RUME 26
2024
Omaha, Nebraska
In Defense of Transformational Activity: Analyzing Students’ Productive Reasoning about Equivalence
Page: 250
Equivalence is a foundational idea in mathematics and a key fixture in the K-16 curriculum. There is considerable evidence, however, that students at all levels experience difficulties with it. A prevailing explanation is that students rely too much on transformations; and yet, transformational activity is absolutely essential: it is the primary means by which one generates more tractable representations that are better suited to the situation at hand. Strikingly, we found no studies that directly examine students’ productive uses of transformational activity. To this end, we conducted a series of task-based interviews with undergraduate students in order to illustrate and account for productive instances of transformational activity across undergraduate mathematics. Our findings affirm a hypothesis from the literature that supplementing one’s transformational activity with notions of equivalence can support productive reasoning. Additionally, we extend this idea by providing detailed analyses of what these supplementary notions of equivalence entail.