Designing Learning Environments for Developing Understanding of Geometry and Space

By Richard Lehrer; Daniel Chazan | Go to book overview

teachers (and parents and curriculum administrators) must be able to start out feeling that what they do, they do for the sake of geometry. But they must be able to end up feeling that what they have done, they have done for the sake of mathematics, and, even more, for the sake of good thinking.


ACKNOWLEDGMENTS

This chapter is adapted from the paper "Making Connections With Geometry," originally prepared for the keynote address to the Geometry Working Group at the International Congress of Mathematics Education, ICME 7, Université Laval, Québec, August 1992, and first published in 1994 in Czech translation in Pokroky matematiky, fyziky a astronomie [Advances in Mathematics, Physics and Astronomy], Association of Czech Mathematicians and Physicists, 39, 275-304. This work was supported in part by the Science Foundation, grant numbers MDR-8954647, MDR-9054677, and MDR-9252952, with additional support from Apple Computer, Inc. The views represented here are not necessarily shared by any of the funders. We are very grateful for the substantial intellectual and editorial contributions made by Glenn Kleiman at various stages of the preparation of this document and its many ancestors.


REFERENCES

Abbott, E. A. ( 1980). Flatland. San Francisco, CA: Arion.

Arcavi, A., & Nachmias, R. ( 1990). "Desperately looking for the focus". Mathematics in School, 19(2), 19-23.

Banchoff, T. ( 1991). "Dimension". In L. Steen (Ed.), On the shoulders of giants (pp. 11-59). Washington, DC: National Academy Press.

Blumberg, S. ( 1991). Michael Moschen: In motion. Great Performances Series, Dance in America. New York: In Motion Productions with WNET.

Cuoco, A. A. ( 1993). "Action to process: Constructing functions from algebra word problems". Intelligent Tutoring Media, 4 (3/4), 117-127.

Cuoco, A. A., & Goldenberg, E. P. ( 1992). "Mathematical induction in a visual context". Interactive Learning Environments, 2 (3/4), 181-203.

Cuoco, A. A., Goldenberg, E. P., & Mark, J. ( 1995). "Connecting geometry with the rest of mathematics". In P. A. House & A. F. Coxford (Eds.), Connecting mathematics across the curriculum; NCTM 1995 yearbook (pp. 183-197). Reston, VA: National Council of Teachers of Mathematics.

Cuoco, A. A., Goldenberg, E. P., & Mark, J. ( 1996). "Habits of mind: An organizing principle for mathematics curriculum". Journal of Mathematical Behavior, 15( 4), 375-402. [http:\\ www.edc.org\LTT\ConnGeo\HOM.html]

Education Development Center, Inc. (in press). Connected geometry. Chicago: Everyday Learning Corporation.

Eisenberg, T., & Dreyfus, T. ( 1991). "On the reluctance to visualize in mathematics". In W. Zimmermann & S. Cunningham (Eds.), Visualization in teaching and learning mathematics (pp. 25-37). Washington, DC: Mathematical Association of America.

Feurzeig, W. ( 1994). "Explaining function machines". Intelligent Tutoring Media, 4 (3/4),97-108.

Goldenberg, E. P. ( 1996). "Habits of mind" as an organizer for the curriculum. Journal of Education, 178, ( 1), 13-34.

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