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  • Gerry Stahl’s assembled texts volume #13

    Essays in Collaborative Dynamic Geometry

    Gerry Stahl

  • Essays in Collaborative Dynamic Geometry

    2

    Gerry Stahl's Assembled Texts

    • Marx and Heidegger

    • Tacit and Explicit Understanding in Computer Support

    • Group Cognition: Computer Support for Building Collaborative Knowledge

    • Studying Virtual Math Teams

    • Translating Euclid: Designing a Human-Centered Mathematics.

    • Constructing Dynamic Triangles Together: The Development of Mathematical Group Cognition

    • Essays in Social Philosophy

    • Essays in Personalizable Software

    • Essays in Computer-Supported Collaborative Learning

    • Essays in Group-Cognitive Science

    • Essays in Philosophy of Group Cognition

    • Essays in Online Mathematics Interaction

    • Essays in Collaborative Dynamic Geometry

    • Adventures in Dynamic Geometry

    • Global Introduction to CSCL

    • Editorial Introductions to ijCSCL

    • Proposals for Research

    • Overview and Autobiographical Essays

    • Theoretical Investigations

    • Works of 3-D Form

  • Essays in Collaborative Dynamic Geometry

    3

    Gerry Stahl’s assembled texts volume #13

    Essays in Collaborative Dynamic

    Geometry

    Gerry Stahl

    2015

  • Essays in Collaborative Dynamic Geometry

    4

    Gerry Stahl

    Gerry@GerryStahl.net

    www.GerryStahl.net

    Copyright © 2015, 2020 by Gerry Stahl

    Published by Gerry Stahl at Lulu.com

    Printed in the USA

    ISBN (paperback)

    ISBN (ebook)

  • Essays in Collaborative Dynamic Geometry

    5

    Introduction

    he essays in this volume are about the Virtual Math Teams project during its later years when it included a multi-user version of GeoGebra, supporting collaborative dynamic geometry. These essays supplement the more

    systematic presentations in Translating Euclid and Constructing Dynamic Triangles Together.

    References The essays in this volume were originally published as: (Stahl et al. 2010; Stahl 2012a; 2012b; 2012c; Öner & Stahl 2015; 2016; Khoo & Stahl 2015; Çakir & Stahl 2015; Stahl, Weimar, Fetter & Mantoan 2014a; 2014b)

    Stahl, G., Ou, J. X., Weusijana, B. K., Çakir, M. P., & Weimar, S. (2010). Multi-user GeoGebra for virtual math teams. GeoGebra: The New Language For The Third Millennium. 1(1), 117-126. Web: http://GerryStahl.net/pub/geogebra_romania.pdf.

    Stahl, G. (2012a). Designing a learning environment for promoting math discourse. In the proceedings of the 12th International Conference on Mathematical Education. Seoul, Korea. Web: http://GerryStahl.net/pub/icme_design.pdf, Slides: http://GerryStahl.net/pub/icme2012.ppt.pdf.

    Stahl, G. (2012b). Supporting group cognition, individual learning and community practices in dynamic geometry. In the proceedings of the 3rd International Conference on Emerging Intelligent Data and Web Technologies (EIDWT 2012). Bucharest, Romania. Web: http://GerryStahl.net/pub/eidwt2012.pdf, http://GerryStahl.net/pub/resources.pdf, http://GerryStahl.net/pub/eidwt.ppt.pdf.

    Stahl, G. (2012c). Evaluating significant math discourse in a learning environment. In the proceedings of the 12th International Conference on Mathematical Education. Seoul, Korea. Web: http://GerryStahl.net/pub/icme_discourse.pdf.

    Öner, D., & Stahl, G. (2015). Poster: Tracing the change in discourse in a collaborative dynamic-geometry environment: From visual to more mathematical. Presented at the

    T

  • Essays in Collaborative Dynamic Geometry

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    CSCL 2015, Gothenburg, Sweden. Web: http://GerryStahl.net/pub/cscl2015oner.pdf.

    Öner, D., & Stahl, G. (2016). Tracing the change in discourse in a collaborative dynamic-geometry environment: From visual to more mathematical. International Journal of Computer-Supported Collaborative Learning. 11 Web: http://GerryStahl.net/pub/esmoner.pdf.

    Öner, D. (2016). Tracing the change in discourse in a collaborative dynamic- geometry environment: From visual to more mathematical. International Journal of Computer-Supported Collaborative Learning. 11(1).

    Khoo, M., & Stahl, G. (2015). Constructing knowledge: A community of practice approach to evaluation in the VMT project. In the proceedings of the CSCL 2015. Gothenburg, Sweden. Web: http://GerryStahl.net/pub/cscl2015khoo.pdf.

    Çakir, M. P., & Stahl, G. (2015). Dragging as a referential resource for mathematical meaning making in a collaborative dynamic-geometry environment [nominated for best paper of conference]. In the proceedings of the CSCL 2015. Gothenburg, Sweden. Web: http://GerryStahl.net/pub/cscl2015cakir.pdf.

    Stahl, G., Weimar, S., Fetter, A., & Mantoan, A. (2014a). Collaborative exploration of geometric dependencies in dynamic geometry. In the proceedings of the Fifth North- American GeoGebra Conference 2014. Toronto, Canada. Web: http://GerryStahl.net/pub/ggb2014research.pdf.

    Stahl, G., Weimar, S., Fetter, A., & Mantoan, A. (2014b). Working group: Developing comprehensive open-source geometry curricula using GeoGebra. Presented at the Fifth North-American GeoGebra Conference 2014, Toronto, Canada. Web: http://GerryStahl.net/pub/ggb2014wg.pdf.

  • Essays in Collaborative Dynamic Geometry

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    Contents

    Introduction ..................................................................................... 5 References ................................................................................................................ 5

    Contents ........................................................................................... 7

    1. Multi-User GeoGebra for Virtual Math Teams ............. 11 The Virtual Math Teams Project ........................................................................ 11 Referencing support for collaboration ............................................................... 12 The VMT lobby, chat room and wiki ................................................................ 13 Integration of tools in the environment ............................................................ 16 Porting GeoGebra to VMT ................................................................................. 17 Designing for multi-user issues ........................................................................... 20 Acknowledgements ............................................................................................... 21 References .............................................................................................................. 22 Biographies ............................................................................................................. 22

    2. Designing a Learning Environment to Promote Math Discourse ....................................................................................... 24

    Introduction ........................................................................................................... 24 An Online Math Collaborative-Learning Environment ................................. 25 A Design-Based Research Approach ................................................................. 27 Technology Development ................................................................................... 29 Designing Activities .............................................................................................. 30 Curricular Goals .................................................................................................... 31 Geometric Dependencies .................................................................................... 32

  • Essays in Collaborative Dynamic Geometry

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    Conclusion ............................................................................................................. 33 References .............................................................................................................. 33

    3. Supporting Group Cognition, Individual Learning and Community Practices in Dynamic Geometry ................................ 36

    Introduction ........................................................................................................... 36 Increasing Skill Levels .......................................................................................... 38 Discourse and Technology about Dependencies ............................................. 40 References .............................................................................................................. 41

    4. Evaluating Significant Math Discourse in a Learning Environment .................................................................................. 43

    Math Cognition as Math Discourse ................................................................... 43 A Learning Environment for Math Discourse ................................................. 44 Researching Discourse Practices ........................................................................ 45 A Design-Based Research Approach ................................................................. 46 Discourse-Building Activities .............................................................................. 48 References ..............................................................................

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