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Full 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.
Contents
Mathematics in Action.- Subitizing: The Neglected Quantifier.- Discerning a Progression in Conceptions of Magnitude During Children's Construction of Number.- Spontaneous mathematical focusing tendencies in mathematical development and education.- Leveraging Relational Learning Mechanisms to Improve Understanding of Place Value.- The complexity of basic number processing: A commentary from a neurocognitive perspective.- Understanding Fractions: Integrating Results from Mathematics Education, Cognitive Psychology, and Neuroscience.- Developing Fractions as Multiplicative Relations: A Model of Cognitive Reorganization.- Developing a Concept of Multiplication of Fractions: Building on Constructivist and Sociocultural Theory.- What's Perception got to do with it? Re-framing Foundations for Rational Number Concepts.- Commentary on Fractions.- Understanding Negative Numbers.- Integers as Directed Quantities.- Cognitive Science Foundations of Integer Understanding and Instruction.- Commentary on Negative Numbers: Aspects of Epistemology, Cognition, and Instruction.- Commentary on Negative Numbers: Aspects of Epistemology, Cognition, and Instruction.- Author index.- Subject index.
