Classroom tools

Edward Cherlin echerlin at
Tue Jan 15 03:13:58 EST 2008

On Jan 14, 2008 10:06 PM, Yoshiki Ohshima <yoshiki at> wrote:
> > But let me say one more thing. Making use of "constructionism" theory
> > doesn't means the unnecessity of the teachers, but the role of the
> > teachers changes.
>   Yes, I think tools for supporting teacher who want to do the
> traditional style of teaching is eventually necessary.
>   And, even in "Learning learning", many subjects that are invented
> are not discoverable by kids' own.  (Alan Kay said "Children are not
> going to invent calculus".)  a kid should be helped by teacher(s) in
> one way or another to learn "powerful ideas".

Alan Kay has examples of children discovering parts of calculus with
some assistance.

It is important that teachers know about the really important ideas,
and about how to introduce children to them without thinking that they
can simply teach it in language. I started working on a Kindergarten
Calculus idea a while ago. Show the children that you can put a
straightedge against any shape to get the direction of that shape at
that point. Ask why the straightedge is level at the top or bottom.
Assist them to find the third case in which the tangent can be level.
That's the essence of differential calculus. The rest is deriving
formulas and doing calculations.

Similarly for integral calculus. Draw a figure on paper, cut it out
and weigh it. Now, how can you help children to discover that these
two operations are inverses? That's the Fundamental Theorem of
Calculus. (I have a solution, but I am sure that there are others.)

Given that we can teach understanding of the fundamental ideas in
Kindergarten, we have the opportunity to rethink at what ages the rest
can be brought in. Traditional thinking is that you can't start until
the students are capable of understanding all of the subject. This is
very close to complete nonsense. Weapons-grade bolonium, in fact.

> -- Yoshiki
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Edward Cherlin
End Poverty at a Profit by teaching children business
"The best way to predict the future is to invent it."--Alan Kay

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