Behavioral Sciences Curriculum Enhanced with Mathematical Modeling

美国国家研究委员会的《生物2010》报告将数学与生物的融合确定为本科课程现代化的重要组成部分。我们建议在行为科学中通过制作一张交互式模拟和数学建模实验的CD来推进这一目标。行为科学不仅依靠数学进行数据分析，还依赖于解释行为及其起源的模型。然而，本科生的课本通常会粉饰建模，而那些教授建模的人几乎没有什么资源。我们正在开发涵盖一系列主题的模块原型。它们打算在行为学课程中一起使用，或者在生物学、生态学和进化论入门课程中单独使用。每个视频都以一段行为视频开始，并促使学生考虑它提出的问题。接下来，通过开发模型引导学生(口头和数学)。然后，学生们形成关于行为的假设，并用模型的图形模拟来测试他们的预测。虽然这些模型背后的数学并不超越代数，但变化参数的影响往往并不明显。交互式模拟允许学生在理解建模并感受模型参数和行为之间的联系的同时，自己进行探索。这个项目的智力价值是通过在学生容易理解和感兴趣的环境中引入数学建模来改进本科生物学课程，并利用技术来推进否则无法实现的教学目标。这个项目对康奈尔大学的大型动物行为课程产生了立竿见影的影响，我们正在进行初步测试。更广泛的影响将来自材料的出版和在其他学院和大学的广泛使用。来自生物、心理学、人类学和数学系的教职员工已经表示，需要这种材料，并愿意在他们的课堂上测试它，作为我们评估计划的一部分。几家出版商，包括使用最广泛的动物行为文本的出版商，都表现出了兴趣，使其在全国范围内传播成为必然。

The Bio2010 report of the National Research Council identifies integration of mathematics into biology as an important part of modernizing the undergraduate curriculum. We propose to advance this goal in the behavioral sciences by producing a CD of interactive simulations and experiments in mathematical modeling. The behavioral sciences rely on mathematics not only for data analysis, but for models that explain behavior and its origins. However, undergraduate texts typically gloss over modeling, and there are few resources for those who would teach it. We are developing prototypes of modules covering a range of topics. They are intended to be used together in a course on behavior or singly in introductory biology, ecology, and evolution. Each starts with a video of a behavior and prompts students to consider the questions it raises. Next, students are led (both verbally and mathematically) through development of a model. Students then form hypotheses about the behavior and test their predictions with a graphical simulation of the model. While the mathematics behind these models does not go beyond algebra, the effect of varying parameters is often not obvious. Interactive simulations allow students to explore on their own as they develop understanding of modeling and a feel for the link between model parameters and behavior. The intellectual merits of this project are the improvement of the undergraduate biology curriculum by introducing mathematical modeling in a context that is accessible and interesting to students and the use of technology to advance teaching goals that cannot otherwise be met. This project is having an immediate impact in Cornell's large animal behavior course, where we are doing initial testing. Broader impact will come from publication of the material and usenationwide in other colleges and universities. Faculty from departments of biology, psychology, anthropology, and mathematics at a variety of other institutions have indicated need for this material and willingness to test it in their classes as part of our evaluation plan. Several publishers, including that of the most widely used animal behavior text, have shown interest, making nationwide dissemination certain.