: > >> >> *********************************************************************************************************** >> This message has been generated through the Mathematics Education email >> discussion list. >> Hitting the REPLY key sends a message to all list members. >> >> *********************************************************************************************************** >> Some of the comments in this thread have been thoughtful and interesting, >> but some are dogmatic born of ignorance. Is there a way of filtering out the >> latter? >> Dietmar >> >> >> On 09/03/2011 10:00, "Alexandre Borovik" >> wrote: >> >> >> *********************************************************************************************************** >> This message has been generated through the Mathematics Education email >> discussion list. >> Hitting the REPLY key sends a message to all list members. >> >> *********************************************************************************************************** >> >> On 09/03/2011 09:07, Candia Morgan wrote: >>> Or if someone needs pencil and paper to solve a problem >>> they have learnt using pencil and paper not mathematics? >>> Different media allow different forms of mathematical >>> activity and thinking. Conventions and power >>> (including assessments) determine which of the >>> possible forms are valued. >> >> There is a natural hierarchy of human modes of communication. In >> mathematics, the most important is the most ancient, voice. Chalk on a >> blackboard, penicil on paper are just assistive tools for human speech. >> >> It is worth noting that, despite all the technological progress, >> teachers are still using speech in teaching, but (at least university >> teachers in this country) do not teach their students to talk about >> mathematics. It is perfectly possible to get a good university degree >> without ever opening mouth. This is one of the main flaws obstructing >> the cycle of reproduction of mathematics in this country. (The situation >> is different on teh continent, where many countries still stick to the >> tradition of public oral examinations). >> >> Alexandre >> -- >> Professor Alexandre Borovik * University of Manchester >> Web: http://www.maths.manchester.ac.uk/~avb/ >> Wordpress: http://micromath.wordpress.com/ >> Academia: http://manchester.academia.edu/AlexandreBorovik >> >> >> This message and any attachment are intended solely for the addressee and >> may contain confidential information. If you have received this message in >> error, please send it back to me, and immediately delete it. Please do not >> use, copy or disclose the information contained in this message or in any >> attachment. Any views or opinions expressed by the author of this email do >> not necessarily reflect the views of the University of Nottingham. >> >> This message has been checked for viruses but the contents of an attachment >> may still contain software viruses which could damage your computer system: >> you are advised to perform your own checks. Email communications with the >> University of Nottingham may be monitored as permitted by UK legislation. >> >> >> >> >> -- >> >> > From M.PETERS at aston.ac.uk Thu Mar 10 09:05:08 2011 From: M.PETERS at aston.ac.uk (Peters, Mike) Date: Thu, 10 Mar 2011 09:05:08 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <7C55AA8D-DD68-4661-AD32-FBD43F1C089E@mathstat.yorku.ca> References: <8B1E41E4B39E4374A2BC3034C3717750@homet4dz4d6xu0> <4D7347B5.5050003@gmail.com> <4D774163.3080409@gmail.com> <124417FE-BBBB-496E-B8EF-8E216D2AF229@ioe.ac.uk> <4D774FBF.1080705@gmail.com> <7C55AA8D-DD68-4661-AD32-FBD43F1C089E@mathstat.yorku.ca> Message-ID: My primary role is teaching mathematics to power engineers. These people work in a safety critical industry and they need to have the ability to interpret what the mathematics is telling them. Although some consider programs such as Excel only useful for Statistics, I use it a lot to give the learners a 'picture' of what the mathematics is telling them. Learners of mathematics also need to have the ability to decide if their resolutions/solutions are sensible. Too often I see learners who are very good at the algorithmic approach but who come unstuck when you ask them (a) to interpret their answer and, (b) is their answer sensible. In my opinion if technology, whether it be an abacus or a sophisticated computer program assists learners in their understanding and interpretation of mathematics, it has got to be a good thing. The only caveat I would add is that the educational need must be the driver not the fact that a computer package exists and therefore must be used. A typical example of this is, what was known as SPSS. It seems to me that some learners can spend their statistics lessons learning how to use the program and lecturers, when asked why they use it, feel they must since that is the accepted wisdom. My point is that not so long ago pencil and paper were the only available options for abstracting a problem. With the right 'tools' (eg. CAS) we have the opportunity to assist learners in some instances of 'visualising' the problem and also to explore 'what if..' type scenarios. Playing devil's advocate, I think it is time that the mathematics curriculum, especially in my sector engineering, was overhauled and the use of ICT and other educational resources became embedded and not viewed as bolt ons. Which has implications for the way we assess mathematical skills/knowledge, but that is another heated debate. Mike Dr. Michael Peters Learning Development Advisor (Mathematics) School of Engineering and Applied Science Aston University Aston Triangle Birmingham B4 7ET Tel: 0121 204 3202 -----Original Message----- From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Walter Whiteley Sent: 09 March 2011 13:38 To: Mathematics Education discussion forum Subject: [Maths-Education] Re: ICT in mathematics *********************************************************************************************************** This message has been generated through the Mathematics Education email discussion list. Hitting the REPLY key sends a message to all list members. *********************************************************************************************************** I have been following the thread as it evolves. I hope the following is still relevant. My point of view starts as a practicing mathematician (applied geometer) but includes some research and writing on visual and kinesthetic reasoning in mathematics and mathematics education, including early childhood. ICT is an integral part of the modern practice of mathematics, both by current mathematicians and by those who use mathematics in other disciplines. I use some versions of ICT very regularly in my mathematical practices. In particular, it is central to my collaborations with people outside mathematics (structural engineers, mechanical engineers, biochemists, biophysicists, material scientists, computational geometers, ... ) To not use the powerful visualization, data processing, and other affordances is to leave students unprepared for future use of mathematics, or even to engage with current uses of mathematics. Let me give a couple of examples: 1. As I also think of statistics as one of the mathematical sciences, I do not know anyone who argues statistics should be learned, and applied, without major support of technology. (These days that is R at the higher levels, often Excel at the lower levels.) Major advances in data visualization are also relevant, and students need to learn to extract information from, modify and critique, and sometimes create appropriate