Mathematics

Validity-related issues are a growing topic within the mathematics education community. Until recently, validation has been treated as something to gather when convenient or is rarely reported in ways that conform to current standards for assessment development. This theoretically-focused proceeding adds to a burgeoning theoretical argument that validation should be considered a methodology within mathematics education scholarship. We connect to design-science research, which is a well-established framework within mathematics education.

In this study we investigate the teaching of the associative property in a natural classroom setting through observation of classroom video of several elementary math classes in a large urban school district. Findings indicate that the associative property was often conflated with the commutative property during teaching. The role of the associative property in many computational tasks remained fully implicit, even after the property had been formally introduced.

The language involved in de-contextualized integer comparisons poses challenges, as students may interpret “most” based on absolute values rather than on order. Using the context of temperature, we explored how students’ integer value comparisons differed based on question phrasing (which temperature is hottest, most hot, least hot, coldest, most cold, least cold) and on numbers presented (positive, negative, mixed). Participants included 88 second graders and 70 fourth graders from a rural school district in the Midwestern USA, and each student solved 36 integer comparisons.