Integrating Research on the Graphical Representation of Functions

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Overview

This volume focuses on the important mathematical idea of functions that, with the technology of computers and calculators, can be dynamically represented in ways that have not been possible previously. The book's editors contend that as result of recent technological developments combined with the integrated knowledge available from research on teaching, instruction, students' thinking, and assessment, curriculum developers, researchers, and teacher educators are faced with an unprecedented opportunity for making dramatic changes.

The book presents content considerations that occur when the mathematics of graphs and functions relate to curriculum. It also examines content in a carefully considered integration of research that conveys where the field stands and where it might go. Drawing heavily on their own work, the chapter authors reconceptualize research in their specific areas so that this knowledge is integrated with the others'strands. This model for synthesizing research can serve as a paradigm for how research in mathematics education can — and probably should — proceed.

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Table of Contents

Contents: T.A. Romberg, T.P. Carpenter, E. Fennema, Toward a Common Research Perspective. Part I:Content. F. Demana, H.L. Schoen, B. Waits, Graphing in the K-12 Curriculum: The Impact of the Graphing Calculator. M. Yerushalmy, J.L. Schwartz, Seizing the Opportunity to Make Algebra Mathematically and Pedagogically Interesting. J. Moschkovich, A.H. Schoenfeld, A. Arcavi, Aspects of Understanding: On Multiple Perspectives and Representations of Linear Relations and Connections Among Them. Part II:Student Thinking. S. Dugdale, Functions and Graphs — Perspectives on Student Thinking. Part III:Teaching Thinking. T.J. Cooney, M.R. Wilson, Teachers' Thinking About Functions: Historical and Research Perspectives. Part IV:Teacher Knowledge. F.A. Norman, Integrating Research on Teachers' Knowledge of Functions and Their Graphs. Part V:Classroom Instruction. C. Kieran, Functions, Graphing, and Technology: Integrating Research on Learning and Instruction. Part VI:Curricular Implications. R.A. Philipp, W.O. Martin, G.W. Richgels, Curricular Implications of Graphical Representations of Functions. Part VII:Reactions. J. Kaput, The Urgent Need for Proleptic Research in the Representation of Quantitative Relationships. S. Williams, Some Common Themes and Uncommon Directions.

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