This volume grew out of a symposium on discourse, tools, and instructional design at Vanderbilt University in 1995 that brought together a small international group to grapple with issues of communicating, symbolizing, modeling, and mathematizing, particularly as these issues relate to learning in the classroom. The participants invited to develop chapters for this book--all internationally recognized scholars in their respective fields--were selected to represent a wide range of theoretical perspectives including mathematics education, cognitive science, sociocultural theory, and discourse theory. The work is distinguished by the caliber of the contributors, the significance of the topics addressed in the current era of reform in mathematics education, and the diversity of perspectives taken to a common set of themes and issues. The book is intended for those who are seeking to expand their understanding of the complexity of learning in order to enhance the learning experiences students have in schools, primarily researchers, instructional designers, and graduate students in mathematics education, as well as those in other fields including science education, instructional design in general, discourse theory, and semiotics.
Author(s): Paul Cobb, Erna Yackel, Kay McClain
Publisher: Routledge
Year: 2000
Language: English
Pages: 412
Book Cover......Page 1
Title......Page 4
Copyright......Page 5
Contents......Page 8
Preface......Page 10
1 Introduction: Perspectives on Semiotics and Instructional Design......Page 12
I THEORETICAL CONSIDERATIONS......Page 26
2 From Representations to Symbolizing: Introductory Comments on Semiotics and Mathematical Learning......Page 28
3 Symbolizing Mathematical Reality Into Being—Or How Mathematical Discourse and Mathematical Objects Create Each Other......Page 48
4 Means for Meaning......Page 110
5 The Appropriation of Mathematical Symbols: A Psychosemiotic Approach to Mathematics Learning......Page 144
6 “If You Look at It the Other Way…”: An Exploration Into the Nature of Symbolizing......Page 188
II INSTRUCTIONAL DESIGN ISSUES RELATED TO SYMBOLIZING, COMMUNICATING, AND MATHEMATIZING......Page 234
7 Symbolizing, Modeling, and Instructional Design......Page 236
8 Designs for Environments That Invite and Sustain Mathematical Thinking......Page 286
9 The Interrelated Development of Inscriptions and Conceptual Understanding......Page 336
10 Symbolizing, Communicating, and Mathematizing: Key Components of Models and Modeling......Page 372
11 Postscript: Integrating Themes on Discourse and Design......Page 396
Author Index......Page 410
Subject Index......Page 416
