Teaching Basic Properties of Addition

This chapter presents two cases on teaching basic addition properties: The commutative and associative properties, with the latter implicitly addressed through the “make a ten to add” strategy. Each case includes two contrasting sub-cases illustrating different instructional approaches. In the TEPS approach (Cases 6a and 7a), worked examples are situated in real-world contexts and modeled with semi-concrete representations (e.g., counters, ten-frames), gradually transitioning to abstract solutions. Deep questions stimulate problem-posing, meaning-making, and comparisons, enhancing students’ understanding of the targeted properties or strategies. In contrast, the conventional approach (Cases 6b and 7b) typically begins with abstract definitions and numerical examples. Semi-concrete representations are used mainly to verify answers, and real-world contexts serve primarily as a pretext for computation. Teacher questions focus on eliciting answers rather than promoting sense-making, and opportunities for comparisons are rarely taken. The chapter employs the three-step process—think and prepare, read and annotate, stop and reflect—to present the cases and analyzes instructional differences using the ICAP framework, highlighting their potential impact on students’ learning and cognitive engagement.