Learning and Mathematics

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Discussion Sessions: Introduction

Researchers in mathematics education, educational psychology, and the psychology of learning constitute an important and relevant group that has heretofore not made its presence felt on the Geometry Forum. They've developed ideas that have led to new methods of instruction currently being used by and taught to teachers, some of which are reflected in the new NCTM Standards. We look forward to their participation with mathematicians in Forum discussions on ideas for solving problems in education.

K. Ann Renninger, of the Swarthmore Program in Education, has been working with students to summarize some of the seminal articles dealing with how students learn mathematics. Since the social science language used in many of these articles may be unfamiliar to some, our summaries will be tested on a mathematician who finds most papers in mathematics education to be completely unintelligible (yours truly).

Our goals are similar to those Alan Schoenfeld had for a book he edited, Cognitive Science and Mathematics Education, the source of one of the articles we have summarized. This book was an outgrowth of two conferences that brought together teachers, mathematicians, mathematics educators, and cognitive scientists in an effort to build interaction and understanding among the groups. About the first of these gatherings Schoenfeld commented:

That first conference was no picnic. Members of the different groups represented at the conference don't talk to each other that often; what one group considers central may seem peripheral to another; what one group considers trivial may seem significant to another. People arrived at the conference with different perspectives and, it seemed at times, speaking different languages. [p.xiv]
Even though researchers into educational psychology and mathematicians may have different perspectives and different languages, as teachers we have compelling reasons to attempt to overcome what barriers may exist and to work to understand each other. Here at the Geometry Forum we wish to generate useful discussions as a result of our various Learning and Mathematics postings.

-- Gene Klotz, Director, The Geometry Forum

We hope here to launch a series of discussions inspired by recent work on how students learn mathematics -- ideas that form the basis of the NCTM Standards. It is our intention that this series be an informative and sometimes provocative overview of the current research and thinking of some key researchers in mathematics education and educational psychology.

Much of the work in this area indicates that the "traditional" classroom needs to be changed if more effective learning (i.e., learning that is more conceptual and less formulaic) is to take place. These summaries include implications for classroom practice.

We plan to cover such topics as problem-solving, peer tutoring, motivation, metacognition (reflecting on how you think), strategy use, and real-world mathematics. If you have questions about the new pedagogy or ideas from mathematics education that inform the Standards, please send a note to me, ann@mathforum.org, and we'll see about developing a posting that addresses them.

-- K. Ann Renninger, Research Coordinator, The Geometry Forum

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