"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. -- Yoshiki At Tue, 15 Jan 2008 00:13:58 -0800, Edward Cherlin wrote: > > On Jan 14, 2008 10:06 PM, Yoshiki Ohshima <[EMAIL PROTECTED]> 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 > > > > _______________________________________________ > > Devel mailing list > > Devel@lists.laptop.org > > http://lists.laptop.org/listinfo/devel > > > > > > -- > Edward Cherlin > End Poverty at a Profit by teaching children business > http://www.EarthTreasury.org/ > "The best way to predict the future is to invent it."--Alan Kay _______________________________________________ Devel mailing list Devel@lists.laptop.org http://lists.laptop.org/listinfo/devel