It is not surprising that artists and designers rely upon spatial reasoning in their work. What is perhaps less obvious is that the ability to think spatially plays an important part in scientific and mathematical problem solving. Moreover, spatial reasoning is not only linked to the work of professional scientists and mathematicians; it appears to be an important element in children's science and mathematics learning as well.
Numerous studies with children have shown that spatial reasoning can be effectively taught, especially through the use of manipulatives. Fewer studies have documented the effectiveness of software in promoting spatial thinking, and an even wider gap exists in exploring the way that spatial thinking can be enhanced by a combination of software and real-world activities with mathematical manipulatives.
This thesis examines the design issues involved in combining real-world manipulatives and software to create an engaging environment--an environment in which children create mathematical paper sculpture and in the process gain practice in spatial thinking activities. The software applications created -- HyperGami and JavaGami -- are designed not to drill spatial concepts into students, but to provide a way for children to engage in activities that are enjoyable and, at the same time, spatially and mathematically rich.
The cognitive results of this dissertation indicate -- with a few caveats -- that HyperGami and JavaGami are effective software environments for enhancing children's spatial thinking: students have shown increases in sophistication in their verbal descriptions of shapes, in their renderings of folding nets of shapes, and in their performance on standardized tests of spatial thinking. Moreover, students of all ages have used the systems in ways that have allowed them to customize their experiences with the software, and they have designed mathematical objects invested with personal meaning.
Chapters are in Adobe Acrobat .pdf format. See http://www.abdobe.com/ to download Acrobat Reader.
1.1 Overview. 1.2 Combining Manipulatives with Software. 1.3 HyperGami. 1.4 JavaGami. 1.5 Results. 1.6 Reader's Guide.
2.1 Some Definitions of Spatial Ability. 2.2 Spatial Ability and Science/Mathematics Achievement. 2.3 Is Spatial Ability Trainable? The Case for Manipulatives. 2.4 Beyond Manipulatives.
3.1 Description. 3.2 Work with Elementary, Middle, and High-School Students. 3.3 Design Lessons Learned. 3.4 Themes Discovered.
4.1 Description. 4.2 Implementation of JavaGami. 4.3 Addressing Design Issues in HyperGami. 4.4 Use of JavaGami.
5.1 Overview. 5.2 Net and Solid Card Matching. 5.3 Verbal Shape Description. 5.4 Polyhedron Drawings. 5.5 Folding Net Drawings. 5.6 Surface Development Test. 5.7 Cube Rotations. 5.8 Chapter Summary.
6.1 Overview. 6.2 Session #1: Getting Started. 6.3 Session #2: Capping and Stretching. 6.4 Session #3: A Goldfish Gift. 6.5 Session #4: Slicing. 6.6 Session #5: Mystery Shapes. 6.7 Discussion.
7.1 Related Work. 7.2 Contributions. 7.3 Future Plans. 7.4 What is REAL?