Constructing Dynamic Triangles Together
The Development of Mathematical Group Cognition

This study illustrates how groups learn through collaboration, mathematical discourse, and problem solving in a guided sequence of online topics.

Gerry Stahl (Author)

9781107127913, Cambridge University Press

Hardback, published 19 November 2015

294 pages, 40 b/w illus. 63 tables
23.7 x 16 x 2.5 cm, 0.6 kg

'Anyone interested in group cognition, online pedagogy, or online curriculum will find this book interesting and useful.' Whitney George, Mathematical Association of America

Rational thinking as exemplified in mathematical cognition is immensely important in the modern world. This book documents how a group of three eighth-grade girls developed specific group practices typical of such thinking in an online educational experience. A longitudinal case study tracks the team through eight hour-long sessions, following the students' meaning-making processes through their mutual chat responses preserved in computer logs coordinated with their geometric actions. The examination of data focuses on key areas of the team's development: its effective team collaboration, its productive mathematical discourse, its enacted use of dynamic-geometry tools, and its ability to identify and construct dynamic-geometry dependencies. This detailed study of group cognition serves as a paradigmatic example of computer-supported collaborative learning, incorporating a unique model of human-computer interaction analysis applied to the use of innovative educational technology. A valuable resource for researchers, instructors, and students alike, it offers concrete suggestions for improving educational practice.

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.

Subject Areas: Human-computer interaction [UYZ], Geometry [PBM], Mathematics [PB], Educational equipment & technology, computer-aided learning [CAL JNV], Educational psychology [JNC], Psychology [JM]