STRUCTURAL REASONING WITH RATIONAL EXPRESSIONS

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STRUCTURAL REASONING WITH RATIONAL EXPRESSIONS

Abstract

Many students struggle to make sense of algebraic expressions in math. This lack of understanding results in students making symbolic manipulation errors, hindering their procedural fluency. Researchers believe these errors are linked to students’ lack of structural reasoning. While research has shown that students rarely engage in expert structural reasoning, little is known about how students actually reason structurally. In this study, I interviewed six high school calculus students to study the way they identified, matched, and evaluated structures as they solved problems involving rational expressions and equations. I analyzed the participant interviews and outlined the matching process they used and the types of evaluations they made during this matching process. Consequently, I was able to confirm that students were using structural reasoning throughout the tasks and that effective student structural reasoning was characterized by identifying structures using operational hierarchical reasoning and matching them to correct rules. These findings have the potential to help teachers better instruct students on using and identifying structure, leading to less frustration by students and teachers in algebra.

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