Bofferding L., Wessman-Enzinger N.M. (Eds.) Exploring the Integer Addition and Subtraction Landscape: Perspectives on Integer Thinking

Springer, 2018. — 308 p. — (Research in Mathematics Education). — ISBN: 978-3-319-90691-1.The emerging foundation of research on thinking about integers highlights students’ sophisticated reasoning about integers, demonstrated even by young children, and critical nonconventional conceptions that they can develop if integers are ignored. Understanding children’s thinking about integers is pivotal for planning better instructional experiences in elementary and middle school, preparing prospective elementary and middle school teachers, and supporting inservice teachers. An increase in research into integer thinking and learning in recent years highlighted the need to bring together multiple viewpoints to establish our current understanding of the integer landscape.Beginning the Journey: Children’s Thinking About Integer Addition and Subtraction
Playing with Integer Concepts: A Quest for Structure
Integer Play and Playing with Integers
Students’ Thinking About Integer Open Number Sentences
Multiple Pathways: Models and Metaphors for Integer Addition and Subtraction
Teaching Integers to Students with Disabilities: Three Case Studies
Take It Away or Walk the Other Way? Finding Positive Solutions for Integer Subtraction
Different Differences: Metaphorical Interpretations of “Difference” in Integer Addition and Subtraction
Challenges of Promoting Conceptual Change with Instructional Contexts
Guiding the Journey: (Prospective) Teachers’ Thinking About Integer Addition and Subtraction
Nuances of Prospective Teachers’ Interpretations of Integer Word Problems
Prospective Teachers’ Attention to Children’s Thinking About Integers, Temperature, and Distance
Using Models and Representations: Exploring the Chip Model for Integer Subtraction
Commentaries
Commentary on Chapters 1 to 3: Using Meaningful Analogies to Reflect on and Make Sense of Integers
Commentary on Chapters 4 to 7: Students’ Learning of Integer Addition and Subtraction Using Models
Commentary on Chapters 8 to 10: Teachers’ Knowledge and Flexibility — Understanding the Roles of Didactical Models and Word Problems in Teaching Integer Operations
Conclusion: Reflecting on the Landscape: Concluding Remarks