Constructing dynamic triangles together : the development of mathematical group cognition / Gerry Stahl, Drexel University.

Format:

Book

Author/Creator:

Stahl, Gerry, author.

Series:

Learning in doing.

Learning in doing : social, cognitive and computational perspectives

Language:

English

Subjects (All):

Geometry--Study and teaching (Middle school).

Geometry.

Middle school education.

Middle school students.

Mathematical ability.

Physical Description:

1 online resource (xix, 270 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2016.

Language Note:

English

Summary:

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.

Contents:

Cover; Half-title; Series information; Title page; Copyright information; Table of contents; List of figures; List of logs; Series foreword; Preface; Acknowledgments; 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 ToolsSession 8: The Team Develops Mathematical Discourse and Action Practices; Contributions to a Theory of Mathematical Group Cognition; Constructing Mathematical Group Cognition; References; Author Index; General Index; Research Context; Presentation Structure; The Historical Development of Mathematical Cognition; The Methodology of Group-Cognitive Development; Focus on Group Practices; Sequential-Interaction Analysis; The Display of Collaborative Development; Tab Welcome; Tab Hints Help; Tab Objects; Tab Dragging; Summary of Learning in Session 1

Tab EquilateralTab Relationships; Tab Where's Waldo; Tab Exploring; Summary of Learning in Session 2; Visual Drawings and Theoretical Constructions; Tab Bisector; Tab Perpendicular; Summary of Learning in Session 3; Tab Right-Triangle; Tab Triangles; Tab Hierarchy; Summary of Learning in Session 4; The Inscribed Triangles Tab; Summary of Learning in Session 5; The Inscribed Triangles Tab, Continued; The Inscribed Squares Tab; Summary of Learning in Session 6; The Transformations Tab; Summary of Learning in Session 7; The Quadrilateral Tab; Poly1: Efficient Analysis; Poly2: Group Memory

Poly3: A Confused AttemptPoly4: Vertices Swinging around Circles; Poly5: It's Restricted Dude; Poly6: A Rectangle?; Poly7: A Final Attempt; Summary of Learning in Session 8; What Did We Learn about What the Team Learned?; How Mathematical Group Cognition Developed; Collaboration and the Development of Group Agency; The Group Discourse of Mathematical Dependency; Dynamic-Geometry Tools Mediating Group Cognitive Development; The Dialectic of Mathematical Cognition; Implications for Designing; Advances and Future Prospects; Dragging as Embodied Group Cognition

Constructing as Situated Group CognitionDesigning as Group Conceptualizing of Dependency

Notes:

Title from publisher's bibliographic system (viewed on 11 Nov 2015).

Includes bibliographical references and indexes.

ISBN:

1-316-44414-7

1-316-44672-7

1-316-44715-4

1-316-44887-8

1-316-44758-8

1-316-44973-4

1-316-42275-5