The Nature of Mathematical Thinking and Problem Solving

点击翻译按钮获取中文摘要

Approximately twenty-five cognitive scientists, mathematicians educators, and philosophers will meet for a three-day conference in the fall of 1988 that will be supported jointly with the Sloan Foundation. The conference will be held in an isolated setting (at a conference center, probably Pajaro Dunes) to promote the substantive, sustained interaction of the conference participants. To establish a context and some uniform background for the conference, conference participants will be mailed two "baseline" documents: the manuscript of Cognitive Science and Mathematics Education and the report "Establishing a research base for science education: Challenges, trends and recommendations". Two advisory boards, one for mathematics and one for cognitive science, will help select attendees and set the conference agenda. The mathematics advisory board consists of Ingram Olkin (Statistics, Stanford), Robert Osserman (Mathematics, Stanford), Henry Pollak (former vice president, Bell Communications Research), and Lynn Steen (Mathematics, St. Olaf); the cognition advisory board consists of James Greeno (Education and Psychology, Stanford), Lauren Resnick (Learning Research and Development Center, Pittsburgh), and Alan Schoenfeld (Education and Mathematics, Berkeley). The advisory boards will frame key issues regarding mathematical understanding that they hope to see addressed by conference participants, including issues regarding a possible research agenda. The participants who prepare papers will be asked to write about those issues in such a way that (a) the papers are accessible to the broad range of participants, and (b) there is enough specific detail (research findings, examples of problems or instructional methods, etc.) to provide a base for substantive discussion. The papers will be mailed to the reactors a month before the meeting. The meeting will open with a general introduction. For the first two days of the conference, papers will be presented in one-hour sessions, with critiques and open discussion. Readers for each paper will be chosen from a cross-section of the disciplines represented, to foster the kinds of interactions the conference is supposed to induce. The third day will be devoted to synthesis and an attempt to set a research agenda. Summary reaction talks will attempt to draw together various themes of the conference: identifying commonalities among the various perspectives, identifying points of controversy, and pointing to lines of communications among the various constituencies that might be pursued. A final session will focus directly on a proposed research agenda. What issues do the participants believe are a important and approachable? What do we need to know in order to make progress? The conference will generate a number of papers which will be compiled as Conference Proceedings. The Proceedings will be edited by the members of the two advisory boards and published through a dissemination medium such as the Mathematical Association of America's MAA Notes series, or through a commercial publisher known for disseminating such work (e.g. Lawrence Eribaum). Presentations based on the results of the conference will be made at meetings of the American Educational Research Association, Mathematical Association of America, and National Council of Teachers of Mathematics.