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Common math misconceptions

Recently I had the opportunity to tutor a college student in geometry. She was taking the class for a third time, to achieve a "C" grade; a requirement for her teaching credential. Her past attempts had only resulted in "D"s. Her case was particularly unique because she suffered from a genetically induced "non-verbal learning disorder" relating to a visual/spatial perceptual impairment. To help her, I attended the class sessions with her, just like any other student would. I have to tell you, it was a real learning experience for me too, in more ways than one might expect. As it turned out, I had a few misconceptions about math that needed some reconciliation.

Geometry is of course math, and it and its' trigonometric counter part, may well represent the most abstract form of mathematic discipline, because these two math forms require you to think in three dimensional terms. It is a very visual form of math, and for someone who doesn't see things, or at lease perceive what they see the same way that most of us "normally" would, given the ambiguity of the word normal, it has to be down right frustrating. I would liken it to somebody who was colorblind taking a course in color photography, a blind person taking art appreciation or someone who is deaf, music appreciation. And yet, almost all of us harbor some anomalous facet of perception which makes us see things just a little differently. Add to that the paradoxical attribute that most people who teach math are gifted at it, love it and in the most extreme cases live with it in almost every aspect of their lives. In other words, they have a collection of neural synapses that has been fine tuned for dealing with mathematical complexities. In contrast, people who don't like math, don't have an aptitude for it, don't have an absolute love of it, don't teach it.

From the perspective of the student striving to deal with concepts foreign to his or her own perspective or sense of reality, and an instructor who deals with mathematical constructs as though they were as plain as the nose on their face, it is understandable that common misconceptions about math arise. Add to that, any level of mental dextral impairment on the part of the student, and you have an untenable situation. I was faced with trying to resolve just such an enigmatic perplexity, how to find some common vernacular to bring about a symbiotic union of a brilliant mathematician and well experience math instructor, with a student

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