Contents: E. Yackel, P. Cobb, K. McClain, Preface. E. Yackel, Introduction: Perspectives on Semiotics and Instructional Design. Part I:Theoretical Considerations. P. Cobb, From Representations to Symoblizing: Introductory Comments on Semiotics and Mathematical Learning. A. Sfard, Symbolizing Mathematical Reality Into Being--Or How Mathematical Discourse and Mathematical Objects Create Each Other. W. Dorfler, Means for Meaning. B. van Oers, The Appropriation of Mathematical Symbols: A Psychosemiotic Approach to Mathematics Learning. R. Nemirovsky, S. Monk, "If You Look at It the Other Way...": An Exploration Into the Nature of Symbolizing. Part II:Instructional Design Issues Related to Symbolizing, Communicating, and Mathematizing. K. Gravemeijer, P. Cobb, J. Bowers, J. Whitenack, Symbolizing, Modeling, and Instructional Design. J. Bransford, L. Zech, D. Schwarts, B. Barron, N. Vye, The Cognition and Technology Group at Vanderbilt, Designs for Environments That Invite and Sustain Mathematical Thinking. R. Lehrer, L. Schauble, S. Carpenter, D. Penner, The Innerrelated Development of Inscriptions and Conceptual Understanding. R. Lesh, H.M. Doerr, Symbolizing, Communicating, and Mathematizing: Key Components of Models and Modeling. J. Bowers, Postscript: Integrating Themes on Discourse and Design.