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.

This book presents recent research on the role of space as a mechanism in language use and learning. It proceeds from the notion that cognition in real time, developmental time, and over evolutionary time occurs in space, and that the physical properties of space may provide insights into basic cognitive processes, including memory, attention, action, and perception. It looks at how physical space and landmarks are used in cognitive representations and serve as the basis of human cognition in a range of core mechanisms to index memories and ground meanings that are not themselves explicitly about space. The editors have brought together experimental psychologists, computer scientists, robotocists, linguists, and researchers in child language in order to consider the nature and applications of this research and in particular its implications for understanding the processes involved in language acquisition.