visualizations of statistical situations to reason and communicate. I don't know anyone who regrets the loss of statistical tables! I don't know who would work with these visualizations without ICT. 2. In geometry (and some other areas) it is possible, even desirable that key communication and reasoning be done visually (either externally supported or internally). Key reasoning is embedded in a sequence of diagrams (with transformations). In line with the theories of Sfaard - thinking is an internalization of the visual communication among peers and with experts. Now - dynamic software such as GSP (what is licensed for all students here) permits some valuable changes in the external visual forms, and in the resulting reasoning. It also supports development of constrained mental visualization, including transformations. Initially, I found the software made visible to my students what I was already 'seeing' in my mind. Now what is in my mind has also been modified. I regularly encounter students who are handicapped in their mathematical practice by their inability to extract information from and to communicate with themselves and others via visual forms (sometimes 3-D). For example, I have encountered a number of students/teachers who 'hit a wall' in their first course of multi- variable calculus and their inability to 'see' the shapes being described. This grew from a number of prior years (senior secondary school) where learning to visualize and reason spatially was considered unimportant. ICT can play a valuable role in supporting spatial reasoning, and words (and gestures) often refer back to prior visual abilities and experiences. Of course, physical manipulatives can also play an important role in spatial communication, and in reasoning. (I have a cupboard of them for my undergraduate and in-service geometry classes. Students use them, and GSP, for in class work, for assignments, for presentations.) These are the ways that young children have learned spatial reasoning (starting in their 3-D world). That pencil and paper has reduced us to 2-D for too much of the elementary curriculum is an artifact of old technology we can overcome. ICT is part of that. I am generally concerned about references to a 'hierarchy' of tools and of communication. I worry about descriptions which place visual reasoning and communication 'down' the hierarchy (as in van Hiele hierarchy). There is now a recognition that these visual forms live (and thrive) at all levels of the reasoning hierarchy, and need the same kinds of teaching / learning support as verbal reasoning, and symbolic reasoning (which has its own key visual components - think visual patterns in matrices). My claims and my concerns are informed by observing that my work (and my teaching) continues to become more centered on visual reasoning, including ICT supports, as my work evolves. This is true for collaborating with other researchers, for supporting research students, for working with in-service teachers, for teaching math undergrads, and for preparing pre-service teachers. Walter Whiteley Mathematics and Statistics, York University Graduate Programs in Mathematics, in Education, in Computer Science, and in Interdisciplinary Studies. http://www.math.yorku.ca/~whiteley/ On 9-Mar-11, at 5:00 AM, Alexandre Borovik wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education > email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > > On 09/03/2011 09:07, Candia Morgan wrote: > > Or if someone needs pencil and paper to solve a problem > > they have learnt using pencil and paper not mathematics? > > Different media allow different forms of mathematical > > activity and thinking. Conventions and power > > (including assessments) determine which of the > > possible forms are valued. > > There is a natural hierarchy of human modes of communication. In > mathematics, the most important is the most ancient, voice. Chalk > on a blackboard, penicil on paper are just assistive tools for human > speech. > > It is worth noting that, despite all the technological progress, > teachers are still using speech in teaching, but (at least > university teachers in this country) do not teach their students to > talk about mathematics. It is perfectly possible to get a good > university degree without ever opening mouth. This is one of the > main flaws obstructing the cycle of reproduction of mathematics in > this country. (The situation is different on teh continent, where > many countries still stick to the tradition of public oral > examinations). > > Alexandre > -- > Professor Alexandre Borovik * University of Manchester > Web: http://www.maths.manchester.ac.uk/~avb/ > Wordpress: http://micromath.wordpress.com/ > Academia: http://manchester.academia.edu/AlexandreBorovik > > > This message and any attachment are intended solely for the > addressee and may contain confidential information. If you have > received this message in error, please send it back to me, and > immediately delete it. Please do not use, copy or disclose the > information contained in this message or in any attachment. Any > views or opinions expressed by the author of this email do not > necessarily reflect the views of the University of Nottingham. > > This message has been checked for viruses but the contents of an > attachment > may still contain software viruses which could damage your computer > system: > you are advised to perform your own checks. Email communications > with the > University of Nottingham may be monitored as permitted by UK > legislation. From alan at rogerson.pol.pl Thu Mar 10 11:51:01 2011 From: alan at rogerson.pol.pl (Alan Rogerson) Date: Thu, 10 Mar 2011 12:51:01 +0100 Subject: [Maths-Education] ICT in Mathematics In-Reply-To: References: Message-ID: <4D78BB25.9080605@rogerson.pol.pl> I came across this horror story, or cautionary tale, about the dangers lurking in for-profit "educational" organisations using, or should that be abusing, on line tuition, which may interest list members. It harks back to some previous comments (some extracts below) contrasting "vested interests" with "independent evaluation" of ICT and specifically on-line tuition. See http://www.huffingtonpost.com/2011/03/09/ashford-university-for-profit-college_n_833735.html As the article notes, this is an increasing and obviously profitable trend in the USA. As far as technology and computers in education are concerned, in general we should therefore never forget the GIGO principle. On the same theme, this blog culled from another List is also relevant: "I have attempted in this blog to start to distinguish different aspects of public engagement, it is so often misused and industry doesn't really understand the term at all .http://www.matterforall.org/blog/ Hilary Sutcliffe, Director, MATTER, Email: hilary at matterforall.org Best wishes, Alan PS If you have found on line USA newspapers very pallid , you might like to try the HuffingtonPost which is nothing if not different, and stimulating! > Message: 5 > Date: Fri, 04 Mar 2011 15:33:01 +0100 > From: Alan Rogerson > To: Mathematics Education discussion forum > > Subject: [Maths-Education] Re: ICT in mathematics > Message-ID:<4D70F81D.1090100 at rogerson.pol.pl> > Content-Type: text/plain; charset=ISO-8859-1; format=flowed > > Dear Sarah, > .......................................... it behooves educationalists themselves to evaluate and > assess the educational merits or otherwise of commercial products, this > is simply a general statement of good practice, common sense even, it > does not in any way impinge on the merits of commercial companies. > Have you tried Google, most questions similar to yours can be