Volume V. Translating Euclid: Creating a Human-Centered Mathematics
Stahl, G. (2013). "Translating Euclid: Creating a Human-Centered Mathematics." Morgan & Claypool Publishers. 221 pages.
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Download a free copy of Chapter 1, which contains an overview of the whole book: http://www.morganclaypool.com/doi/suppl/10.2200/S00492ED1V01Y201303HCI017
Chapter 1. Vision: The Cognitive Potential of Collaborative Dynamic Geometry
Chapter 2. History: The Origin of Geometry
Chapter 3. Philosophy: The Obfuscation of Geometry
Chapter 4. Mathematics: Demythologizing Geometry
Chapter 5. Technology: Deconstructing Geometry
Chapter 6. Collaboration: Group Geometry
Chapter 7. Research: Analyzing Geometry
Chapter 8. Theory: Resources for Geometry
Chapter 9. Pedagogy: Designing Geometry
Chapter 10. Practice: Doing Geometry
Chapter 11. Design-Based Research: Human-Centered Geometry
* Download pre-print: Translating Euclid preprint pdf
The following review was for a chapter published in the International Handbook of Collaborative Learning that was very similar in content to parts of Chapter 3 of Translating Euclid.
Book Review: Learning With and From Others: A Review of The International Handbook of Collaborative Learning
The International Handbook of Collaborative Learning. Cindy E. Hmelo-Silver, Clark A. Chinn, Carol K. K. Chan, & Angela O’Donnell (Eds.) (2013). New York, NY: Routledge, 516 pp. ISBN: 978-0-415-80573-5 (hb) $295. ISBN: 978-0-415-80574-2 (pb) $114.95.
Reviewed by Alan H. Schoenfeld, University of California at Berkeley
Chapter 4, “Theories of Cognition in Collaborative Learning,” by Gerry Stahl, provides an acute commentary on the state of the art. Stahl focuses on computer-supported collaborative learning (CSCL), but his findings are more general.
Stahl begins with a terse but useful historical and philosophical summary, tracing the evolution of theoretical perspectives that focus on the individual mind: (from Socrates through Kant and Husserl) to theories that are social in character (from Hegel’s conceptualization of the individual as a social being to the critical social theory, existential phenomenology and linguistic analysis engendered respectively by Marx, Heidegger, and Wittgenstein). These, in turn, provide the underpinnings for the approaches of contemporary theorists such as Latour, Engeström, Lave, Hutchins, Suchman, Kling and Schegloff.
What I find most useful about Stahl’s chapter, however, is a critique that resonates deeply with my own sense of what matters—a need for theory-based explanations at a level of mechanism with careful specification of the unit(s) of analysis. In critiquing the current state, Stahl also points the way forward:
The CSCL-related literature on small groups and on post-cognitive phenomena provide some nice studies of the pivotal role of small groups, but they rarely account for this level of description theoretically. They are almost always in the final analysis based on either a psychological view of mental processes at the individual level or a sociological view of rules at the community level. They lack a foundational conception of small groups as a distinct level of analysis and description. They often confuse analysis at the small-group level and at the societal level, and they lack a developed account of the relationships among the individual, small group, and community of practice. Yet, there are distinct phenomena and processes at each of these levels, and analyses at different levels of description reveal different insights. (pp. 83–84)
Although Stahl restricts his comments to CSCL, his comments apply much more broadly. Reflecting (and acting) on these issues would be good for all empirical researchers.
YouTube link: http://youtu.be/h66yKE48atE (50 min)
Lecture given by Gerry Stahl at the LINCS Center at the University of Gothenburg, Sweden, October 9, 2013. Presentation on the process of designing the technology, curriculum and research reported in "Translating Euclid".
Abstract: How should one translate the classic-education approach of Euclid’s geometry into the contemporary vernacular of social networking, computer visualization and discourse-centered pedagogy? How should one design the technology, mathematics, resources and presentation to incorporate collaborative discourse, computer manipulation and hands-on experience to support deep learning of mathematical thinking? What design-based-research approach can be used to explore and assess collaborative learning of dynamic geometry? (See Ch. 1, 5, 6, 11.)
