Student Developmental Progressions in Multiplication and Division supports teachers in interpreting elementary students’ thinking and responding instructionally as they learn mathematics over time. Children in grades 3-5 undergo fascinating cognitive shifts as their math lessons grow more complex, but how can teachers prepare to observe and respond instructionally? With decades of experience in Cognitively Guided Instruction, author James Brickwedde provides problem types, emerging strategies, and instructional approaches to help teachers cognitively guide students' transitions within multiplication and division. Each chapter introduces a core mathematical idea alongside a summary and set of reflection questions to extend understanding. Topics include social conventions and language, the properties of operation needed in multiplication and division, strategy progressions, place value as a rate of ten, working with factors of ten, and much more. Ideal for elementary teachers reading together in a professional learning community or book study, this book demystifies students’ maturations from additive to multiplicative thinking and empowers teachers to be more strategic in their decision-making.

James Brickwedde is a veteran teacher and researcher in elementary, higher education, and professional development settings. He directs the Project for Elementary Mathematics in Minnesota, supporting teachers’ understanding of Cognitively Guided Instruction frameworks and practices. His research focuses on place value development and student transitions from additive to multiplicative thinking.