ABSTRACT
The four chapters in this section of the book all focus on semiotics as it relates to mathematical learning. The authors are therefore concerned with symbols and their role in mathematical communication. Each chapter offers a perspective on the subtle interplay between the modification and use of symbols on the one hand and the development of mathematical meaning on the other. In this introduction, I first consider common assumptions that cut across all four chapters and then compare and contrast the specific perspectives developed in each chapter. My purpose in doing so is to orient the reader to the general theoretical commitments made by the various authors. As Dörfler observes in his chapter (chap. 4), these differing theoretical conceptions of meaning constrain the research questions addressed and thus what is describable and observable. Dörfler goes on to note that theoretical commitments of this type have pedagogical impact in that teachers' preconceptions of mathematical understanding and of the meaning of the subject matter strongly influence the judgments they make about students' mathematical activity (cf. Thompson, 1992).
