Designing Learning Environments for Developing Understanding of Geometry and Space

Linda Zech, Nancy J. Vye, John D. Bransford, Susan R. Goldman, Brigid J. Barron, Dan L. Schwartz, Rachelle Kisst-Hackett, Cynthia Mayfield-Stewart, and the Cognition and Technology Group

Vanderbilt University

In this chapter we describe preliminary research on three geometry adventures that are part of The Adventures of Jasper Woodbury problem- solving series ( Cognition and Technology Group at Vanderbilt University [ CTGV], 1990). The overall goal of the series (12 adventures) is to anchor or situate mathematics instruction in meaningful, authentic, real-life problem-solving environments that provide a basis for understanding the value and excitement of mathematical thinking. After solving a Jasper adventure, students are encouraged to reflect on their problem-solving strategies and deepen their understanding by continuing to explore important mathematical concepts that were involved in the adventure (e.g., CTGV, 1992, 1993, 1994).

The three Jasper adventures that focus on geometry are consistent with Geddes ( 1992) recommendations for teaching geometry in the middle school. She emphasized the need for students to explore their world and enjoy new applications of mathematics in their environment. Much of the current instruction in geometry fails to help students appreciate its usefulness for solving real-world problems ( Zech et al., 1994).

Our experiences with students' lack of knowledge of the usefulness and applications of geometry had a major impact on our design of the three Jasper geometry adventures that we discuss in this chapter. Our goal was to create situations that would help students (and often their teachers) understand the power of geometrical thinking in everyday problem solving. Like all the other Jasper adventures, the three that focus on geometry include a 15- to 20-min video story involving one or two main characters. At the end of the story, the characters are faced with a challenge. When the challenge is posed, students in the classroom move from the passive role of watching the videodisc to the active role of trying to "meet" the chal

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