Springer, 2018. — 381 p. — (Research in Mathematics Education). — ISBN: 3319987666.
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.
Psychological PerspectivesHow Much as Compared to What: Relative Magnitude as a Key Idea in Mathematics Cognition
From Intuitive Spatial Measurement to Understanding of Units
Spatial Reasoning: A Critical Problem-Solving Tool in Children’s Mathematics Strategy Tool-Kit
More Space, Better Mathematics: Is Space a Powerful Tool or a Cornerstone for Understanding Arithmetic?
What Processes Underlie the Relation Between Spatial Skill and Mathematics?
CommentariesPart I Commentary 1: Deepening the Analysis of Students’ Reasoning About Length
Part I Commentary 2: Visualization in School Mathematics Analyzed from Two Points of View
Part I Commentary 3: Proposing a Pedagogical Framework for the Teaching and Learning of Spatial Skills: A Commentary on Three Chapters
Part I Commentary 4: Turning to Temporality in Research on Spatial Reasoning
Educational PerspectivesAnalyzing the Relation Between Spatial and Geometric Reasoning for Elementary and Middle School Students
Learning Through and from Drawing in Early Years Geometry
The Interaction Between Spatial Reasoning Constructs and Mathematics Understandings in Elementary Classrooms
Geometric Modeling of Mesospace Objects: A Task, its Didactical Variables, and the Mathematics at Stake
Visualization Abilities and Complexity of Reasoning in Mathematically Gifted Students’ Collaborative Solutions to a Visualization Task: A Networked Analysis
CommentariesPart II Commentary 1: Mathematics Educators’ Perspectives on Spatial Visualization and Mathematical Reasoning
Part II Commentary 2: Disparities and Opportunities: Plotting a New Course for Research on Spatial Visualization and Mathematics
Part II Commentary 3: Linking Spatial and Mathematical Thinking: The Search for Mechanism
On the Multitude of Mathematics Skills: Spatial-Numerical Associations and Geometry Skill?