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. For comparisons with positive number choices, students had more difficulty with “coldest” than “hottest”; however, the results were reversed for comparisons with only negative number choices. When working with mixed comparisons, students often chose the least of the cold as opposed to the least cold, suggesting that they saw hot and cold as categorical opposites rather than opposites on a continuum, with zero as a boundary.
Bofferding, L. & Farmer, S. (2018). Most and Least: Differences in Integer Comparisons Based on Temperature Comparison Language. International Journal of Science and Mathematics Education, 17(3), 545-563.