Practical Research on Integrated Courses in Physics and Mathematics

物理与数学综合课程的实践研究

基本信息

批准号：
13680205
负责人：
HARA Yasuo
金额：
$ 1.34万
依托单位：
TEIKYO-HEISEI UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2003
项目状态：
已结题

项目摘要

Physics and mathematics (math) are usually taught independently though there is a close relationship between them. That is, physics provides concrete examples to understand math and the knowledge of math is indispensable in the study of physics. Thus, an effective way to teach physics and math is to teach them in an integrated way as if we let students to climb up zigzag ladders built between the physics building and the math building.The important purpose for students to study physics and math is to foster mathematical reasoning skill and to obtain basic knowledge necessary for the reasoning. The mathematical reasoning skill is a skill to build a mathematical model by choosing suitable variables, to find functional relations among them, to solve the relations and to understand the practical meaning of the solutions.I have completed a textbook suitable for the integrated course. In this course students are required to understand the meaning of variables and functional relationships among them, and to learn how to draw and interpret graphs representing the functions, at first. Then, they learn the trigonometric functions which represent oscillations, the exponential functions which represent exponential increases and decays, and the logarithmic functions which represent logarithmic increases and decays. Finally, they learn the differential, the integral and differential equations together with mechanics, oscillation and electromagnetic phenomena.The textbook can be distributed through the Internet and the users can modify them in order to make them suitable for their classes.

尽管它们之间存在密切的关系，但通常会独立教授物理和数学（数学）。也就是说，物理学提供了理解数学的具体示例，并且在物理学研究中，数学知识是必不可少的。因此，一种教学物理和数学的有效方法是以综合的方式教它们，就好像我们让学生爬上锯齿形梯子在物理大楼和数学建筑之间建立的锯齿形梯子一样。学生学习物理学和数学的重要目的是培养数学推理技能，并获得推理所需的基本知识。数学推理技能是一种通过选择合适的变量，找到功能关系，解决关系并理解解决方案的实际含义的技能。我完成了适合综合课程的教科书。在本课程中，要求学生了解变量和功能关系之间的含义，并学习如何绘制和解释代表功能的图形。然后，他们学习代表振荡的三角函数，代表指数增加和衰减的指数函数，以及代表对数增加和衰减的对数函数。最后，他们学习差异，积分和微分方程以及力学，振荡和电磁现象。教科书可以通过互联网分发，用户可以修改它们以使其适合其课程。