Symbolizing and Communicating in Mathematics Classrooms: Perspectives on Discourse, Tools, and Instructional Design

Symbolizing and Communicating in Mathematics Classrooms: Perspectives on Discourse, Tools, and Instructional Design

Symbolizing and Communicating in Mathematics Classrooms: Perspectives on Discourse, Tools, and Instructional Design

Symbolizing and Communicating in Mathematics Classrooms: Perspectives on Discourse, Tools, and Instructional Design

Synopsis

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.

Excerpt

In 1993, we, in collaboration with Koeno Gravemeijer of the Fruedenthal Institute, Utrecht, The Netherlands, began working on a National Science Foundation-funded project titled "Mathematizing, Modeling, and Communicating in Reform Classrooms." A major purpose of the project was to investigate the role of models and symbols in mathematical learning, thereby addressing a previously underdeveloped area of learning theory. Our intention was to build on and extend previous research by coordinating a cognitive analysis of the role of modeling in mathematical development with an analysis of the fundamentally social nature of model and symbol use in innovative classrooms. To that end, we conducted a series of classroom teaching experiments in first-, second-, and third-grade mathematics classes where mathematics instruction followed an inquiry tradition. These teaching experiments differed significantly from those that we had conducted in our previous work in that, in these, we were guided not only by our understanding of individual students' mathematical conceptual development, but also by the instructional design theory of Realistic Mathematics Education (RME). Of particular importance in each case was developing one or more realistic (in the sense of RME) scenarios that could serve as starting points for students' initial informal activity and that had the potential to facilitate students' development of more formal mathematical reasoning. In the process we were able to investigate the role that student-generated models can play in supporting their transition from informal, situated problem solving to more formal yet personally-meaningful mathematical activity.

As the project progressed it became apparent to us that it would be helpful to engage in in-depth discussions with others who were also grappling with issues of communicating, symbolizing, modeling, and mathematizing, particularly as these issues relate to learning in the classroom. It was for this purpose that we assembled a small international group at Vanderbilt University in the fall of 1995 for a sympo-

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