Constructing Number: Merging Perspectives from Psychology and Mathematics Education

Description

The book synergizes research on number across two disciplines—mathematics education and psychology. The underlying problem the book addresses is how the brain constructs number. The opening chapter frames the problem in terms of children’s activity, including mental and physical actions. Subsequent chapters are organized into sections that address specific domains of number: natural numbers, fractions, and integers. Chapters within each section address ways that children build upon biological primitives (e.g., subitizing) and prior constructs (e.g., counting sequences) to construct number. The book relies on co-authored chapters and commentaries at the end of each section to create dialogue between junior faculty and senior researchers, as well as between psychologists and mathematics educators. The final chapter brings this work together around the framework of children’s activity and additional themes that arise in the collective work. The book is aimed to appeal to mathematics educators, mathematics teacher educators, mathematics education researchers, educational psychologists, cognitive psychologists, and developmental psychologists. Front Matter ....Pages i-xxi Mathematics in Action (Anderson Norton, Martha W. Alibali)....Pages 1-10 Front Matter ....Pages 11-11 Subitizing: The Neglected Quantifier (Douglas H. Clements, Julie Sarama, Beth L. MacDonald)....Pages 13-45 Discerning a Progression in Conceptions of Magnitude During Children’s Construction of Number (Catherine Ulrich, Anderson Norton)....Pages 47-67 Spontaneous Mathematical Focusing Tendencies in Mathematical Development and Education (Jake McMullen, Jenny Yun-Chen Chan, Michèle M. M. Mazzocco, Minna M. Hannula-Sormunen)....Pages 69-86 Leveraging Relational Learning Mechanisms to Improve Place Value Instruction (Kelly S. Mix, Linda B. Smith, Sandra Crespo)....Pages 87-121 The Complexity of Basic Number Processing: A Commentary from a Neurocognitive Perspective (Bert De Smedt)....Pages 123-132 Front Matter ....Pages 133-133 Understanding Fractions: Integrating Results from Mathematics Education, Cognitive Psychology, and Neuroscience (Andreas Obersteiner, Thomas Dresler, Silke M. Bieck, Korbinian Moeller)....Pages 135-162 Developing Fractions as Multiplicative Relations: A Model of Cognitive Reorganization (Ron Tzur)....Pages 163-191 Developing a Concept of Multiplication of Fractions: Building on Constructivist and Sociocultural Theory (Martin A. Simon)....Pages 193-212 What’s Perception Got To Do with It? Re-framing Foundations for Rational Number Concepts (Percival G. Matthews, Ryan Ziols)....Pages 213-235 Commentary on Fractions (Sybilla Beckmann)....Pages 237-248 Front Matter ....Pages 249-249 Understanding Negative Numbers (Laura Bofferding)....Pages 251-277 Integers as Directed Quantities (Nicole M. Wessman-Enzinger)....Pages 279-305 Cognitive Science Foundations of Integer Understanding and Instruction (Sashank Varma, Kristen P. Blair, Daniel L. Schwartz)....Pages 307-327 Commentary on Negative Numbers: Aspects of Epistemology, Cognition, and Instruction (Guershon Harel)....Pages 329-339 Synergizing Research on Constructing Number: Themes and Prospects (Martha W. Alibali, Anderson Norton)....Pages 341-353 Back Matter ....Pages 355-370