[Maths-Education] Re: ICT in mathematics
Hugh Burkhardt
Hugh.Burkhardt at nottingham.ac.uk
Wed Mar 9 15:53:24 GMT 2011
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:
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> 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
>
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> 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 <dietmar.kuchemann at kcl.ac.uk>wrote:
>
>>
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>> 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" <alexandre.borovik at gmail.com>
>> wrote:
>>
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>> 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
>>
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