Preface / Erna Yackel, Paul Cobb and Kay McClain
1. Introduction: Perspectives on Semiotics and Instructional Design / Erna Yackel
2. From Representations to Symbolizing: Introductory Comments on Semiotics and Mathematical Learning / Paul Cobb
3. Symbolizing Mathematical Reality Into Being - Or How Mathematical Discourse and Mathematical Objects Create Each Other / Anna Sfard
4. Means for Meaning / Willi Dorfler
5. Appropriation of Mathematical Symbols: A Psychosemiotic Approach to Mathematics Learning / Bert van Oers
6. "If You Look at it the Other Way ...": An Exploration Into the Nature of Symbolizing / Ricardo Nemirovsky and Stephen Monk
7. Symbolizing, Modeling, and Instructional Design / Koeno Gravemeijer, Paul Cobb and Janet Bowers / [et al.]
8. Designs for Environments That Invite and Sustain Mathematical Thinking / John Bransford, Linda Zech and Dan Schwarts / [et al.]
9. Innerrelated Development of Inscriptions and Conceptual Understanding / Richard Lehrer, Leona Schauble and Susan Carpenter / [et al.]
10. Symbolizing, Communicating, and Mathematizing: Key Components of Models and Modeling / Richard Lesh and Helen M. Doerr
11. Postscript: Integrating Themes on Discourse and Design / Janet Bowers.
