I was asked early this week to substitute for a colleague. The subject is visualization in Analysis. I taught the class some time ago in the same program, but I did not particularly emphasize the visual part of it. I am more algebra oriented, than geometry oriented. Nevertheless computers are an ideal translator for these two types of intelligence.
In one evening I got all the plots I needed from WolframAlpha, and wrote all the equations with [;\TeX;] the World. , I presented the issue of iterated equations, and put it in very simple terms.
The purpose of this note is to give a little description of my philosophy.
I believe that concrete operations help any student, not only children. In some sense when presented with a new subject, even though we may be fluent in the prerequisites requires a little getting used to.
I still remember what happened in 1973, when I landed in the Los Angeles International Airport (LAX), I was already 23, but for the better part of one year, I talked like a moron. My ego got a beating. I've always prided myself for my speaking abilities, and that was the first time I spoke in English all the time.
Why shouldn't other people, feel awkward also when confronted with simple stuff in a new way?
I do believe that all of us while in the novice stage of ANY subject, somehow regress in our development. I even believe that the pain is so insufferable in some cases, that we just refuse to learn new things.
Anyways, today when I saw that my graduate students got stumped by high school algebra, without flinching an eye, I just went ahead with an explanations as simple as I could muster.
I want to believe that I succeeded, and that by doing so, I helped these young people to move ahead in their understanding of math.
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