answered > by several hours work sifting through the many pages there? There are as > you surely know many, many programmes, software, projects, and so called > virtual schools handling ICT, but very much less objective or > educational research being done on them. I was, however, very impressed > with the Nationally supported Educational work on ICT coordinated from > Chichester University, when I visited them for a day several years ago. > You might like to ask them? > Having worked myself in the field of ICT (as it is now called) since > about 1966 could I also especially draw to your attention the Virtual > School for the Gifted, now defunct but at one time the world's only > genuine interactive virtual school, with whom I worked for ten years as > a teacher, the last two years as Manager or Coordinator. I believe it > provided a very effective model for ICT learning and there was > considerable anecdotal evidence of its success in helping children learn > mathematics, and other subjects! > Best wishes, > Alan > >>> *********************************************************************************************************** >>> This message has been generated through the Mathematics Education email discussion list. >>> Hitting the REPLY key sends a message to all list members. >>> *********************************************************************************************************** >>> >>> Hi >>> I am trying to find some evidence about whether ICT has a positive impact on attainment in mathematics and wonder if anyone has any good examples? If you look at syntheses of research they tend to find little or no positive impact, over and above good teaching. However, I believe there are some examples of where the findings are more positive, usually in terms of a particular kind of ICT in a particular context. Can anyone let me know which are the key research reports in this area? I am particularly interested in impact on attainment rather than motivation or engagement (even though ultimately this is likely to improve attainment), so ICT use that directly helps with understanding of particular concepts for example. >>> >>> Thanks for your help. >>> >>> Sarah >>> >>> Sarah Maughan >>> Director of Research >>> National Foundation for Educational Research From D.K.Jones at soton.ac.uk Thu Mar 10 13:11:15 2011 From: D.K.Jones at soton.ac.uk (Jones D.K.) Date: Thu, 10 Mar 2011 13:11:15 +0000 Subject: [Maths-Education] BSRLM workshop on NC review, 12 March 2011 Message-ID: <5F338719C0D0DE44BDFDD2B83D3FF7A1CBAD1981FC@UOS-CL-EX7-L3.soton.ac.uk> Colleagues attending BSRLM on 12 March 2011 http://www.bsrlm.org.uk/nextmeeting.html A working group session at BSRLM on 12 March 2011 provides the opportunity to discuss the evidence base (covering both primary and secondary) that might inform the construction and content of a revised mathematics National Curriculum for England, given the recently-announced review: http://www.education.gov.uk/schools/teachingandlearning/curriculum/nationalcurriculum A short input will begin the working session; after that, the bulk of the time is open to participants. Everyone is welcome to attend. If you are planning to attend the working group session, you are invited to let me know, especially if you would like to make a short contribution to the session to stimulate discussion. With this information (which you are invited to send just to me, and not necessarily to the whole list) I will devise a rough structure for the session (which can, of course, be modified depending on what happens as the session develops). Given the workshop is one of seven parallel sessions, and given it extends across breaks between other sessions, I will try to structure the working session around the session breaks at 11.00 and 11:35. This means that participants can join, or leave, the working group at these times if they are presenting or attending research sessions that take place in parallel to the working group session. Even if you are only able to attend part of the working group session, if you would like to contribute a short input please let me know (including letting me know the timing when you can be in the working group session). Many thanks in advance Keith PS: note that while the session provides the opportunity to discuss possible responses to the "call for evidence"; the session is not about formulating a single response --------- Keith Jones Mathematics and Science Education Research Centre Southampton Education School University of Southampton http://www.soton.ac.uk/education/research/centres.page From debutler at argonet.co.uk Thu Mar 10 13:30:38 2011 From: debutler at argonet.co.uk (Douglas Butler (Argonet)) Date: Thu, 10 Mar 2011 13:30:38 -0000 Subject: [Maths-Education] TSM residential Workshop (Oundle, 12-14 July) Message-ID: Members of this list may be interested in, or may know teachers who would benefit from, a 3-day concentrated blast of ICT for Mathematics teaching. This is possibly an apposite announcement following the recent thread on the effectiveness of it all! Anyway, details are on www.tsm-resources.com/2011 Another objective of this workshop is to train trainers, and last year we had 53 taking this extra dimension. Anyone interested in this needs to plan to arrive on the Monday for the trainers' workshop. == from Douglas Butler < debutler at argonet.co.uk > == Director, iCT TRAINING CENTRE (OUNDLE) PO Box 46, Oundle, Peterborough PE8 4EJ, UK T: +44 (0)1832 273444 F: 273529 M: +44 (0)7860 843462 www.tsm-resources.com www.autograph-maths.com From D.K.Jones at soton.ac.uk Thu Mar 10 13:28:21 2011 From: D.K.Jones at soton.ac.uk (Jones D.K.) Date: Thu, 10 Mar 2011 13:28:21 +0000 Subject: [Maths-Education] Re: BSRLM workshop on NC review, 12 March 2011 Message-ID: <5F338719C0D0DE44BDFDD2B83D3FF7A1CBAD198235@UOS-CL-EX7-L3.soton.ac.uk> I meant to say that responses to the message below can send to me via email: d.k.jones at soton.ac.uk Thanks Keith > -----Original Message----- > From: maths-education-bounces at lists.nottingham.ac.uk > [mailto:maths-education-bounces at lists.nottingham.ac.uk] On > Behalf Of Jones D.K. > Sent: 10 March 2011 13:11 > To: 'Mathslist.Uk' > Subject: [Maths-Education] BSRLM workshop on NC review, 12 March 2011 > > ************************************************************** > ********************************************* > This message has been generated through the Mathematics > Education email discussion list. > Hitting the REPLY key sends a message to all list members. > ************************************************************** > ********************************************* > Colleagues attending BSRLM on 12 March 2011 > http://www.bsrlm.org.uk/nextmeeting.html > > A working group session at BSRLM on 12 March 2011 provides > the opportunity to discuss the evidence base (covering both > primary and secondary) that might inform the construction and > content of a revised mathematics National Curriculum for > England, given the recently-announced review: > http://www.education.gov.uk/schools/teachingandlearning/curric > ulum/nationalcurriculum > > A short input will begin the working session; after that, the > bulk of the time is open to participants. Everyone is welcome > to attend. > > If you are planning to attend the working group session, you > are invited to let me know, especially if you would like to > make a short contribution to the session to stimulate > discussion. With this information (which you are invited to > send just to me, and not necessarily to the whole list) I > will devise a rough structure for the session (which can, of > course, be modified depending on what happens