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E-raamat: Constructing Dynamic Triangles Together: The Development of Mathematical Group Cognition

(Drexel University, Philadelphia)
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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.

A longitudinal study of eight sessions of online teamwork by three girls learning geometry as novices, this book presents innovative approaches and persuasive insights into computer-supported collaborative learning of mathematics. It offers valuable resources for researchers, instructors, and students interested in group cognition, educational technology, mathematics education, and human-computer interaction.

Arvustused

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

Muu info

This study illustrates how groups learn through collaboration, mathematical discourse, and problem solving in a guided sequence of online topics.
List of Figures x
List of Logs xii
Series Foreword xv
Preface xvii
Acknowledgments xix
Introduction to the Analysis 1(10)
Research Context
1(3)
Presentation Structure
4(7)
Researching Mathematical Cognition 11(11)
The Historical Development of Mathematical Cognition
12(4)
The Methodology of Group-Cognitive Development
16(6)
Analyzing Development of Group Cognition 22(22)
Focus on Group Practices
22(9)
Sequential-Interaction Analysis
31(7)
The Display of Collaborative Development
38(6)
Session 1: The Team Develops Collaboration Practices 44(44)
Tab Welcome
46(23)
Tab Hints Help
69(3)
Tab Objects
72(5)
Tab Dragging
77(4)
Summary of Learning in Session 1
81(7)
Session 2: The Team Develops Dragging Practices 88(21)
Tab Equilateral
88(11)
Tab Relationships
99(4)
Tab Where's Waldo
103(1)
Tab Exploring
104(1)
Summary of Learning in Session 2
105(4)
Session 3: The Team Develops Construction Practices 109(20)
Visual Drawings and Theoretical Constructions
109(2)
Tab Bisector
111(12)
Tab Perpendicular
123(1)
Summary of Learning in Session 3
124(5)
Session 4: The Team Develops Tool Usage Practices 129(13)
Tab Right-Triangle
129(5)
Tab Triangles
134(4)
Tab Hierarchy
138(1)
Summary of Learning in Session 4
139(3)
Session 5: The Team Identifies Dependencies 142(12)
The Inscribed Triangles Tab
142(10)
Summary of Learning in Session 5
152(2)
Session 6: The Team Constructs Dependencies 154(17)
The Inscribed Triangles Tab, Continued
154(3)
The Inscribed Squares Tab
157(9)
Summary of Learning in Session 6
166(5)
Session 7: The Team Uses Transformation Tools 171(13)
The Transformations Tab
171(11)
Summary of Learning in Session 7
182(2)
Session 8: The Team Develops Mathematical Discourse and Action Practices 184(33)
The Quadrilateral Tab
185(1)
Poly1: Efficient Analysis
186(2)
Poly2: Group Memory
188(14)
Poly3: A Confused Attempt
202(2)
Poly4: Vertices Swinging around Circles
204(1)
Poly5: It's Restricted Dude
205(1)
Poly6: A Rectangle?
206(2)
Poly7: A Final Attempt
208(1)
Summary of Learning in Session 8
209(6)
What Did We Learn about What the Team Learned?
215(2)
Contributions to a Theory of Mathematical Group Cognition 217(24)
How Mathematical Group Cognition Developed
218(2)
Collaboration and the Development of Group Agency
220(5)
The Group Discourse of Mathematical Dependency
225(7)
Dynamic-Geometry Tools Mediating Group Cognitive Development
232(9)
Dragging as Embodied Group Cognition
235(2)
Constructing as Situated Group Cognition
237(1)
Designing as Group Conceptualizing of Dependency
238(3)
Constructing Mathematical Group Cognition 241(10)
The Dialectic of Mathematical Cognition
241(2)
Implications for Designing
243(3)
Advances and Future Prospects
246(5)
References 251(10)
Author Index 261(2)
General Index 263
Gerry Stahl is Professor Emeritus at Drexel University's College of Computing and Informatics. He is the founding editor of the International Journal of Computer-Supported Collaborative Learning, and his publications include Group Cognition: Computer Support for Building Collaborative Knowledge, Translating Euclid: Designing a Human-Centered Mathematics, and Studying Virtual Math Teams.