Visualizing Mathematics: The Role of Spatial Reasoning in Mathematical Thought

Description

This unique volume surveys recent research on spatial visualization in mathematics in the fields of cognitive psychology and mathematics education. The general topic of spatial skill and mathematics has a long research tradition, but has been gaining attention in recent years, although much of this research happens in disconnected subfields. This volume aims to promote interaction between researchers, not only to provide a more comprehensive view of spatial visualization and mathematics, but also to stimulate innovative new directions in research based on a more coordinated effort. It features ten chapters authored by leading researchers in cognitive psychology and mathematics education, as well as includes dynamic commentaries by mathematics education researchers on cognitive psychology chapters, and by cognitive psychologists on mathematics education chapters. Among the topics included: From intuitive spatial measurement to understanding of units. Spatial reasoning: a critical problem-solving tool in children’s mathematics strategy tool-kit. What processes underlie the relation between spatial skill and mathematics? Learning with and from drawing in early years geometry. Communication of visual information and complexity of reasoning by mathematically talented students. Visualizing Mathematics makes substantial progress in understanding the role of spatial reasoning in mathematical thought and in connecting various subfields of research. It promises to make an impact among psychologists, education scholars, and mathematics educators in the convergence of psychology and education. Front Matter ....Pages i-xv Front Matter ....Pages 1-1 How Much as Compared to What: Relative Magnitude as a Key Idea in Mathematics Cognition (Jamie Jirout, Nora S. Newcombe)....Pages 3-24 From Intuitive Spatial Measurement to Understanding of Units (Eliza L. Congdon, Marina Vasilyeva, Kelly S. S. Mix, Susan C. Levine)....Pages 25-46 Spatial Reasoning: A Critical Problem-Solving Tool in Children’s Mathematics Strategy Tool-Kit (Beth M. Casey, Harriet Fell)....Pages 47-75 More Space, Better Mathematics: Is Space a Powerful Tool or a Cornerstone for Understanding Arithmetic? (Krzysztof Cipora, Philipp Alexander Schroeder, Mojtaba Soltanlou, Hans-Christoph Nuerk)....Pages 77-116 What Processes Underlie the Relation Between Spatial Skill and Mathematics? (Christopher Young, Susan C. Levine, Kelly S. S. Mix)....Pages 117-148 Front Matter ....Pages 149-149 Part I Commentary 1: Deepening the Analysis of Students’ Reasoning About Length (Michael T. Battista, Leah M. Frazee, Michael L. Winer)....Pages 151-163 Part I Commentary 2: Visualization in School Mathematics Analyzed from Two Points of View (A. Gutiérrez)....Pages 165-169 Part I Commentary 3: Proposing a Pedagogical Framework for the Teaching and Learning of Spatial Skills: A Commentary on Three Chapters (Tom Lowrie, Tracy Logan)....Pages 171-182 Part I Commentary 4: Turning to Temporality in Research on Spatial Reasoning (Nathalie Sinclair)....Pages 183-191 Front Matter ....Pages 193-193 Analyzing the Relation Between Spatial and Geometric Reasoning for Elementary and Middle School Students (Michael T. Battista, Leah M. Frazee, Michael L. Winer)....Pages 195-228 Learning Through and from Drawing in Early Years Geometry (Nathalie Sinclair, Joan Moss, Zachary Hawes, Carol Stephenson)....Pages 229-252 The Interaction Between Spatial Reasoning Constructs and Mathematics Understandings in Elementary Classrooms (Tom Lowrie, Tracy Logan)....Pages 253-276 Geometric Modeling of Mesospace Objects: A Task, its Didactical Variables, and the Mathematics at Stake (Patricio Herbst, Nicolas Boileau)....Pages 277-308 Visualization Abilities and Complexity of Reasoning in Mathematically Gifted Students’ Collaborative Solutions to a Visualization Task: A Networked Analysis (A. Gutiérrez, R. Ramírez, C. Benedicto, M. J. Beltrán-Meneu, A. Jaime)....Pages 309-337 Front Matter ....Pages 339-339 Part II Commentary 1: Mathematics Educators’ Perspectives on Spatial Visualization and Mathematical Reasoning (Beth M. Casey)....Pages 341-345 Part II Commentary 2: Disparities and Opportunities: Plotting a New Course for Research on Spatial Visualization and Mathematics (Kelly S. S. Mix, Susan C. Levine)....Pages 347-353 Part II Commentary 3: Linking Spatial and Mathematical Thinking: The Search for Mechanism (Nora S. Newcombe)....Pages 355-359 On the Multitude of Mathematics Skills: Spatial-Numerical Associations and Geometry Skill? (Krzysztof Cipora, Philipp A. Schroeder, Hans-Christoph Nuerk)....Pages 361-370 Back Matter ....Pages 371-378