as the session > develops). > > Given the workshop is one of seven parallel sessions, and > given it extends across breaks between other sessions, I will > try to structure the working session around the session > breaks at 11.00 and 11:35. This means that participants can > join, or leave, the working group at these times if they are > presenting or attending research sessions that take place in > parallel to the working group session. Even if you are only > able to attend part of the working group session, if you > would like to contribute a short input please let me know > (including letting me know the timing when you can be in the > working group session). > > Many thanks in advance > > Keith > > PS: note that while the session provides the opportunity to > discuss possible responses to the "call for evidence"; the > session is not about formulating a single response > > --------- > Keith Jones > Mathematics and Science Education Research Centre > Southampton Education School > University of Southampton > http://www.soton.ac.uk/education/research/centres.page > > This message and any attachment are intended solely for the > addressee and may contain confidential information. If you > have received this message in error, please send it back to > me, and immediately delete it. Please do not use, copy or > disclose the information contained in this message or in any > attachment. Any views or opinions expressed by the author of > this email do not necessarily reflect the views of the > University of Nottingham. > > This message has been checked for viruses but the contents of > an attachment > may still contain software viruses which could damage your > computer system: > you are advised to perform your own checks. Email > communications with the > University of Nottingham may be monitored as permitted by UK > legislation. > > From aprice at brookes.ac.uk Thu Mar 10 14:46:46 2011 From: aprice at brookes.ac.uk (Alison Price) Date: Thu, 10 Mar 2011 14:46:46 +0000 Subject: [Maths-Education] Re: Early algebra references In-Reply-To: References: Message-ID: I am doing some work on early sorting, matching, categorisation leading into handling data and graphing etc.. I am finding it difficult to find much research on the early stages of this - lots of babies' understanding of categorisation but little at the 3-6 age group that is not either anecdotal or from a theoretical mathematical perspective (e.g. set theory) but not clearly related to an understanding of how children develop these ideas. What am I missing? Alison Price -- Rev Dr Alison Price Principal Lecturer in Primary Education Oxford Brookes University Harcourt Hill Oxford OX2 9AT Tel 01865 488516 From alexandre.borovik at gmail.com Thu Mar 10 15:04:26 2011 From: alexandre.borovik at gmail.com (Alexandre Borovik) Date: Thu, 10 Mar 2011 15:04:26 +0000 Subject: [Maths-Education] Re: Early algebra references In-Reply-To: References: Message-ID: <4D78E87A.5010509@gmail.com> I share Alison's frustration -- it is very difficult to find research information on early categorisation. I would be most happy to find any advice where to look for it. Many thanks -- Alexandre On 10/03/2011 14:46, Alison Price wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > I am doing some work on early sorting, matching, categorisation leading into > handling data and graphing etc.. > I am finding it difficult to find much research on the early stages of this > - lots of babies' understanding of categorisation but little at the 3-6 age > group that is not either anecdotal or from a theoretical mathematical > perspective (e.g. set theory) but not clearly related to an understanding of > how children develop these ideas. > What am I missing? > Alison Price -- Professor Alexandre Borovik * University of Manchester Web: http://www.maths.manchester.ac.uk/~avb/ Wordpress: http://micromath.wordpress.com/ Academia: http://manchester.academia.edu/AlexandreBorovik From bob.ansell at northampton.ac.uk Thu Mar 10 15:19:29 2011 From: bob.ansell at northampton.ac.uk (Bob Ansell) Date: Thu, 10 Mar 2011 15:19:29 +0000 Subject: [Maths-Education] Re: Early algebra references In-Reply-To: References: Message-ID: <4D78EC01.9030403@northampton.ac.uk> Hi Alison, We are using Algebra in the Early Grades, Edited by James Kaput, David Carraher and Maria Blanton. This is proving effective on our Williams Maths Specialist Programme. It is a substantive text and offers a 'research-based early algebra story' to quote from the preface. It presents a wide range of pedagogical perspectives. Bob Ansell On 10/03/2011 14:46, Alison Price wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > I am doing some work on early sorting, matching, categorisation leading into > handling data and graphing etc.. > I am finding it difficult to find much research on the early stages of this > - lots of babies' understanding of categorisation but little at the 3-6 age > group that is not either anecdotal or from a theoretical mathematical > perspective (e.g. set theory) but not clearly related to an understanding of > how children develop these ideas. > What am I missing? > Alison Price > > This e-mail is private and may be confidential and is for the intended recipient only. If you are not the intended recipient you are strictly prohibited from using, printing, copying, distributing or disseminating this e-mail or any information contained in it. We virus scan all E-mails leaving The University of Northampton but no warranty is given that this E-mail and any attachments are virus free. You should undertake your own virus checking. The right to monitor E-mail communications through our networks is reserved by us. From larry_francis at soesd.k12.or.us Fri Mar 4 23:29:42 2011 From: larry_francis at soesd.k12.or.us (Larry Francis) Date: Fri, 4 Mar 2011 15:29:42 -0800 Subject: [Maths-Education] Re: Pi Day (3-14) In-Reply-To: References: Message-ID: <2340C7DB54EE0C409CF59ED12F6577A0033F818A@mail.soesd.k12.or.us> Pi Day (March 14th) approaches! It's not too soon to start making plans! Here are a few links with animations, multimedia, info, and lessons: The Exploratorium's 2010 - 22nd Annual Pi Day Celebration http://www.exploratorium.edu/pi/index.html NPR: "Pi Day Celebrates a Mysterious Number" http://www.npr.org/templates/story/story.php?storyId=88226443 NPR: "Pi Day: An Infinite Number of Ways to Celebrate" http://www.npr.org/templates/story/story.php?storyId=88239845 lower on the page is "Happy Pi Day from the Pi Guy" Wikipedia: Pi and Albert Einstein http://en.wikipedia.org/wiki/Pi Wikipedia has a great animation called "Pi-unrolled" (shown above). You can see a large version of the it at http://en.wikipedia.org/wiki/Image:Pi-unrolled-720.gif Albert Einstein was born March 14, 1879. There's a lot of info about him at http://en.wikipedia.org/wiki/Albert_Einstein and even more at http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Einstein.html including the essay "Geometry and Experience" "Pi, Pi, Mathematical Pi" (to the music of "Bye, Bye Miss American Pie") http://www.vvc.edu/ph/TonerS/mathpi.html (The authors' personal pages are at http://www.alltooflat.com/about/personal/ton/ and http://www.stevetoner.com/ Check out Steve's terrific (and free!) games "Duplicon" (shape recognition), "Magic Pen" (mechanics and logic), and "Building Houses" (perspective),"Filler" (motion and logic), and CoBaCoLi (angles, motion, and logic). Talking about Pi http://www.cecm.sfu.ca/~jborwein/pi_cover.html Archimedes' proof for the area of a circle Here's a very nice flash illustration-with audio in French http://www.mathkang.org/swf/archimede.html Here's a couple in English from Tom Richmond: http://www.wku.edu/~tom.richmond/circle1.html and http://www.wku.edu/~tom.richmond/circle2.html You may also find them at the National Curve Bank: http://curvebank.calstatela.edu finding the value of pi http://mathforum.org/isaac/problems/pi1.html more pages from the math forum on pi http://mathforum.org/library/topics/pi/ NCTM's Illuminations site also has some resources you might find useful: www.nctm.org/resources/content.aspx?id=28520 Enjoy! --Larry Larry Francis, Southern Oregon ESD Computer Information Services www.soesd.k12.or.us/support/training and www.soesd.k12.or.us/math/math_resources larry_francis at soesd.k12.or.us or 541.858.6748 -------------- next part -------------- A non-text attachment was scrubbed... 