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Full Description
Over the past few decades there has been increased interest in how students and teachers think and learn about negative numbers from a variety of perspectives. In particular, there has been debate about when integers should be taught and how to teach them to best support students' learning. This book brings together recent work from researchers to illuminate the state of our understanding about issues related to integer addition and subtraction with a goal of highlighting how the variety of perspectives support each other or contribute to the field in unique ways.
In particular, this book focuses on three main areas of integer work: students' thinking, models and metaphors, and teachers' thinking. Each chapter highlights a theoretically guided study centered on integer addition and subtraction. Internationally known scholars help connect the perspectives and offer additional insights through section commentaries. This book is an invaluable resource to thosewho are interested in mathematics education and numerical thinking.
Contents
Chapter1: Playing with Integer Concepts: A Quest for Structure.- Chapter2: Integer Play and Playing with Integers.- Chapter3: Students' Thinking about Integer Open Number Sentences.- Chapter4: Teaching Integers to Students with Disabilities: Three Case Studies.- Chapter5: Take it Away or Walk the Other Way? Finding Positive Solutions for Integer Subtraction.- Chapter6: Different Differences: Metaphorical Interpretations of 'Difference' in Integer Addition and Subtraction.- Chapter7: Challenges of Promoting Conceptual Change with Instructional Contexts.- Chapter8: Nuances of Prospective Teachers' Interpretations of Integer Word Problems.- Chapter9: Prospective Teachers' Attention to Children's Thinking about Integers, Temperature, and Distance.- Chapter10: Using Models and Representations: Exploring the Chip Model for Integer Subtraction.- Chapter11: Commentary on Chapters 1 to 3 - Using Meaningful Analogies to Reflect on and Make Sense of Integers.- Chapter12: Commentary on Chapters4 to 7 - Students' Learning of Integer Addition and Subtraction using Models.- Chapter13: Commentary on Chapters 8 to 10 - Teachers' Knowledge and Flexibility: Understanding the Roles of Didactical Models and Word Problems in Teaching Integer Operations.- Chapter14: Reflecting on the Landscape: Concluding Remarks.
