You are here

Constructing Dynamic Triangles Together

Gerry Stahl
Cambridge University Press
Publication Date: 
Number of Pages: 
Learning in Doing: Social, Cognitive and Computational Perspectives
[Reviewed by
Whitney George
, on

Constructing Dynamic Triangles Together: The Development of Mathematical Group Cognition provides empirical support, within a mathematics education context, for the theory and practice of group cognition. This case study is part of a series of publications from the Virtual Math Teams (VMT) Project, a long-term collaboration among researchers at Drexel University, the Math Forum, and Rutgers University at Newark.

Constructing Dynamic Triangles Together uses 8 hours of online interaction between a virtual math team consisting of three 8th grade students during winter 2013 to provide rich examples of computer-supported collaborative learning and human-computer interactions. Unlike many attempts to study collaborative learning, this case study involves the students’ initial encounters with the given subject matter of dynamic-geometry construction and thus provides a very thorough investigation of the team’s development of the group unit for analysis.

The set-up is designed for easy reading. The first two chapters are devoted to understanding, developing, and analyzing mathematical cognition. The next 8 chapters each represent one hour of the 8-hour interaction between the students. Each hour focuses on a certain skill set that the students acquire during that time frame. The last two chapters summarize the case studies to provide an in-depth analysis of how a group of students can increase their mathematical knowledge. The findings are put into the context of the VMT Project framework for collaboration and group work and were used for improving future projects.

The 8 hours of student interaction are focused on a group called Cereal Team with members named Fruitloops, Cornflakes, and Cheerios. This team was chosen as the most collaborative team out of 34 teams of middle school students during WinterFest 2013. The eight chapters summarizing the group interactions are sprinkled with group mathematical practices such as “Drag points to test if geometric relationships are maintained” and “Drag vertices to explore what objects are dependent upon the positions of other objects.” The team practices represent teamwork and the ability to think and construct knowledge as a group. The 8 chapters covering the case study include screen shots of Cereal Team’s geometry construction chat dialogues which accompany the reading nicely and end with a summary of what was learned by the students and how the curriculum can be improved based off of issues that were experienced by Cereal Team.

When the Virtual Math Teams (VMT) Project began in 2003, the goal was to create an online environment for students to discuss math. The project turned into much more with VMT researchers meeting weekly and developing a scalable pedagogical model. This model was put to the test, so to speak, in Constructing Dynamic Triangles Together. While at times the book delves deep into theory and research, most of the book is easy reading. Anyone interested in group cognition, online pedagogy, or online curriculum will find this book interesting and useful.

Whitney George is an Assistant Professor at University of Wisconsin- La Crosse whose training is in Contact Topology and Mathematics Education. She has been involved with online teaching and learning through various organizations for the last 6 years. 

Introduction to the analysis
Researching mathematical cognition
Analyzing development of group cognition
Session 1: the team develops collaboration practices
Session 2: the team develops dragging practices
Session 3: the team develops construction practices
Session 4: the team develops tool-usage practices
Session 5: the team identifies dependencies
Session 6: the team constructs dependencies
Session 7: the team uses transformation tools
Session 8: the team develops mathematical discourse and action practices
Contributions to a theory of mathematical group cognition
Constructing dynamic triangles together.