Robert Ferney capnregex at gmail.com
Mon Nov 22 19:16:17 CET 2004

On Mon, 22 Nov 2004 09:45:14 -0800, Kirby Urner <urnerk at qwest.net> wrote:
> However, there's no one route.  I prefer the metaphor of a terrain, and
> giving students a map.  One has many trails through this terrain.  You may
> walk them all eventually, but there'll be forks in the road, with signage we
> hope, and the teacher won't necessarily push in either direction -- up to
> each student to choose.

There are two basic reasons for understanding which principles are
prerequisite to other principles..

The first is to be able to map ways to get there from where you are at.

The second is to know what principles to review when you have trouble. 

I saw an example of this while I was assisting in a class of young
kids at the local private school where I teach. ( I teach an art class
in the afternoons )
The student was learning the principle of borrowing for subtraction. I
pulled out some beans to use as counters, and illustrated the
principle visually. Then I had the student practice, first with the
beans, then on paper. She did just fine with the practice, and I am
confident that the principle of borrowing is understood. However, As
she was practicing, I noticed that she was still struggling with the
more basic skill of being able to subtract numbers larger than 10.
Most likely she just needs some practice in that area.

After looking at it, it may not be as good of an example as I would
have liked, but hopefully yall can see the idea anyway.


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