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Name: image005.gif Type: image/gif Size: 3182 bytes Desc: image005.gif URL: From jdg at polya.uklinux.net Sat Mar 12 20:07:11 2011 From: jdg at polya.uklinux.net (Julian Gilbey) Date: Sat, 12 Mar 2011 20:07:11 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: References: <8B1E41E4B39E4374A2BC3034C3717750@homet4dz4d6xu0> <4D7347B5.5050003@gmail.com> <4D774163.3080409@gmail.com> <124417FE-BBBB-496E-B8EF-8E216D2AF229@ioe.ac.uk> <4D774FBF.1080705@gmail.com> <7C55AA8D-DD68-4661-AD32-FBD43F1C089E@mathstat.yorku.ca> Message-ID: <20110312200711.GA13732@d-and-j.net> On Thu, Mar 10, 2011 at 09:05:08AM +0000, Peters, Mike wrote: > Playing devil's advocate, I think it is time that the mathematics curriculum, especially in my sector engineering, was overhauled and the use of ICT and other educational resources became embedded and not viewed as bolt ons. Which has implications for the way we assess mathematical skills/knowledge, but that is another heated debate. I fully agree. Sadly, the current reality is far from that in (at least some) schools. I am currently a secondary mathematics teacher, and my school has recently built a new maths building. (We are now in our second year of using it.) It has two computer rooms and eight regular classrooms. Unfortunately, though, the computer rooms are almost in constant use for teaching this subject called "ICT", which is a synonym for "Microsoft Office", and so are almost never available for teaching mathematics. (Dr) Julian Gilbey From jhmason27 at googlemail.com Thu Mar 10 23:57:12 2011 From: jhmason27 at googlemail.com (John Mason) Date: Thu, 10 Mar 2011 23:57:12 +0000 Subject: [Maths-Education] Early Sorting Message-ID: <4D796558.1090604@open.ac.uk> Hi Alison, Alexandre None of this is large scale empirical in basis, but might be helpful. A) Edouard Clapar?de (1919), proposed a Law of Awareness, often cited approvingly by Piaget, which took thinking to be a standby activity, invoked only when existing habits failed to deliver an adequate response. Clapar?de, E. 1919: La conscience de la ressemblance et de la difference chez l'enfant. /Archives de Psychologie/, XVII, 67-80 Law of Awareness is quoted by Vygotsky as saying 'awareness of difference precedes awareness of likeness' (Vygotsky p163). Vygotsky, L. (1986/1997) A. Kozulin (Ed.) /Thought & Language/. London: MIT Press. This links closely to Ference Marton's Variation Theory. B) It is a well known phenomenon (I would look in Brown 1973 for possible confirmation) that children distinguish particulars from general (e.g. crows from birds) before they assemble them into class inclusion. Brown, R. 1973, /A First Language,/ MIT, Cambridge. There might be something in one of these as well: Hudson, Liam, 1968, Frames of Mind, Methuen, London. Hughes, M. (1986). /Children and Number/: /difficulties in learning mathematics/ Oxford : Basil Blackwell. JohnM From lefouque at gmail.com Mon Mar 14 06:39:25 2011 From: lefouque at gmail.com (Ng Foo Keong) Date: Mon, 14 Mar 2011 14:39:25 +0800 Subject: [Maths-Education] Re: Maths-Education Digest, Vol 77, Issue 12 In-Reply-To: References: Message-ID: The conventional wisdom may or may not be correct. I feel it iis not about the wisdom, it is about the actions of the interested parties and how we can work together. We can do much much more to encourage more of the Sugata Mitras, Markus Hohenwarters and Salman Khans of this world to come forward than to just sit around and complain about the lack of progress. sincerely yours, Ng, Foo Keong On 07/03/2011 06:05, Ng Foo Keong wrote: > > i'd like us to distinguish between the potential of ICT and what has > > actually been achieved in our evaluations of the effectiveness of ICT. > > This goes against the conventional wisdom which can be traced not just > centuries, millenia back in time: "The proof of the pudding is in the > eating" (14th century, according to Oxford Dictionary), "Rhodes is here, > here is where you jump!" (Aesop). > > Alexandre Borovik > > -- > Professor Alexandre Borovik * University of Manchester > Web: http://www.maths.manchester.ac.uk/~avb/ > Wordpress: http://micromath.wordpress.com/ > Academia: http://manchester.academia.edu/AlexandreBorovik > From skf6 at leicester.ac.uk Tue Mar 15 12:44:32 2011 From: skf6 at leicester.ac.uk (Forsythe, Susan K.) Date: Tue, 15 Mar 2011 12:44:32 +0000 Subject: [Maths-Education] Re: Maths-Education Digest, Vol 77, Issue 12 In-Reply-To: References: Message-ID: I know that the interesting discussion on the value of ICT has moved on a bit since it first started but I wanted to share my experience. For my Masters dissertation, which I completed in 2006, I enquired into whether teaching and learning of geometrical concepts through the medium of Dynamic Geometry Software (DGS) could be shown to be effective. I was still a classroom teacher at this point and, for my study, I taught two parallel classes in year 7, two of the geometry topics from the year 7 programme of study (from the English National Framework for Teaching Mathematics). The target group worked with DGS and the control group worked using pencil and paper methods. Both classes had the same number of lessons for the two topics and the control group did a lot of practical activities so that it would not be all bookwork and I, as the teacher, would be as enthusiastic about their lessons as with the computer based lessons. The study used quantitative methods to analyse the effectiveness of the two teaching methods (by testing the children). This had to be done using pencil and paper tests because the control class had not learnt to use the software. By the end of the study there was a statistically significant difference between the test results of the two classes. The target class, who had learnt through the medium of the computer, achieved better results in the tests. The results were even more pronounced for the target boys. I appreciate that this is only a study carried out for a Masters degree and only for a small sample size of two school classes. However, if anyone is interested then I would be happy to email them my dissertation. I also wrote an article based on my results in Mathematics Teaching, no. 202. Sue Forsythe Lecturer in Mathematics Education School of Education University of Leicester -----Original Message----- From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Ng Foo Keong Sent: 14 March 2011 06:39 To: maths-education at lists.nottingham.ac.uk Subject: [Maths-Education] Re: Maths-Education Digest, Vol 77, Issue 12 *********************************************************************************************************** This message has been generated through the Mathematics Education email discussion list. Hitting the REPLY key sends a message to all list members. *********************************************************************************************************** The