Too often, mathematics and science are taught in isolation from each other and from meaningful problems that matter to students. This book draws on the authors' experiences with teacher colleagues, including time spent in their classrooms co-developing and refining lessons. The core of their approach is to encourage learners to pursue solutions to…

This book seeks to illustrate the research on mathematics competencies and disposition in China according to the conceptual development and empirical investigation perspective. Mathematics education in China has a distinguishing feature a focus of attention to mathematical competency. Paradoxically, there has not been an explicit, refined, and…

What is the relationship between addition and subtraction? How do individuals know whether an algorithm will always work? Can they explain why order matters in subtraction but not in addition, or why it is false to assert that the sum of any two whole numbers is greater than either number? It is organized around two big ideas and supported by…

Metaphors and analogies are more than figurative language suitable only for English classes and standardized test questions. They are "power tools" that can electrify learning in every subject and at all grade levels. Metaphors show students how to make connections between the concrete and the abstract, prior knowledge and unfamiliar concepts, and…

With the Seeing and Thinking Mathematically materials, students learn mathematics by doing mathematics, by using and connecting mathematical ideas, and by actively constructing their own understandings. In this unit students learn to see probability through a mathematical lens by exploring and creating games and simulations and by applying the…

Making connections becomes increasingly important as students proceed through middle school and high school. This book shows ways of embedding connective processes in instruction in grades 9-12. Problems invite mathematical modeling, unify diverse content, call for different representations, and encourage students to look back at their work to…

This document describes the contributions of African peoples to the science of mathematics. The development of a number system is seen as related to need. Names of numbers, time reckoning, gesture counting, and counting materials are examined. Mystical beliefs about numbers and special meanings in pattern are presented. Reproductions of patterns,…