Translating Euclid : designing a human-centered mathematics /
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
San Rafael, Calif. :
Morgan & Claypool,
[2013]
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| Series: | Synthesis digital library of engineering and computer science.
Synthesis lectures on human-centered informatics ; # 17. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Figures
- Tables
- Logs
- Acknowledgments
- 1. Vision: the cognitive potential of collaborative dynamic geometry
- 1.1 Translation
- 1.2 The classic potential
- 1.3 The failed potential
- 1.4 The vision of potential
- 1.5 The key dependency
- 1.6 Virtual math teams
- 1.7 Group cognition
- 1.8 Resources theory
- 1.9 Design of resources
- 1.10 Introductory resources
- 1.11 Design-based research
- 10. Practice: doing geometry
- 11. Design-based research: human-centered geometry
- 2. History: the origin of geometry
- 2.1 Folk geometry
- 2.2 The first geometers
- 2.3 Plato's academy
- 2.4 Euclid's elements
- 2.5 Roman and English translations
- 2.6 Axiomatic geometry
- 2.7 Changing approaches to teaching geometry
- 3. Philosophy: the obfuscation of geometry
- 3.1 Epochs of ontological translation
- 3.2 The dialectic of reification
- 3.3 Beyond the ideology of individualism
- 3.4 Dynamic geometry as human centered
- 4. Mathematics: demythologizing geometry
- 4.1 Heirarchies of triangles and quadrilaterals
- 4.2 The mystery of the triangle incenter
- 4.3 Topics to explore triangles and their incenters
- 5. Technology: deconstructing geometry
- 5.1 The origin of dynamic geometry
- 5.2 An example of dynamic-geometry construction
- 5.3 Defining custom tools
- 5.4 Dynamic dragging
- 5.5 Dynamic construction
- 5.6 Dynamic dependencies
- 6. Collaboration: group geometry
- 6.1 Supporting collaborative discourse and action
- 6.2 Supporting dynamic dragging and co-presence
- 6.3 Supporting dynamic construction and intersubjective understanding
- 6.4 Supporting dynamic dependencies and group cognition
- 6.5 Supporting reflection, assessment, and research
- 7. Research: analyzing geometry
- 7.1 Researchers design dependencies
- 7.2 Teachers design dependencies
- 7.3 Students design dependencies
- 7.4 Working with dependencies
- 8. Theory: resources for geometry
- 8.1 An excerpt of computer-supported discourse
- 8.2 Co-presence in computer-supported discourse
- 8.3 Intersubjective shared understanding
- 8.4 Group cognition
- 8.5 Resources for connecting levels of analysis
- 8.6 Interconnected planes
- 8.7 The collaborative emergence of resources
- 8.8 Research on artifacts
- 8.9 Resources for collaboration and mathematics
- 8.10 Referential resources for a math problem
- 8.11 Toward a theory of resources
- 9. Pedagogy: designing geometry
- 9.1 Design-based research cycles of trials
- 9.2 A trial without curricular resources
- 9.3 Overcoming technological barriers
- 9.4 Discourse about math difficulties
- 9.5 Cycles of problems
- 9.6 Curriculum design criteria
- 9.7 Practices as resources
- Author index
- Bibliography
- Author's biography.