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Do your students suppose that 1/3 is greater than 1/2, since 3 is greater than 2? Do they believe that having "halves" means having two, and only two, congruent "pieces" of a whole?

What tasks can you offer--what questions can you ask--to determine what your students know or don't know--and move them forward in their thinking?

This book focuses on the specialised pedagogical content knowledge that you need to teach fractions effectively in grades 3-5. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that...

Do your students have "concept images" that limit their ideas of shapes to specific examples, oriented in particular ways? Do they confuse the size of an angle with the length of the rays in a drawing of an angle? When solving problems, do they mix up the concepts of perimeter-the distance around a shape, measured in linear units-and area-the region within the shape, measured in square units? What tasks can you offer-what questions can you ask-to determine what they know or don't know-and move them forward in their thinking? This book focuses on the specialized pedagogical content knowledge...

Curriculum materials are among the most pervasive and powerful influences on school mathematics. In many mathematics classes, student assignments, the questions the teacher asks, the ways students are grouped, the forms of assessment, and much more originate in curriculum materials. At the same time, teachers have considerable latitude in how they use their curriculum materials. Two classes making use of the same materials may differ markedly in what mathematics content is emphasized and how students are engaged in learning that content. This volume considers a variety of research tools for...