Designing Learning Environments for Developing Understanding of Geometry and Space

are too intriguing to ignore (see, e.g., Cuoco & Goldenberg, in press). So is the evidence in students' eyes and on their faces. We must come to understand the new terrain well, so that its roughness becomes a part of, and not a detraction from, its beauty.

The perspective, rationale, planning, and writing of this chapter were supported in part by development funds from Education Development Center, Inc. (EDC), with additional support from the National Center for Research in Mathematical Sciences Education (NCRMSE) and EDC's Connected Geometry project, funded by the National Science Foundation (grant MDR-9252952). Major funding for the interviews with Jean-Marie and Colette Laborde and others at Institut d'Informatique et Mathématiques Appliquées (IMAG) was provided by NCRMSE, with additional support from Connected Geometry. Interviews with Nick Jackiw, Eugene Klotz, Judah Schwartz, and Michal Yerushalmy (whose significant intellectual contributions are, as yet, only partially reflected in this writing) and the final preparation of this chapter were supported in part by National Science Foundation grant RED-9453864. We are particularly grateful to Jean-Marie and Colette for the time they spent not only during our initial discussions, but also in reviewing the manuscript. We also acknowledge the contributions of Nicolas Balacheff, Bernard Capponi, and James King. Opinions (and errors) are ours, and do not necessarily reflect the views of any of the funders or contributors.

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