Proposition . Students should learn to solve problems in multiple ways. Can this be so or are we asking yet again our students learn even more than what is needed? The short answer is "yes." Let me explain. First, the math teaching community has embraced, I think correctly, the idea of multiple representations. This means looking at data and functions in multiple ways graphs, tables, formulas, and the like. In fact, I've written on this. See http://disted6.math.tamu.edu/newsletter/newsletters_new.htm#current_issue for the three articles. Second and more generally, the more facets of the same thing a person is familiar with, the better is his knowledge of it. When it comes to problem solving, the same rule applies. If a person can solve a problem in two or more different ways, this is an indicator of their understanding of the problem and techniques to solve it. If they can solve it in only one way, this is an indicator that they have a single me...
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