Teaching Basic Properties of Multiplication

This chapter presents three cases on teaching the basic properties of multiplication: commutative, associative, and distributive. Each case includes two contrasting sub-cases demonstrating different instructional approaches. In the TEPS approach (Cases 8a, 9a, and 10a), worked examples are situated in real-world contexts and modeled with semi-concrete representations (e.g., cubes, drawings) that gradually transition to abstract solutions. Each task is solved using two or multiple strategies, which are compared to illustrate the targeted concept. Deep questions promote problem-solving, meaning-making, and comparisons, supporting students’ understanding of the properties. By contrast, the conventional approach (Cases 8b, 9b, and 10b) typically begins with abstract definitions and numerical examples, followed by semi-concrete representations to verify them. Real-world contexts, if included, primarily serve as a pretext for computation. Teacher questioning focuses on obtaining correct answers, allowing any method, which limits opportunities for sense-making. Lessons may leave misconceptions unaddressed, and comparisons, when opportunities arise, are often overlooked. The chapter applies the ICAP framework to analyze these instructional differences and their potential impact on students’ cognitive engagement.