[plt-scheme] Re: The Philosophy of DrScheme

From: Greg Woodhouse (gregory.woodhouse at gmail.com)
Date: Mon Dec 1 13:26:16 EST 2008

A minor nit: There is no reason why mathematics cannot be taught as an
active process of discovery. The problem (well, one problem) is that the
only way to really learn mathematics is by doing, and that means
calculating. Still, there is no reason it can't be interesting. I'll give
you an example: one thing that always intrigued me, even as a child, is that
there are only 5 regular polyhedra (the tetrahedron, octahedron, cube,
dodecahedron and icosohedron), but I didn't realize until much later how
accessible a result it really is. You could almost make it a homework
exercise! Start with Euler's famous formula V - E + F = 2 (for a topological
sphere) and then suppose you have refgular polyhedron the faces of which are
n-gons. It all comes down to counting: If there are m of them, how many
times will you count each vertex in m times n vertices per face? How many
times will you count each edge? What happens if you plug these numbers in
Euler's formula? Even if youer students take euler's formula on faith, the
result is still impressive.

On Thu, Nov 27, 2008 at 5:52 AM, Eduardo Bellani <ebellani at gmail.com> wrote:

> Well, I guess great minds think alike :)
> >From what I'm seeing so far the target population are a bit different,
> yours being mostly the undergrad students, Papert's being children,
> but I guess the goal is pretty much the same:
> "We therefore believe that the study of program design deserves the same
> central
> role in general education as mathematics and English. Or, put more
> succinctly,
> everyone should learn how to design programs.  On one hand, program design
> teaches the same analytical skills as mathematics. But, unlike mathematics,
> working with programs is an active approach to learning." - HtDP
> "In many schools today, the phrase "computer-aided instruction"
> means making the computer teach the child. One might say the
> computer is being used to program the child. In my vision, the
> child programs the computer and, in doing so, both acquires a
> sense of mastery over a piece of the most modern and powerful
> technology and establishes an intimate contact with some of the
> deepest ideas from science, from mathematics, and from the art of
> intellectual model building." - Mindstorms, Children, Computers and
> Powerful Ideas
> Just by curiosity
> > I ran into Logo and the book a year after I finished most of HtDP.
> What book are you talking about?
> --
> Eduardo Bellani
> www.cnxs.com.br
> "What is hateful to you, do not to your fellow men. That is the entire
> Law; all the rest is commentary." The Talmud
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