The Nature of Mathematical Thinking and Problem Solving

数学思维和解决问题的本质

• 批准号: 8751520
• 负责人: Alan Schoenfeld
• 金额: $ 4.79万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-09-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8751520&HistoricalAwards=false
• 关键词: Nature; Mathematical; Thinking; Problem; Solving

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.

大约25名认知科学家、数学家、教育家和哲学家将在1988年秋天参加一个为期三天的会议，会议将与斯隆基金会共同支持。会议将在与世隔绝的环境中举行(会议中心，可能是Pajaro Dunes)，以促进会议参与者之间实质性的、持续的互动。为了确定会议的背景和一些统一的背景，将向与会者邮寄两份“基线”文件：认知科学和数学教育手稿和报告“建立科学教育研究基地：挑战、趋势和建议”。两个咨询委员会，一个负责数学，另一个负责认知科学，将帮助挑选与会者并设定会议议程。数学咨询委员会由Ingram Olkin(斯坦福大学统计学)、Robert Osserman(数学，斯坦福)、Henry Pollak(贝尔传播研究前副总裁)和Lynn Steen(数学，圣奥拉夫)组成；认知咨询委员会由James Greeno(斯坦福大学教育与心理学)、Lauren Resnick(匹兹堡学习研究与发展中心)和Alan Schoenfeld(伯克利教育与数学)组成。咨询委员会将制定他们希望与会者解决的有关数学理解的关键问题，包括有关可能的研究议程的问题。编写论文的参与者将被要求以这样的方式写下这些问题：(A)广泛的参与者可以阅读论文，以及(B)有足够的具体细节(研究结果、问题的例子或教学方法等)。为实质性讨论提供基础。这些文件将在会议前一个月邮寄给反应堆。会议将以一个一般性的介绍开始。在会议的头两天，论文将以一小时的时间提交，并带有批评和开放讨论。每篇论文的读者将从代表的学科的横截面中挑选出来，以促进会议应该引发的各种互动。第三天将致力于综合和尝试制定研究议程。简要反应会谈将试图将会议的各种主题汇集在一起：确定不同观点之间的共同点，确定争议点，并指出不同支持者之间可能采取的沟通方式。最后一次会议将直接集中讨论拟议的研究议程。与会者认为哪些问题是重要的和可接近的？我们需要知道什么才能取得进展？会议将产生一些论文，这些论文将汇编成会议记录。会议记录将由两个咨询委员会的成员编辑，并通过传播媒介，如美国数学协会的MAA笔记系列，或通过以传播这类作品而闻名的商业出版商(如Lawrence Eribaum)出版。会议结果将在美国教育研究协会、美国数学协会和全国数学教师委员会的会议上发表。