[IAEP] another book

Steve Thomas sthomas1 at gosargon.com
Mon Apr 25 12:32:47 EDT 2011

Thank you.

In your book (Davis chapter) you write:

The following anecdote captures the root of the problem. A teacher who had
taken part in a workshop on "discovery learning" came back almost in tears
complaining that the students had "discovered it wrong." Bob Davis himself
and his virtuoso disciples could work with a class of children, sensitively
guiding the discovery process. In particular, they could pick out the germs
of good insight in what the less understanding teacher saw as simply
"wrong." The problem is deep: People brought up with a view of mathematics
as discrete facts to be mastered do not easily discard this view. The
reformer is faced with the problem:
We cannot tell teachers all they need to know about teaching—we must choose.
Indeed, we must choose not merely content, but also the kind of content, and
in fact even the media by which and form in which this "knowledge" is
The problem is compounded by what happens in the next year with "untrained"

Do you know where I can find copies of the scripts Bob Davis used as part of
the Madison project?
So what is the way out of this problem (that scales)?

Also in your book  (Papert chapter) you write:

Papert pursues such questions as,
*(1)* What experiences and knowledge lead children to change
their theories, and
*(2)* why do they learn some things without formal instruction and not learn
other things despite formal instruction?

I also struggle with the first question a lot.  In my experience the answer
depends a good deal on knowing what theories the child holds, so I guess my
main question is are there any proven techniques to help the child

a) see the hole/problem with their current theories (which to them make
perfect logical sense)

I usually attempt to cause "cognitive dissonance" by finding questions and
examples that do not fit their model as I perceive it, or more easily as
they verbalized it. That can work, but does not scale, also in an OLPC model
where there may be no teacher or no teacher with subject matter expertise,
what do you do?

b) what does research say about proven techniques to help kids change their
mental models once they see the "holes"?

Regarding the 2nd question I would add: "Why do they learn some things
despite formal instruction?"

Also in your book  (Papert chapter) you write:

the process of doing elementary school mathematics so that it draws on
children's intuition and everyday commonsense thinking.
How Papert differs from Suppes, Davis, and Dwyer might be summed up in what
I call the Papert principle: If you want to teach arithmetic to children,
arithmetic might not be the best route into these ideas for an easy
understanding of the topic. What is needed is a way of mathematizing the
child; thereafter particular mathematical topics become easy.

This reminds me of something I heard from Keith Devlin either
in his Natural Math talk <http://mathfuture.wikispaces.com/KeithDevlin>,
which was:

It comes down to finding new representations of mathematics.

So does anyone have any good examples of new representations?

Lastly, one of the great things from the Madison project is what I
call it "Taking
Tic-Tac-Toe to the next
where the key rule of the game is you can't tell anyone the rules.  Kids
play the game and have to figure out the rules by playing. Kids can learn
about cartesian coordinates, positive and negative numbers and practice "a
number is all the ways you can name it" all without being told what to do or
how to do it.

If you give a child an answer,
you solve a problem for the day.
Teach a child to find the answers,
you prepare her for a life.
      - Mr. Steve's Science

On Mon, Apr 25, 2011 at 6:38 AM, Cynthia Solomon <cynthia at media.mit.edu>wrote:

> I just posted my book, Computer Environments for Children: A Reflection on
> Theories of Learning and Education.
> http://computerenvironments.wikispaces.com
> --Cynthia
> _______________________________________________
> IAEP -- It's An Education Project (not a laptop project!)
> IAEP at lists.sugarlabs.org
> http://lists.sugarlabs.org/listinfo/iaep
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