Teaching Mathematical Modeling in the Behavioral Sciences

行为科学中的数学建模教学

• 批准号: 0716592
• 负责人: Robert Wyttenbach
• 金额: $ 47.49万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0716592&HistoricalAwards=false
• 关键词: Teaching; Mathematical; Modeling; Behavioral; Sciences

Biological Sciences (61). This project is developing instructional modules at the undergraduate level that focus on mathematical modeling in the behavioral sciences. These modules cover such topics as mating strategies, contests, habitat selection, foraging, cooperation and conflict, and communication. The focus is on well-understood models of animal behavior, with students encouraged to extend the models to human behavior, politics, and economics. Modules can be used together in behavior courses or singly in introductory biology, ecology, evolution, sociology, or psychology courses. A secondary aspect of the project is enhancement of mathematics classes by introducing behavioral applications. Each module actively engages the student in developing a model. After watching video of a behavior that illustrates a question, a student identifies the relevant variables, formulates a model, translates it to mathematical form, makes predictions based on the model, tests those predictions with a graphical simulation, and designs real-world experiments that would test the model. These exercises give students experience with probability, game theory, and optimization methods. A manual for instructors suggests ways to incorporate the material into a variety of courses and indicates areas that students may explore further on their own. This material is being tested at a diverse group of colleges and universities. Evaluation includes comparative tests (lecture-only vs. module) and longer-term tests of retention and transfer of knowledge. Dissemination of the material through national meetings, educational publications, and distribution by a textbook publisher is broadening the impact of the project and increasing the exposure of undergraduates nationwide to mathematical modeling of behavior.

生物科学（61）.该项目正在开发本科阶段的教学模块，重点是行为科学中的数学建模。这些模块涵盖了交配策略，比赛，栖息地选择，觅食，合作与冲突，以及沟通等主题。重点是动物行为的良好理解模型，鼓励学生将模型扩展到人类行为，政治和经济。模块可以在行为课程中一起使用，也可以在生物学、生态学、进化论、社会学或心理学课程中单独使用。该项目的第二个方面是通过引入行为应用程序来增强数学课程。每个模块都积极地让学生参与开发模型。在观看说明问题的行为视频后，学生识别相关变量，制定模型，将其转换为数学形式，基于模型进行预测，用图形模拟测试这些预测，并设计真实世界的实验来测试模型。这些练习让学生体验概率论、博弈论和优化方法。教师手册建议如何将材料纳入各种课程，并指出学生可以自己进一步探索的领域。这一材料正在不同的学院和大学进行测试。评估包括比较测试（仅讲课与模块）和知识保留和转移的长期测试。通过全国性会议、教育出版物和教科书出版商的分发，这些材料的传播正在扩大该项目的影响，并增加全国本科生对行为数学建模的接触。