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

[目的]本研究旨在对数学教育进行改革，形成数学教育数据库。我们通过使用符号代数系统来开发程序，该系统促进了数学教育，并在分析、线性代数、概率和静力学以及应用数学领域使用了它的设备。我们正在整合已经开发的计算机辅助教学方法。[结果和问题]1)在本文中，我们首先提出了一种使用计算机和OHP的方法，特别是在一个相当明亮的教室中由它们产生的动态图像，但考虑到设备和资源，我们发现这种方法在目前的情况下很难引入。因此，我们研究了另一种方法，它使用图形计算器和动态OHP。因此，我们发现这种方法应该是经济实用的，如果再做一些改进，它可以在许多学校使用。2)作为…的教学材料更多的广告，我们选择了两种。一种是那些在实际实验、演示或用图形显示时应该能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，但当我们将符号代数系统应用到他们身上时可以制作成好材料的材料。然后，我们用这些教材编制了计算机程序。我们可以报告的成果还很少，但到目前为止，我们已经在日本数学教育学会的KOSEN BUKAI会刊上展示了其中之一，题为中心极限定理的数值实验。3)我们一直在收集有关符号代数系统的案例，这些案例不仅在日本，而且在美国也出现在日本数学教育学会等各种协会或研究会议上。我们也一直在开发该系统，使任何人都能接触到这些案件，但我们还没有提供数据库。我们已经用实际的方法研究了利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。我们一直致力于实现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

[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