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One of the most important mathematical concepts at every level is the concept of form.Starting in elementary school arithmetic, continuing through high school algebra and trigonometry, throughout calculus and in advanced graduate mathematics, students are taught and graded on how to change forms.Many students who master the techniques of such form changes as completing the square, factoring and expanding polynomials do not know why or when to perform these operations.Little is said about the concept of forms or about the important aspects of forms.There is more to know about forms than how to change forms.Form changes should be treated as tactics in the strategies of analytical problem solving.This paper describes the principles concerning forms, which are usually omitted from the appropriate texts, and the important place of forms in the strategies of mathematics.
Andrew Grossfield (Wed,) studied this question.