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Volume 4. Studying Virtual Math Teams

Stahl, G. (2009). "Studying Virtual Math Teams." New York, NY: Springer. 626 pages.

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Studying Virtual Math Teams centers on detailed empirical studies of how students in small online groups make sense of math issues and how they solve problems by making meaning together. These studies are woven together with materials that describe the online environment and pedagogical orientation, as well as reflections on the theoretical implications of the findings in the studies. The nature of group cognition and shared meaning making in collaborative learning is a foundational research issue in CSCL. More generally, the theme of sense making is a central topic in information science. While many authors allude to these topics, few have provided this kind of detailed analysis of the mechanisms of intersubjective meaning making.

This book presents a coherent research agenda that has been pursued by the author and his research group. The book opens with descriptions of the project and its methodology, as well as situating this research in the past and present context of the CSCL research field. The core research team then presents five concrete analyses of group interactions in different phases of the Virtual Math Teams research project. These chapters are followed by several studies by international collaborators, discussing the group discourse, the software affordances and alternative representations of the interaction, all using data from the VMT project. The concluding chapters address implications for the theory of group cognition and for the methodology of the learning sciences. In addition to substantial introductory and concluding chapters, this important new book includes analyses based upon the author's previous research, thereby providing smooth continuity and an engaging flow that follows the progression of the research.

The VMT project has dual goals: (a) to provide a source of experience and data for practical and theoretical explorations of group knowledge building and (b) to develop an effective online environment and educational service for collaborative learning of mathematics. Studying Virtual Math Teams reflects these twin orientations, reviewing the intertwined aims and development of a rigorous science of small-group cognition and a Web 2.0 educational math service. It documents the kinds of interactional methods that small groups use to explore math issues and provides a glimpse into the potential of online interaction to promote productive math discourse.

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errata of the published book

These are the only errata in the published version known to the author as of the latest update of this page. They have been corrected in the pre-publication version. Please notify the author at Gerry@GerryStahl.net if you discover any additional errors.

p. 5 bottom: “four” => “five”
p. 114: add “drawing actions”
p. 129 top: Komis’
p. 149: 139 I believe so Ref to 128
p. 174: .54 ish => 4.54 ish
p. 250: peppers => pepperoni
p. 270: it’s => its
p. 363: 19 => 47
p. 363: 88 => 55
Pre-publication metadata for author was “Gerry G. Stahl” should be “Gerry Stahl”
Pre-publication metadata for title was “Exploring Group Cognition: Virtual Math Teams” should be “Studying Virtual Math Teams”
Metadata for Alan Zemel has arz27@drexel.edu rather than arz26@drexel.edu

download the pre-publication version here

* Download PDF free for reading online or printing: svmt.pdf

Note: The following materials were last revised January 1, 2009, from the final manuscript. This is a pre-publication version of the book. This version has not been edited, laid out or paginated by Springer Press. Please do not cite page numbers from this version or quote from it. This version is only for informal use and may not be duplicated.

table of contents

Click on a chapter title below to download a pdf file of that chapter
or download the whole draft: studying.pdf (24 MB).





Authors and Collaborators

Part I: Introducing Group Cognition in Virtual Math Teams

1. A chat about chat
2. The VMT vision
3. Mathematical discourse as group cognition
4. Interactional methods and social practices in VMT
5. From individual representations to group cognition

Part II: Studying Group Interaction in Virtual Math Teams

6. The sequential co-construction of the joint problem space (Johann W. Sarmiento)
7. The joint organization of visual, narrative and symbolic interactions (Murat Perit Cakir)
8. Question co-construction in VMT chats(Nan Zhou)
9. Resolving differences of perspective in a VMT session (Ramon Prudencio S. Toledo)

Part III: Studying Group Discourse in Virtual Math Teams

10. Representational practices in VMT (Richard Medina, Dan Suthers & Ravi Vatrapu)
11. Group agency in a VMT session (Elizabeth S. Charles & Wesley Shumar)
12. Group creativity in VMT (Johann W. Sarmiento)
13. Inscriptions, mathematical ideas and reasoning in VMT (Arthur B. Powell & Frank Lai)
14. Reading's work in VMT (Alan Zemel & Murat Cakir)

Part IV: Designing the VMT Collaboration Environment

15. The integration of dual interaction spaces (Martin Muehlpfordt & Martin Wessner)
16. designing a mix of synchronous and asynchronous media for VMT
17.Deictic referencing in VMT
18. Scripting group processes in VMT
19. Helping agents in VMT (Yue Cui, Rohit Kumar, Sourish Chaudhuri, Gahgene Gweon & Carolyn Rosé)

Part V: Representing Group Interaction in VMT

20. Thread-based analysis of patterns in VMT (Murat Cakir, Fatos Xhafa & Nan Zhou)
21. Studying response-structure confusion in VMT (Hugo Fuks)
22. A multi-dimensional coding procedure for VMT (Jan-Willem Strijbos)
23. Combining coding and conversation analysis of VMT chats(Alan Zemel, Fatos Xhafa, Murat Cakir)
24. Polyphonic inter-animation of voices in VMT (Stefan Trausan-Matu & Traian Rebedea)
25. A model for analyzing math knowledge buiding in VMT (Juan Dee Wee & Chee-Kit Looi)

Part VI: Conceptualizing Group Cognition in VMT

26. Meaning making in VMT
27. Critical ethnography in the VMT project (Terrence W. Epperson)
28. Toward a science of group cognition



Index of Names

Index of Terms