Teaching Additive Inverses

This chapter presents two cases on teaching the additive inverse using part-whole and comparison models, each with two contrasting sub-cases illustrating different instructional approaches. In the TEPS approach (Cases 1a and 2a), tasks are situated in real-world contexts, and tape diagrams support the transition from concrete to abstract solutions. Deep questions promote problem-posing, meaning-making, and structural understanding of inverse relations, engaging students at constructive and interactive ICAP levels. By contrast, the conventional approach (Cases 1b and 2b) emphasizes computation, often beginning with abstract or semi-concrete representations. Word problems, if included, typically appear only at the end, and deep questions are rarely posed, keeping students’ cognitive engagement at passive or active levels. Each case is presented through a three-step process: readers first “think and prepare” by drafting a plan, then “read and annotate” the cases, and finally “stop and reflect” on representation use, deep questioning, ICAP level, and insights gained. The chapter provides analysis for the first three questions and summarizes common preservice teacher responses for the fourth, supporting readers’ learning and reflection.