[Maths-Education] Re: ICT in mathematics

[David H Kirshner]

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


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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

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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:

>
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> 
> 
> 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
> 
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