[IAEP] [Grassroots-l] Concise explanation of Constructionism from the Learning Team

[Bill Kerr]

On Sun, Aug 17, 2008 at 1:32 AM, Bastien <bastienguerry at googlemail.com>wrote:

> "Bill Kerr" <billkerr at gmail.com> writes:
>
> >   • intuition
>
> [...]
>
> >   • different ways of looking at maths (constructive and intuitive
> compared
> >     with rule driven and formal)
>
> [...]
>
> >   • other mathematicians who hold similar views - Poincare, Brouwer,
> Godel)
>
> I'd be curious on how Cynthia relates mathematical theories (like
> intuitionism) to pedagogical theories.  What is the "similar views"
> that Poincaré, Brouwer and Gödel are holding?  Is that views about
> pedagogy or views about mathematics (namely intuitionism)?
>
> Can you tell me more about this? (or send me pointers?)
>
> Thanks!
>
> --
> Bastien


hi Bastien,

Cynthia is reporting on Papert's ideas about deficiencies in School maths.
eg. that focusing on number is just one way of doing maths and that there
may be other ways that tap into more natural ways of children learning, eg.
body syntonic turtle geometry.

She relates this to a philosophical divide in approaching maths dating back
to Whitehead and Russell's *Principia Mathematica*, in which all maths is
reduced to logic. Hence the contrast between and intuitive and constructive
approach on the one hand compared with a rule driven and formal approach on
the other.

So, Cynthia, is reporting on Papert's views that the content of school
maths needs to be changed as well as the process of how it is taught
(computers offering new opportunities here).

I think that's a very strong and positive feature of her book, that she
situates the discussion as part of a historical and philosophical debate on
the nature of maths.

Some pointers, apart from Cynthia's book:
Mindstorms by Papert, Chapter 6: Powerful Ideas in Mind-size Bites
illustrates that mathematical intuition is quite central to Papert's
thinking
Godel, Escher, Bach by Hofstadter has several are references to intuition,
programming intuition and Godel and introspection
Minsky's The Emotion Machine pursues these ideas in the AI field and
includes a section on Poincare (7-7 Poincare's Unconscious Processes),
Minsky's book is available on line at his MIT site
Brouwer - I don't know, I was just quoting from Cynthia's book here

So, the answer to your question is that it's about both the nature of
mathematics and pedagogy but arising from Papert's view of the nature of
mathematics (contrasted to the purely logical, rule driven approach) and
that the learning of mathematics could be structured better to fit the
natural ways by which children learn, as discovered by Piaget.

I read Edwards reply too, which seems to be at odds with this thinking

cheers
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