conventional wisdom may or may not be correct. I feel it iis not about the wisdom, it is about the actions of the interested parties and how we can work together. We can do much much more to encourage more of the Sugata Mitras, Markus Hohenwarters and Salman Khans of this world to come forward than to just sit around and complain about the lack of progress. sincerely yours, Ng, Foo Keong On 07/03/2011 06:05, Ng Foo Keong wrote: > > i'd like us to distinguish between the potential of ICT and what has > > actually been achieved in our evaluations of the effectiveness of ICT. > > This goes against the conventional wisdom which can be traced not just > centuries, millenia back in time: "The proof of the pudding is in the > eating" (14th century, according to Oxford Dictionary), "Rhodes is here, > here is where you jump!" (Aesop). > > Alexandre Borovik > > -- > Professor Alexandre Borovik * University of Manchester > Web: http://www.maths.manchester.ac.uk/~avb/ > Wordpress: http://micromath.wordpress.com/ > Academia: http://manchester.academia.edu/AlexandreBorovik > This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. This message has been checked for viruses but the contents of an attachment may still contain software viruses which could damage your computer system: you are advised to perform your own checks. Email communications with the University of Nottingham may be monitored as permitted by UK legislation. From J.Tomalin at shu.ac.uk Tue Mar 15 12:57:00 2011 From: J.Tomalin at shu.ac.uk (Tomalin, Jo) Date: Tue, 15 Mar 2011 12:57:00 +0000 Subject: [Maths-Education] Re: ICT in mathematics In-Reply-To: <20110312200711.GA13732@d-and-j.net> References: <8B1E41E4B39E4374A2BC3034C3717750@homet4dz4d6xu0> <4D7347B5.5050003@gmail.com> <4D774163.3080409@gmail.com> <124417FE-BBBB-496E-B8EF-8E216D2AF229@ioe.ac.uk> <4D774FBF.1080705@gmail.com> <7C55AA8D-DD68-4661-AD32-FBD43F1C089E@mathstat.yorku.ca> <20110312200711.GA13732@d-and-j.net> Message-ID: <4869C6E6150B9548B6D3F3B39D919B56027382927D@HOLLYHOCK.hallam.shu.ac.uk> I am currently working in mathematics teacher education with PGCE and undergraduate students. We have the same problem with access to ICT suites, which give priority to those working with ICT teachers. There are still considerable barriers both in educating students to use ICT appropriately and in allowing them to use it once in schools, which make it difficult to evaluate what the most effective practice could be. Jo Tomalin Senior Lecturer Sheffield Hallam -----Original Message----- From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Julian Gilbey I fully agree. Sadly, the current reality is far from that in (at least some) schools. I am currently a secondary mathematics teacher, and my school has recently built a new maths building. (We are now in our second year of using it.) It has two computer rooms and eight regular classrooms. Unfortunately, though, the computer rooms are almost in constant use for teaching this subject called "ICT", which is a synonym for "Microsoft Office", and so are almost never available for teaching mathematics. (Dr) Julian Gilbey From tandiclausenmay at gmail.com Wed Mar 16 08:42:15 2011 From: tandiclausenmay at gmail.com (Tandi Clausen-May) Date: Wed, 16 Mar 2011 08:42:15 -0000 Subject: [Maths-Education] Re: Maths-Education Digest, Vol 77, Issue 12 In-Reply-To: References: Message-ID: <6D6AAC196FBC4CDF995C4C2909C18239@homet4dz4d6xu0> Sue Forsythe's study, as limited as she says it is, at least addresses Sarah Maugham's initial request for 'evidence about whether ICT has a positive impact on attainment in mathematics'. But action research carried out by teachers in their own classroom doesn't carry the kudos (or the funding) of academic research. Yours, Tandi Tandi Clausen-May Independent Consultant Mathematics curriculum and assessment Special education Tel: 01628 776 204 -----Original Message----- From: maths-education-bounces at lists.nottingham.ac.uk [mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Forsythe, Susan K. Sent: 15 March 2011 12:45 To: 'Mathematics Education discussion forum' Subject: [Maths-Education] Re: Maths-Education Digest, Vol 77, Issue 12 **************************************************************************** ******************************* For my Masters dissertation, which I completed in 2006, I enquired into whether teaching and learning of geometrical concepts through the medium of Dynamic Geometry Software (DGS) could be shown to be effective. I was still a classroom teacher at this point and, for my study, I taught two parallel classes in year 7, two of the geometry topics from the year 7 programme of study (from the English National Framework for Teaching Mathematics). The target group worked with DGS and the control group worked using pencil and paper methods. Both classes had the same number of lessons for the two topics and the control group did a lot of practical activities so that it would not be all bookwork and I, as the teacher, would be as enthusiastic about their lessons as with the computer based lessons. The study used quantitative methods to analyse the effectiveness of the two teaching methods (by testing the children). This had to be done using pencil and paper tests because the control class had not learnt to use the software. By the end of the study there was a statistically significant difference between the test results of the two classes. The target class, who had learnt through the medium of the computer, achieved better results in the tests. The results were even more pronounced for the target boys. I appreciate that this is only a study carried out for a Masters degree and only for a small sample size of two school classes. However, if anyone is interested then I would be happy to email them my dissertation. I also wrote an article based on my results in Mathematics Teaching, no. 202. Sue Forsythe Lecturer in Mathematics Education School of Education University of Leicester From daniel.pead at nottingham.ac.uk Mon Mar 21 13:30:45 2011 From: daniel.pead at nottingham.ac.uk (Daniel Pead) Date: Mon, 21 Mar 2011 13:30:45 +0000 Subject: [Maths-Education] Educational Designer Issue 4 Message-ID: <38747BF4-6439-4B89-864F-EF05F865A611@nottingham.ac.uk> Educational Designer is a free, on-line journal covering the research-led design of materials, curricula and strategies in (primarily) Mathematics and Science education. Issue 4 is now available at: www.educationaldesigner.org The articles in this issue are: * Thomas C. Reeves - Can Educational Research Be Both Rigorous and Relevant? * Lara Alcock and Nicola Wilkinson - e-Proofs: Design of a Resource to Support Proof Comprehension in Mathematics * A Designer Speaks - Charles Lovitt and Doug Clarke Thanks to the authors and to the editor, Susan McKenney for their work on this issue. Yours, Daniel Pead. From L.J.Alcock at lboro.ac.uk Mon Mar 21 15:47:55 2011 From: L.J.Alcock at lboro.ac.uk (Lara Alcock) Date: Mon, 21 Mar 2011 15:47:55 +0000 Subject: [Maths-Education] Re: Educational Designer Issue 4 In-Reply-To: <38747BF4-6439-4B89-864F-EF05F865A611@nottingham.ac.uk> References: <38747BF4-6439-4B89-864F-EF05F865A611@nottingham.ac.uk> Message-ID: Thanks Daniel. What happened with that author agreement? Cheers, Lara. ________________________ Lara Alcock Mathematics Education Centre Loughborough University Loughborough LE11 3TU L.J.Alcock at lboro.ac.uk On 21 Mar 2011, at 13:30, Daniel Pead wrote: > *********************************************************************************************************** > This message has been generated through the Mathematics Education email discussion list. > Hitting