Re: Disability? Re: [xmca] Help in teaching and learning maths

i had wanted to comment on the discourse of "discalculia" and "disability" too,
because bits of discourses can get mixed and retold into one's life story and
become part of one's identity (i.e. they become a self-fulfilling prophecy).

i am a critical realist. the foregoing paragraph shows the "critical"
part of me.
the "realist" part of me will admit that there is a possibility of a
person really
having discalculia independent of social factors, and independent of our
discourse, i.e. say, due to brain damage (by any name). however such cases
are rare. if someone is scoring like 40/100 for maths, i'll look for
factors other
than a biological cognitive impairment (and even so if it is 0/100).

some comment about "fun" - it seems to suggest some kind of inclination
towards expecting that learning should (only?) take place when somebody
enjoys it. i have nothing against that. that is what psychologists
call "extrinsic motivation" and is powerful for learning. from the point of
view of developing a mathematical identity, like doing what a
mathematician would
do when encountering a real mathematical puzzle or problem (not those boring
decontextualized school set-exercises), we see that they go through very long
periods of struggle (e.g. Andrew Wiles solving the "Fermat's Last Theorem"),
sometimes without success in sight, that can hardly be called "fun" and yet they
perservere. The "fun" (that "top of the world feeling") comes only at the end,
when/if one manages to solve it. The behaviourist will say "Ah!
Unequally spaced
out 'positive reiforcement' of unexpected magnitude, no wonder
'reponse' behaviour
to 'stimuli' is being optimized".

But it is hard to just read about it and write about it. The
Community of Practice
guys will say, you need personal experience, a first-hand taste, of this praxis
(i.e. delaying of instant gratification in struggling to solve something
non-trivial) in a practitioner context to really learn what it means.
I have not
hid in the attic for 7 years trying to crack, say, the Goldbach Conjecture,
but I have spent 2 weeks to 2 years being stuck on some mathematical problems
or quests. People might say only weirdos / geeks or sadist are willing to go
through such mental torture. however, it is "fun" -- but only in the
end, if ever.
(and yes, I have my share of mathematical frustrations and orgasms - you can't
have one without the other, it seems) you need to experience it to
know what it
is like.

Perhaps "delaying of gratification" could run counter to certain
cultural norms or
expectations in certain societies, and that may partly explain some
maths learning
(i.e. "learning-to-be", not "learning about") difficulties. There are
also many other
possibilities - e.g. school maths learning is not really maths
learning (learning-to-be
like a mathematician), school maths exercises promote roboting rote-learning
(learning to be an instruction-following machine, rather than a creative human
problem-solver) and has got nothing to do with real life (decontextualized), so
learners view maths as an "uncreative" endeavour and they get p***ed
off by school
"math" which had long since become a paradody of the real thing.

just my 2 cents' worth.

Sophus F.K. Ng

2008/6/10 Shirley Franklin <s.franklin@dsl.pipex.com>:
> Hi,
>
> We are touching on interesting ground here, if we describe a problem in
> getting maths as a disability.
>
> There is what I think is a very dodgy notion of discalculia, which implies
> there is something wrong with the brain.
>
> Problems with Maths I think can relate to a variety of factors. Thinking
> that you cant, and being around other maths-phobic people can promote maths
> phobia!
>
> Teaching out of the zone also promotes maths failure. But then establishing
> where the zpd is is what is important.
>
> Valerie Walkerdine wrote a lovely piece on how kids can get stuck in the
> metaphor that is used to teach Maths, rather than the metonym, the concept.
> For eg I always think of quarters (the metonym) as juicy pieces of chocolate
> cake (the ,metaphor). So learning how to teach Maths means being able to
> effectively use metaphors to teach the abstract metonym. (ref: Walkerdine,
> V. (1982):'From Context to Text: a psychosemiotic approach to
> abstractthought' in M. Beveridge, (ed.), Children Thinking Through
> Language. Arnold .)
>
>
> I think with Andy's niece she needs an I CAn approach ,as a starter! And fun
> stuff that shows how she uses Maths in her everyday life. Then showing how
> what she uses can be developed to become a bit more complex, and used in
> other contexts...
>
> So this is me thinking on the spur of the moment, cos I love teaching Maths.
> I think most kids here these days are not phobic, unless there is a language
> problem.
>
> Please do not medicalise or label having a difficulty with Maths! Analyse
> what the problem is and make Maths fun!
>
> Hope this is mildly helpful
>
> Shirley
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Received on Tue Jun 10 08:38 PDT 2008