Translating Euclid : designing a human-centered mathematics /

Bibliographic Details
Main Author: Stahl, Gerry
Format: eBook
Language:English
Published: San Rafael, Calif. : Morgan & Claypool, [2013]
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.