Variables : what are they and why are they important?
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As a student in MATH 412 last semester, I encountered literature that suggested Algebra I students’ difficulty with that subject stemmed from their misconceptions concerning the concept of variable. Indeed, the transition from junior high school to high school mathematics is challenging enough and these things that we call variables truly form the base from which the concepts of Algebra develop. A variable can be identified as a special type of mapping, from a set of objects onto a number system. This mapping is based upon the measurement of some characteristic of the objects. Frequently, a variable is not named using a word or a phrase, but rather with an abstract symbol (i.e. a letter). Most of the Algebra textbooks I have examined have defined a variable as a letter that stands for a number. This seemingly simplistic treatment of the concept of variable may form the basis for why students’ understanding of variables is too narrow.