Tools, Tricks and Topics Teachers Use for Integer Arithmetic

Abstract

Integer arithmetic is difficult for students worldwide. Although students’ integer thinking has frequently been studied, little is known about typical instructional practice for this difficult topic. Thus, to investigate what resources teachers use in their instruction, we surveyed U.S. middle-grade teachers who teach negative numbers. About half the teachers said they need more integer resources and most used Teachers Pay Teachers to seek such resources. More than 90% reported that number line models, thermometers, elevation, and money were at least somewhat important and more than 80% believed this for chip models. Moreover, which specific tool features students experience were analyzed. Horizontal number lines were used significantly more often than vertical. The physical tools used for chip models reflected arbitrary valence associations significantly more than meaning-based associations, but this was not true for virtual tools. The most common chip color-association was due to the commercial availability of yellow/red counters (73%), whereas each meaning-based color-association was used by fewer than 10% of teachers. Therefore, we need to a) study the integer learning impacts of the features of classroom resources actually used, b) reduce for-profit influences by making quality integer resources accessible to U.S. teachers in the spaces they look and c) provide criteria to support teachers to select resources irrespective of commercial availability.