Do mathematicians interpret equations asymmetrically?

Abstract

In studies of children's reasoning about equations, a major finding is that many children understand equality to be asymmetric. In this study, we investigate how experts interpret equations in order to determine whether and why they interpret equations asymmetrically. We do so by using a breaching experiment in which we present nine mathematicians with equations that have been purposefully reordered to see if they critique or correct the ordering. We found clear evidence that they apply norms of ordering to critique the texts. We characterize their explanations for why they prefer or expect one order over another by using six rationales that express why experts read equations asymmetrically. We consider the implications for how we characterize sophisticated meanings of the equals sign. Our findings show that mathematicians attend to the coherence of a text, the communicational needs of the reader, and imagined context to determine appropriate equation order.