Designing Learning Environments for Developing Understanding of Geometry and Space

By Richard Lehrer; Daniel Chazan | Go to book overview

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A Role for Geometry in General Education
E. Paul Goldenberg, Albert A. Cuoco, and June Mark Education Development Center, Inc.Readers of a book with this title certainly don't need to be sold on the virtues of geometry. But virtues are not enough to justify elevating any one body of knowledge or ideas--whether as a discrete course, or as a thread interwoven into other courses--to a status that takes significant time away from other virtuous bodies of knowledge or ideas. There is a great deal worth learning, and it cannot all be taught in school. So, why geometry?Geometry is not merely an attractive side dish in a balanced mathematical diet, but an essential part of the entrée. We make two claims: Geometry, broadly conceived, can help students connect with mathematics, and geometry can be an ideal vehicle for building what we call a "habits-of-mind perspective." After a brief outline of the argument, the majority of this chapter is devoted to giving meaning and support, with examples: the notion of "geometry, broadly conceived," the proposition that it helps students connect, the further claim that the connection is with mathematics, and the notion of a habits-of-mind perspective and its importance. Claim 1: Geometry Can Help Students Connect with Mathematics
Students connect well with properly selected geometric studies. The many hooks include no less than art, physical science, imagination, biology, curiosity, mechanical design, and play.
Geometry also connects richly with the rest of mathematics. Assuming a kind of transitive property, geometry's connections, both to students and to the rest of mathematics, might help us build good bridges, attracting more students--and a more diverse group of students--to mathematics in general.

As we explain briefly next (for greater detail, see Goldenberg, 1996), the needs of both the general education student and those students who will

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Designing Learning Environments for Developing Understanding of Geometry and Space
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