Download of Powerpoint slides for presentation: http://GerryStahl.net/pub/designing.pdf
Alternative downloads of video: http://GerryStahl.net/elibrary/euclid/designing.mp4 (400 mB), http://GerryStahl.net/elibrary/euclid/designing_hd.mp4 (2,350 mB), http://GerryStahl.net/elibrary/euclid/designing_fullhd.mp4 (12,200 mB)
YouTube link: http://youtu.be/Os75d3LFhk4 (52 min)
Discussion session following lecture given by Gerry Stahl at the LINCS Center at the University of Gothenburg, Sweden, October 9, 2013, on the process of designing the technology, curriculum and research reported in "Translating Euclid".
Alternative download of video: http://GerryStahl.net/elibrary/euclid/designing_discussion.mp4 (400 mB)
YouTube link: http://youtu.be/GDVO4Q4B6ss (1 hour)
Lecture given by Gerry Stahl at the LINCS Center at the University of Gothenburg, Sweden, October 10, 2013. Presentation on the curriculum resources reported in "Translating Euclid".
Abstract: Euclidean geometry has trained students for over 2,000 years in rational, deductive thinking and mathematical practices. Computer-based dynamic geometry (Geometer’s Sketchpad, Cabri, GeoGebra, etc.) adds three dimensions: dynamic dragging, dynamic construction (including programming custom tools) and dynamic dependencies. With these, students can drag figures to discover dependencies as well as construct figures to create dependencies. Rather than accepting geometric propositions as otherworldly truths, students can now conceive them as results of their own “creative discovery” within a local knowledge community. How can geometry education be structured to emphasize this? (See Ch. 4, 5, 9, 10.)
Download of Powerpoint slides for presentation: http://GerryStahl.net/pub/didactics.pdf
Alternative downloads of video: http://GerryStahl.net/elibrary/euclid/didactics.mp4 (574 mB), http://GerryStahl.net/elibrary/euclid/didactics_hd.mp4 (3,000 mB),
YouTube link: http://youtu.be/Uvgb1Fjsx_Y (16 min)
Discussion session following lecture given by Gerry Stahl at the LINCS Center at the University of Gothenburg, Sweden, October 10, 2013, on the curricular resources reported in "Translating Euclid".
Alternative download of video: http://GerryStahl.net/elibrary/euclid/didactics_discussion.mp4 (142 mB)
YouTube link: http://youtu.be/6o1AlZlVbL4 (3 hours)
Data session led by Gerry Stahl with the NAIL group at the University of Gothenburg, Sweden, October 11, 2013. Analysis of the interaction data reported in "Translating Euclid".
Abstract: Students learning collaborative dynamic geometry must acquire various practical, interactive and cognitive skills. The data sessions will focus on logs taken from a sequence of eight hour-long online chat sessions involving three middle-school students recorded in Spring 2013. The students interacted in the Virtual Math Teams (VMT) collaboration environment incorporating the GeoGebra dynamic-mathematics software. Each session was guided by a written topic involving GeoGebra tasks. The logs capture all chat posts and GeoGebra actions (opening a GeoGebra tab, selecting a GeoGebra tool, creating or dragging a GeoGebra object, etc.). The logs will be available as spreadsheets that can be configured and filtered in useful ways. In addition, the sessions can be replayed in a digital replayer system, allowing for detailed study of actions and interactions. For the workshop, a series of excerpts will be selected from the eight sessions, chosen to capture changes in the student team’s ability to engage in collaboration, software usage and geometry task accomplishment. Analysis will aim to document how the team learned the underlying practices of engaging in dynamic geometry. (See Ch. 7.)
Download of Powerpoint slides for presentation: http://GerryStahl.net/pub/analysis.pdf
Alternative download of video: http://GerryStahl.net/elibrary/euclid/analysis.mp4 (1,410 mB).
YouTube link: http://youtu.be/vogBZjdniME (lecture version, 78 min)
YouTube link: http://youtu.be/GkwI7JBq1ZQ (alternate version, 106 min)
"Translating Euclid into CSCL: Issues in design-based research on computer-supported collaborative learning of significant mathematical discourse"
The Distinguished Lecture by Gerry Stahl in the School of Communication and Information, Rutgers University, New Brunswick, NJ. February 24, 2012.
Download of Powerpoint slides for presentation: http://GerryStahl.net/pub/rutgers2012.ppt.pdf.