[Maths-Education] Re: ICT in mathematics

Mon Mar 7 16:15:55 GMT 2011

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

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@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:
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> 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
>
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> 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
>
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> 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
>
>
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--
Professor Alexandre Borovik * University of Manchester
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