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The Impact of Scale on Children’s Spatial Thought

Cathleen Heil
Publication Date: 
Number of Pages: 
[Reviewed by
Mary Beth Rollick
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This book is part of a series of theoretical and empirical studies in Mathematics Research in collaboration with Springer’s counterpart in Germany, Spektrum. This book would be of importance to researchers who are interested in the area of spatial thinking especially as it relates to children. The empirical study described in the book would also provide important information to those who are interested in geometry education in schools.  
The book contributes to the literature and understanding of spatial thinking in several key areas. This was a unique spatial reasoning study because it focused on school-aged children in real space. The empirical data was collected from fourth graders. Age-specific measures for small-scale and new large-scales tasks were developed and analyzed for validity. Finally, the dissertation study looked at the interaction of these small-scale tasks and large-scale tasks using correlation and regression analysis. 
The development of small-scale tasks fell into two categories: object-based transformation (OB) and egocentric perspective tasks (EGO). Examples of OB tasks are finding another view of a given shape after it had been rotated or identifying how a piece of paper had been folded then punched to produce a given result. Examples of EGO tasks include mentally going through a maze and identifying pictures of the path or making Left-Right judgments on a map. An interesting observation is that the directions for these tasks are written in German in the Appendix. 
No large-scale tests were available as a starting point so this study had to develop these measures. Tasks were focused on three subclasses based upon whether the child moved or not. An example of an environment-to-map task asked the child to use a pointer to indicate the direction of a certain unseen landmark.  An example of a map-to-environment task was to give the child a map with a location identified and ask the child to go to that location to place a disk there. And the example of the third category is the Treasure Hunt.    
Careful consideration was given not only to task development but also to scoring methods and a pilot study was used to help make these decisions. Results of the actual study suggest that there is an interaction between small-scale abilities and large-scale abilities. From this finding, it is suggested that while children would benefit from having experiences with the classroom activities like the OB and EGO tasks, children also need the experience of reasoning with maps.
Although the study was conducted on children, the findings are important across ages. Because the literature suggests that spatial abilities can be improved, this book provides a basis for including activities with maps in real space and gives suggestions for tasks that emphasize locating oneself in that real space.


Mary Beth Rollick is Professor Emerita at Kent State University, in Kent, Ohio. She continues to tutor undergraduate students and enjoys helping them to understand the “why” as well as the “how” of mathematics.