Organization and Freedom in Geometry Learning and Teaching
Rina Hershkowitz Weizmann Institute of Science
Writing this epilogue was not an easy task for me. I originally intended to reflect on each chapter, as well as on the book as a whole. However, especially in such a rich book, I found that focusing on the tapestry of the whole often led me away from particular, albeit worthy, issues raised in every chapter. Accordingly I foreground what seems to be at the heart of the book and only occasionally focus on particulars raised in any one of the chapters. Nonetheless, I commend each and every chapter because the authors have individually and collectively crafted ground-breaking work in the field.
This volume asserts a focus on "designing-learning environments for developing understanding of space and geometry," and indeed almost all the chapters can be viewed and examined on a continuum of a design and development process. The book in its three parts and its 19 different chapters expresses a unique and holistic approach to geometry learning, in which some characteristics seem especially prominent. The authors exercise a refreshing democracy of content, adopting a broad vision of what geometry and visualization could be, rather than what they often are in school. The authors also attend carefully to how students develop knowledge about space and geometry across a wide range of contexts.
The volume is characterized first by the variety of contexts that can serve as "geometrical starting points" or "geometrical springboards," as expressed by Lehrer, Jacobson, et al. in chapter 7, for designing learning environments in geometry. The chapters represent a diverse collection of meaningful situations and problems, a diversity that far exceeds that