Beyond PEMDAS: Teaching Students to Perceive Algebraic Structure
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Evidence shows that transforming expressions is a major stumbling block for many algebra students. Using Sfard's (1991) theory of reification, I highlight the important roles that the process of parsing and the notions of subexpression and structural template play in competent expression transformation. Based on these observations, I argue that one reason students struggle with expression transformation is the inattentiveness of traditional curricula to parsing, subexpressions, and structural templates. However, simply refocusing attention on these ignored aspects of algebra will not alone ensure that students avoid common pitfalls. After examining evidence that students are very prone to overgeneralize, I argue for a connectionist view of how people's minds work when they are learning algebra. Utilizing these additional insights, the instructional strategies I ultimately recommend are strategies that focus on structure, but in ways that will make structure a winning competitor for student attention.