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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.
Nicole M. Wessman-Enzinger is an assistant education professor at George Fox University. Previously, she was an assistant mathematics professor at Olivet Nazarene University (2010-12). She earned a PhD in mathematics education from Illinois State University in 2015. Her research interests are centered on children's and prospective teachers' thinking about integers and ways to playfully engage in mathematics.
Laura Bofferding is an associate professor of mathematics education at Purdue University. She earned a PhD in Curriculum Studies at Stanford University in 2011. She is the recipient of an NSF CAREER award for Leveraging Contrasting Cases to Investigate Integer Understanding. Her research interests include pre-K and elementary students' cognitive development and understanding of mathematics, with a current focus on negative numbers; use of games, stories, and contrasting worked examples to support children's numerical understanding; the interplay between teachers'use of questioning, number talks, and students' mathematical reasoning; and the sequencing of mathematical topics.
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.
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