Translating Euclid: Designing a Human-Centered Mathematics (Paperback)

Gerry Stahl


Translating Euclid reports on an effort to transform geometry for students from a stylus-and-clay-tablet corpus of historical theorems to a stimulating computer-supported collaborative-learning inquiry experience.

The origin of geometry was a turning point in the pre-history of informatics, literacy, and rational thought. Yet, this triumph of human intellect became ossified through historic layers of systematization, beginning with Euclid’s organization of the Elements of geometry. Often taught by memorization of procedures, theorems, and proofs, geometry in schooling rarely conveys its underlying intellectual excitement. The recent development of dynamic-geometry software offers an opportunity to translate the study of geometry into a contemporary vernacular. However, this involves transformations along multiple dimensions of the conceptual and practical context of learning.

Translating Euclid steps through the multiple challenges involved in redesigning geometry education to take advantage of computer support. Networked computers portend an interactive approach to exploring dynamic geometry as well as broadened prospects for collaboration. The proposed conception of geometry emphasizes the central role of the construction of dependencies as a design activity, integrating human creation and mathematical discovery to form a human-centered approach to mathematics.

This book chronicles an iterative effort to adapt technology, theory, pedagogy and practice to support this vision of collaborative dynamic geometry and to evolve the approach through on-going cycles of trial with students and refinement of resources. It thereby provides a case study of a design-based research effort in computer-supported collaborative learning from a human-centered informatics perspective.

Table of Contents: Acknowledgments / Background / Vision: The Cognitive Potential of Collaborative Dynamic Geometry / History: The Origin of Geometry / Philosophy: The Obfuscation of Geometry / Mathematics: Demythologizing Geometry / Technology: Deconstructing Geometry / Collaboration: Group Geometry / Research: Analyzing Geometry / Theory: Resources for Geometry / Pedagogy: Designing Geometry / Practice: Doing Geometry / Design-Based Research: Human-Centered Geometry / Author Indes / Bibliography / Author's Biography






目錄:致謝 / 背景 / 願景:協作動態幾何的認知潛力 / 歷史:幾何學的起源 / 哲學:幾何學的混淆 / 數學:解密幾何學 / 技術:解構幾何學 / 協作:群體幾何學 / 研究:分析幾何學 / 理論:幾何學資源 / 教學法:設計幾何學 / 實踐:實踐幾何學 / 基於設計的研究:以人為中心的幾何學 / 作者索引 / 參考文獻 / 作者簡介