yoshiki at vpri.org
Tue Jan 15 03:42:55 EST 2008
"One way or another" is what I wrote, and letting them cut papers
and weigh is a great idea, I think.
As you wrote, it is important to have teachers understand, or able
to help, impotant ideas. And assembling a repository of what are
impotant ideas and techiniques to teach them would be essential
addition to the current OLPC effort.
At Tue, 15 Jan 2008 00:13:58 -0800,
Edward Cherlin wrote:
> On Jan 14, 2008 10:06 PM, Yoshiki Ohshima <yoshiki at vpri.org> 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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