The Power of Structure: Understanding Multiplicative Thinking
This workshop is part of the four-day institute Building Structure, Fluency, and Mathematical Reasoning lead by prominent researchers in math instruction. Create a personalized learning experience by attending a single session or the full institute.
This session will deepen participants’ understanding of multiplicative reasoning and how it differs fundamentally from additive reasoning. We will explore key multiplicative structures, including equal groups, comparison situations using “times as many,” arrays and fundamental differences, rate problems, to build a solid conceptual foundation. Participants will examine how students form composite units and why this shift in thinking is essential for fluent multiplication and division. The session will highlight a range of representations that make multiplicative structure visible, supporting stronger reasoning and problem solving. Finally, we will look at worked examples that clearly connect visual models to procedures, helping learners internalize the logic behind efficient strategies.
Key Learning Objectives:
- understanding how multiplicative reasoning fundamentally differs from additive reasoning, and why this shift matters for students’ mathematical development
- familiarity with major multiplicative structures, including equal groups, “times as many” comparison problems, arrays/area models, and rate situations
- insight into how learners build composite units and how to support this critical cognitive move
- strategies for using representations that reveal multiplicative structure, helping students see and make sense of relationships
- explore worked examples that connect visual models to formal procedures, building conceptual and procedural fluency
Presenter: Jonté Meyers, PhD
Grades: 3-8