the REPLY key sends a message to all list members. > *********************************************************************************************************** > Educational Designer is a free, on-line journal covering the research-led design of materials, curricula and strategies in (primarily) Mathematics and Science education. > > Issue 4 is now available at: > > www.educationaldesigner.org > > The articles in this issue are: > > * Thomas C. Reeves - Can Educational Research Be Both Rigorous and Relevant? > > * Lara Alcock and Nicola Wilkinson - e-Proofs: Design of a Resource to Support Proof Comprehension in Mathematics > > * A Designer Speaks - Charles Lovitt and Doug Clarke > > Thanks to the authors and to the editor, Susan McKenney for their work on this issue. > > Yours, > Daniel Pead. > > > > This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. Please do not use, copy or disclose the information contained in this message or in any attachment. Any views or opinions expressed by the author of this email do not necessarily reflect the views of the University of Nottingham. > > This message has been checked for viruses but the contents of an attachment > may still contain software viruses which could damage your computer system: > you are advised to perform your own checks. Email communications with the > University of Nottingham may be monitored as permitted by UK legislation. > From dpearcy at stnicholas.com.br Mon Mar 21 20:29:44 2011 From: dpearcy at stnicholas.com.br (Daniel Pearcy) Date: Mon, 21 Mar 2011 17:29:44 -0300 Subject: [Maths-Education] Singapore vs Japan - Teaching Styles and Learning Message-ID: Dear all, I teach Maths at an International School in Sao Paulo, Brazil and am currently interested in International Education. In particular, I?m looking at the difference in teaching and learning between Schools in Singapore and Japan. I was able to find many different sources on what teaching and learning looks like in a 'typical' Japanese lesson that all point towards a problem based environment. The students try to find strategies to solve these problems and the strategies are discussed as a class. However, I found conflicting views on what a typical Singapore lesson looks like. There are sources that still point to a teacher dominated rote-learning style and sources that point to a huge improvement over the last 13 years in a more problem based, investigatory style since the introduction of Government Schemes such as, "Thinking School, Learning Nation." I would like to know what a typical lesson looks like in Singapore? I became interested in this after looking at the PIA international data (2009) on comparisons in mathematics results and noticed that Japan and Singapore are Countires that consistently do well on an international scale. Parental attitudes, cultural attitudes and percentage of students who attend classes outside school are simililar in both Countries so I would like to know if the teaching styles are also similar. I also know that there is a strong emphasis on pedagody in Japanese teacher training but am not sure if this is the case in Singapore. If not, and most Singapore teachers do indeed teach by rote, it is interesting to note that Singapore consistently out-performs Japan on an international scale. This would certainly change some of my perceptions on what constitutes as 'good learning' in a mathematics lesson. Thanks, Daniel Pearcy From vivientownsend at warwickshire.gov.uk Mon Mar 28 11:04:54 2011 From: vivientownsend at warwickshire.gov.uk (vivientownsend at warwickshire.gov.uk) Date: Mon, 28 Mar 2011 11:04:54 +0100 Subject: [Maths-Education] change of details Message-ID: Hi Peter, Please can you update your records about me. >From 1st April 2011, I will be working as a freelance mathematics and ICT consultant and will be available through the following contact details: viv at vivientownsend.co.uk 07956 645353 www.vivientownsend.co.uk I'd really like to still be a member and to receive the emails. Best wishes, Viv This transmission is intended for the named addressee(s) only and may contain sensitive or protectively marked material up to RESTRICTED and should be handled accordingly. Unless you are the named addressee (or authorised to receive it for the addressee) you may not copy or use it, or disclose it to anyone else. If you have received this transmission in error please notify the sender immediately. All email traffic sent to or from us, including without limitation all GCSX traffic, may be subject to recording and/or monitoring in accordance with relevant legislation. -------------- next part -------------- A non-text attachment was scrubbed... Name: not available Type: image/jpeg Size: 42623 bytes Desc: not available URL: From Peter.Gates at nottingham.ac.uk Mon Mar 28 17:46:49 2011 From: Peter.Gates at nottingham.ac.uk (Peter Gates) Date: Mon, 28 Mar 2011 17:46:49 +0100 Subject: [Maths-Education] Colour edition "African Pythagoras" Message-ID: From: Paulus Gerdes [mailto:paulus.gerdes at gmail.com] Sent: Monday, March 28, 2011 5:03 PM To: gzhu at bjtu.edu.cn Cc: ggreenfi at richmond.edu; Nguerekata at aol.com; Peter.Gates at nottingham.ac.uk; gert.schubring at uni-bielefeld.de; Ggilme at aol.com; ghanna at oise.on.ca; K.Glevey at ioe.ac.uk; goduk1in at cmich.edu; Greta.VanKeymeulen at arteveldehs.be; j.vangroenendael at science.ru.nl; j.j.gray at open.ac.uk; mgray at american.edu; vmasanja at gmail.com; gsarhangi at towson.edu; guy.brousseau at wanadoo.fr; ribasg71 at gmail.com; darvasg at iif.hu; darvasg at helka.iif.hu Subject: Colour edition "African Pythagoras" Please forward to those who may be interested: Dear friends and colleagues, I have the pleasure to announce the publication of the first colour edition of my book "AFRICAN PYTHAGORAS: A Study in Culture and Mathematics Education" (ISBN 978-1-257-16100-3, 124 pp., available as printed book and as download from: http://stores.lulu.com/pgerdes) "AFRICAN PYTHAGORAS: A study in culture and mathematics education" shows how diverse African ornaments and artefacts may be used to create an attractive context for the discovery and the demonstration of the Pythagorean Theorem and of related ideas and propositions. The first black-and-white edition of "African Pythagoras" was published in 1992 in Portuguese, and in 1994 in English. Some parts of the book were reproduced in Chapter 2 'From African designs to discovering the Pythagorean Theorem' (pp. 54-86) of the author's book "Geometry from Africa: Mathematical and Educational Explorations" (Mathematical Association of America, Washington DC, 1999) ('Outstanding Academic Book,' Choice Magazine, 2000). The 2011 edition of "African Pythagoras" is the first colour edition and contains as afterword a review by Jens Hoyrup (Roskilde University, Denmark). >From the afterword: "Teachers and textbook authors will ... find substance and an abundance of ideas for the introduction of many essential aspects of geometrical reasoning, not least geometrical reasoning about real-world phenomena. There is no reason that only African teachers should draw on this inspiration, ... [as] sub-Saharan African geometrical art ... possesses a universal value of which the mathematics education of the global village should take advantage." Keywords: Africa, African culture, African art, Pythagoras, Pythagorean Theorem, Pappus, geometry, proof, heuristics, magic squares, Latin squares, trigonometry, fractals, mathematics, mathematics education, mathematics teacher education, ethnomathematics, ethnogeometry Best regards, Paulus Gerdes March 27, 2011 -- Paulus Gerdes Vice-President for Southern Africa, African Academy