Re-Formation of Mathematical Education with symbolic Algebra System, and Its Database Formation

用符号代数体系重构数学教育及其数据库构建

• 批准号: 07680299
• 负责人: TSUBOKAWA Takehiro
• 金额: $ 1.22万
• 依托单位: Fukui National College of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07680299/
• 关键词: Engineering Mathematics Education; Symbolic Algebra System; Graphing Calculator; Numerical Experiment; Central Limit Theorem; 数学教育; Muthemutica

[Purpose]This study has been performed for the purpose of re-formation of mathematical education and forming its database. We were developing the programs by using Symbolic algebra System, which facilitates mathematical education and the utilization of its equipment in the fields of analysis, linear algebra, probabilities and statics, and applied mathematics. We were integrating computer-aided teaching methods which have been already developed.[Results and problems]1)In this paper, we first suggest one method which uses a computer and an OHP,and especially the dynamic images created by them in a fairly bright classroom, but we have found this method difficult to introduce in the present situation in view of equipment and resources. So we examine another method which uses a graphing calculator and an OHP dynamically instead. As a result, we have found this method should be economical and practical, and it can be used at many schools if some more improvements are made.2)As teaching mater … More ials, we chose two types. One is from those materials which are supposed to help students understand better when they are actually experimented, demonstrated or shown by graphics, and the other from those which haven't been used as teaching materials yet, but can be made into good materials when we apply the Symbolic Algebra System to them. Then we made the computer programs with those teaching materials. The achievements we can report are few yet, but we have presented by now one of them in the Transactions of KOSEN BUKAI of Japan Society of Mathematical Education, which is entitled A Numerical Experiment of Central Limit Theorem.3)We have been gathering the cases dealing with the symbolic algebra system which were presented at many kinds of associations or research meetings like Japan Society of Mathematical Education not only in Japan, but also in the United States. We also have been engaged in development of the system which enables anyone to have access to those cases, but we have not made the database available yet. We have been working on it.4)We have examined in practical ways the significance and possibilites of the utilization of the computer including the graphical calculator, but we have not reached the formulation yet. We have been aiming at the systematization of computer-aided mathematical education. The research is in progress in collaboration with other math teachers at different national colleges of technology. Less

[目的]本研究旨在改革数学教育并形成数学教育数据库。我们正在使用符号代数系统开发程序，该系统有助于数学教育及其设备在分析、线性代数、概率和静力学以及应用数学领域的利用。我们正在整合已经发展起来的计算机辅助教学方法。[结果与问题]1）在本文中，我们首先提出了一种使用计算机和OHP的方法，特别是在相当明亮的教室中由它们创建的动态图像，但我们发现鉴于设备和资源的现状，这种方法很难引入。因此，我们研究另一种动态使用图形计算器和 OHP 的方法。因此，我们发现这种方法应该经济实用，如果再做一些改进，可以在很多学校使用。2）教材方面，我们选择了两种类型。一种是那些在实际实验、演示或图形展示时应该帮助学生更好地理解的材料，另一种是那些还没有用作教材，但当我们应用符号代数系统时可以成为好的材料的材料。然后我们用这些教材编写了计算机程序。我们能报道的成果还很少，但目前我们已经在日本数学教育学会KOSEN BUKAI的汇刊上发表了其中一项，题为“中心极限定理的数值实验”。3）我们一直在收集涉及符号代数系统的案例，这些案例不仅在日本，而且在美国的日本数学教育学会等各种协会或研究会议上发表。我们还致力于开发系统，使任何人都可以访问这些案例，但我们尚未提供数据库。我们一直在努力。4）我们已经以实际的方式研究了使用计算机（包括图形计算器）的意义和可能性，但我们还没有得出公式。我们一直致力于计算机辅助数学教育的系统化。这项研究正在与不同国家理工学院的其他数学教师合作进行。较少的