Integrating Research on the Graphical Representation of Functions

Integrating Research on the Graphical Representation of Functions

Integrating Research on the Graphical Representation of Functions

Integrating Research on the Graphical Representation of Functions


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.


This volume is concerned with the integration of research on teaching, learning, curriculum, and assessment with respect to an increasingly important mathematical domain, the graphical representation of functions. The effort at integration reflects an ambitious attempt, from a common perspective, to focus the research of a number of scholars on critical problems in the study of this domain. Research in this area is sparse, but with the increasing use of computers and graphing calculators, a coherent body of knowledge about how the connections are developed among tables, graphs, and the algebraic expressions related to functions is desperately needed.

The primary audience for this book consists of researchers in mathematics learning and teaching. We anticipate that university professors and their graduate students will use the volume as a basis for a rich set of studies during the coming decade. However, because of the growing importance of the topics covered, we expect many teacher educators, textbook authors, and teachers of mathematics will find the chapters enlightening.

The strategy that was followed in planning this book is one that has been previously used with considerable success. Over ten years ago, the Wisconsin Center for Education Research sponsored a conference that brought together researchers from around the world who had studied children's addition and subtraction concepts and skills. An outcome of that conference was the book, Addition and Subtraction: A Cognitive Perspective (Carpenter, Moser, & Romberg, 1982). However, more importantly, the conference served to initiate an ongoing research effort that, during the ensuing decade, clarified our understanding of how addition and subtrac-

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