Knowing, doing, and teaching multiplication

摘要: This investigation analyzes the structure and process of multidigit multiplication. It includes a review recent theories mathematical knowledge description several fourth-grade math lessons conducted in regular classroom setting. Four types are identified: intuitive, concrete, computational, principled knowledge. The author considers each type terms its relation to instructional issues suggests that instruction should focus on strengthening connections among four types. Illustrations from sessions show children generating testing hypotheses when salient made between concrete materials principled, computational practices. Implications for teaching discussed along with suggestions future research.