of Sciences Chairman, AMU Commission for the History of Mathematics in Africa President, International Studygroup for Ethnomathematics C.P. 915, Maputo, Mo?ambique paulus.gerdes at gmail.com http://stores.lulu.com/pgerdes From T.Roper at education.leeds.ac.uk Tue Mar 29 15:28:11 2011 From: T.Roper at education.leeds.ac.uk (Tom Roper) Date: Tue, 29 Mar 2011 15:28:11 +0100 Subject: [Maths-Education] Post in mathematrci8s education at University of Leeds Message-ID: Dear Colleagues, Lecturer / Senior Lecturer in Mathematical Education at the University of Leeds Details of this post are available on: http://jobs.leeds.ac.uk/fe/tpl_universityofleeds01.asp?KEY=69354217&C=994551476298&PAGESTAMP=dbecsjvhxrgeccszgv&nexts=INIT_JOBLISTSTART&nextss=&mode=1&newQuery=yes&searchrefno=&searchindustry=0&searchgrade=3089&searchjobgenerallist1id=0&searchjobgenerallist2id=0&searchtext=&formsubmit4=Search+and+Apply I'd like to add that from my perspective: (i) the research profile is very important (ii) this is an equal opportunities post with regard to nationality (I mention this lest the mention of PGCE makes people think it is only for Brits). Please feel free to pass this on to anyone who may be interested. Best wishes, John Monaghan Tom Roper Senior Lecturer in Mathematics Education Telephones Work?? 0113 3434547 Fax??? 0113 3434541 From T.Roper at education.leeds.ac.uk Tue Mar 29 15:32:14 2011 From: T.Roper at education.leeds.ac.uk (Tom Roper) Date: Tue, 29 Mar 2011 15:32:14 +0100 Subject: [Maths-Education] Symposium ATATEMLO Message-ID: >From John Monaghan (University of Leeds) on behalf of Fabrice Vandebrouck (University of Paris 7) Symposium ATATEMLO "Activity theoretic approaches to technology enhanced mathematics learning orchestration" Call for short proposals (deadline 10 of May) Activity Theory (AT) is a cross disciplinary theory adopted for studying various forms of human practices, such as teaching/learning, that are seen as developmental processes mediated by artefacts, where individual and social levels are simultaneously interlinked. It gives us a framework, a vocabulary as well as notions associated with those terms, useful for understanding and informing the design of technology enhanced learning orchestrations in the domain of mathematics as well as conceptualising various mediations occurring in these situations. By orchestration we mean the process of productively coordinating supportive interventions across multiple learning activities occurring at multiple social levels (Fischer and Dillenbourg 2006), including classroom orchestration of technology involving students and teachers as well as other settings where human being can learn mathematics from various sources and collaborations. The goal of the symposium is to share and integrate competences, methodologies and ideas of researchers in the field of AT and mathematical teaching and learning, in order to better address issues related to orchestrations of mathematics learning with technology. The final output will be a peer-reviewed book or a special issue of a scientific journal. AT has its roots in the classical German philosophy of Kant and Hegel, the dialectical materialism of Marx and the socio cultural and socio historical tradition of Russian psychologists such as Vygotsky, Leontiev and Luria. In the domain of mathematical education with technology, it allows one to state the mediation role played by technological tools during the teaching and learning situations. Beyond these roots, recent developments of AT have taken place in several directions. - The French school of cognitive ergonomic (Vergnaud, Leplat, Rogalski) developed AT to study cognition at the workplace and introduced the idea of instrumental genesis (Rabardel and Verillon) which gives rise to a dialectic by which learner and artefact are mutually shaped in action. This focus has been specified to mathematical teaching/learning situations by Artigue, Lagrange, Guin and Trouche. Robert and Rogalski also developed a didactical and ergonomic approach to study teaching practices and learning situations initially not devoted to technological situations but now adapted to such situations. - In other countries, the initial theory was extended to communities (teachers and/or learners) : particularly Cole and Engestr?m conceived a systemic model expressing the complex relationships between elements in an activity, useful for studying the relationships that take place in teaching/learning activity with technological tools. Wertsch has developed the dialectic between agent and mediational means. Saxe developed a cultural approach with three components of which the first, based on a four parameters model and the notion of emergent goals, has been used in studies examining teaching with technology. Several researchers in math education and technology used some of the above AT frameworks in order to address specific issues linked to technology enhanced orchestrations, especially the role of the teacher in organising and conducting technology based lessons. These works are promising, but remain unconnected. In parallel, the functioning of a mathematics classroom using technological artefacts, and more generally the complex orchestration of learning with technology, remains very problematic. We expect that activity theoretic approaches will offer tools to address learning orchestrations in terms of dynamical features of the activities to be carried out by learners and teachers. These are related with new elements involved in classroom orchestration such as the nature of the tasks for the students, with new forms of interactions occurring in computer-based pedagogical settings, offering more opportunities for experimentation with dynamic and interconnected mathematical representations and with the challenge of integrating these aspects into teachers' activity. The outputs of the symposium are expected to contribute to existing research at two levels: 1) the level of theoretical work in technology enhanced mathematics learning (e.g. integrating research approaches following an AT perspective, highlighting the role of AT concepts in designing, implementing and analyzing research studies in the field of mathematics education); 2) the level operational approaches for orchestrating and instrumentalising mathematics learning with technology and for taking critical aspects of context into account. The proposals, not longer than 10 pages, will be articulated around some or all of the four following questions - What key aspects in the complexity of technology enhanced learning (TEL) situations does your AT framework help to address? What tools does it provide to support teachers and designers? - How does your AT framework help to conceptualize the changing roles and relationship to mathematics knowledge by learners and teachers? - How does your AT framework help to conceptualize constraints specific to the orchestration of learning, like the necessity of assessing and certifying knowledge and skills in the context of digital technologies? - How does your AT framework help to take into account the ways in which TEL orchestration are mediated by the context. The symposium will be held in October in Paris. Proposals will only be made at the invitation of the organizing committee and are expected to September 30. Interested candidates should send before May the 10th a summary of one page. The organizing committee of the symposium will be held during May to decide on invitations. Please send your proposal to Fabrice Vandebrouck, vandebro at math.jussieu.fr Tom Roper Senior Lecturer in Mathematics Education Telephones Work?? 0113 3434547 Fax??? 0113 3434541