Constructing Number (eBook)

Anderson Norton is Professor in the Department of Mathematics at Virginia Tech. His research focuses on the epistemology of mathematics. This work has generated interdisciplinary collaborations with psychologists and neuroscientists. Prior to this volume, Norton served as chair of the steering committee for the North American Chapter of the International Group for the Psychology of Mathematics Education, chair of the editorial panel for the Journal for Research in Mathematics Education, and guest editor (along with Julie Nurnberger-Haag) for a special issue of the Journal of Numerical Cognition—bridging frameworks from psychology and mathematics education. Martha W. Alibali is Vilas Distinguished Achievement Professor in the Departments of Psychology and Educational Psychology atthe University of Wisconsin-Madison. Her research investigates processes of knowledge change in cognitive development and mathematics learning. She also conducts basic research on gestures and on communication processes in instructional settings. She collaborates with scholars from a range of fields, including mathematics education, educational psychology, communicative disorders and computer science. She is a recipient of the Friedrich Wilhelm Bessel Research Prize from the Alexander von Humboldt Foundation, and she is co-author (with Robert Siegler) of the cognitive development textbook, Children’s Thinking.

1. Mathematics in Action2. Subitizing: The Neglected Quantifier3. Discerning a Progression in Conceptions of Magnitude During Children’s Construction of Number4. Spontaneous mathematical focusing tendencies in mathematical development and education5. Leveraging Relational Learning Mechanisms to Improve Understanding of Place Value6. The complexity of basic number processing: A commentary from a neurocognitive perspective7. Understanding Fractions: Integrating Results from Mathematics Education, Cognitive Psychology, and Neuroscience8. Developing Fractions as Multiplicative Relations: A Model of Cognitive Reorganization9. Developing a Concept of Multiplication of Fractions: Building on Constructivist and Sociocultural Theory10. What’s Perception got to do with it? Re-framing Foundations for Rational Number Concepts11. Commentary on Fractions12. Understanding Negative Numbers13. Integers as Directed Quantities14. Cognitive Science Foundations of Integer Understanding and Instruction15. Commentary on Negative Numbers: Aspects of Epistemology, Cognition, and Instruction16. Commentary on Negative Numbers: Aspects of Epistemology, Cognition, and InstructionAuthor indexSubject index