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

【目的】以数学教育的改革和数学教育数据库的形成为目的进行本研究。我们通过使用符号代数系统开发程序，这有助于数学教育和在分析、线性代数、概率和静力学以及应用数学领域使用其设备。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)本文首先提出了一种使用计算机和OHP的方法，特别是在一个相当明亮的教室中使用它们产生的动态图像，但由于设备和资源的限制，我们发现这种方法在目前的情况下很难引入。因此，我们研究了另一种使用图形计算器和动态OHP代替的方法。因此，我们发现这种方法应该是经济和实用的，如果再做一些改进，它可以在许多学校使用。作为教学材料，我们选择了两种类型。一种是用来帮助学生更好地理解实际实验、演示或图形展示的材料，另一种是那些还没有被用作教材的材料，但当我们应用符号代数系统时，它们可以成为很好的材料。然后我们用这些教材编写计算机程序。我们可以报道的成果还很少，但目前我们已经在日本数学教育学会会刊上发表了其中一个成果，题为《中心极限定理的数值实验》。3)我们一直在收集在日本和美国的日本数学教育学会等各种协会或研究会议上发表的关于符号代数系统的案例。我们也一直在开发一个系统，使任何人都能访问这些案件，但我们还没有提供数据库。我们一直在努力。我们已经以实际的方式考察了利用包括图形计算器在内的计算机的意义和可能性，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技术学院的其他数学教师合作进行。少

[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