A developmental study on teaching materials concerning connection between high school mathematics and college mathematics

目前，大学数学课程与高中数学课程之间存在差距，这给大学生顺利学习数学课程带来了一定的困难。这个项目的目的是为那些通过自学来克服上述困难的学生提供这种补充的“模块材料”。另一方面，由藤田教授和寺田教授领导的两个高中数学教育研究项目开发了一种新的数学课程编制思想，称为“核心选项模块”课程。本课程由两部分组成，一部分是所有学生都应该学习的核心部分，另一部分是选修部分，它们以学习模块的形式按内容单独安排。通过将核心模块和选项模块相结合，可以应对学生的多样性。本项目所设计的模块材料与用于学习的选项模块基本相同，使核心部分更加丰富或高级。为了实现这一理念，通过对在职教师的问卷调查和项目成员的讨论，选出了一系列的主题，并在选定的主题中勾画出以下四个单元的大纲。整数的性质2。指数和对数函数3。数字和方程4。区分和整合在大纲的起草中，强调了两个原则，即通过丰富的数值实验和积极使用计算器和微型计算机的动态图形表现来帮助直观和/或归纳理解，以及在一个模块中有一个连贯的故事。

At present, there are gaps between mathematics courses in colleges and those in senior high schools, result of which makes it defficult for college students to follow mathematics courses smoothly. This project started for the purpose of providing such supplementary "module materials" for those students that may help them to overcome the above-mentioned difficulty by studying the materials by themselves.On the other hand, the two research projects on mathematics education in senior high school, one headed by Prof. Fujita, the other by Prof. Terada, developed a new idea for mathematics curriculum making, called "core-option modules" curriculum. This curriculum is composed of two parts, one being the core part which should be learned by all students, and the other being optional parts which are arranged separately content by content in a form of learning module. By combination of the core and option modules diversity of students would be coped with.The module materials intended by this project is essentially same as those option modules for learning to make the core parts more enriched or advanced. At the same time, those freshmen who failed to learn some topics in their senior high schools may study the topics by themselves individually by using these modules.In order to realize the above idea, a series of topis was selected after a survey by questionaire to inservice teachers and discussion among the project members, and the outlines of modules were drawn for the following four among the selected topics.1. Properties of integer2. Exponential and logarithmic functions3. Figures and equations4. Differentiation and integrationIn draftion the outline, the two principles were emphasized, namely, to help intuitive and or inductive understanding by rich numerical experiments and dynamic graphic representation with active use of calculator and microcomputer, and to have a coherent story throughout one module.