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，导致大学生很难顺利学习数学课程。这个项目的目的是为学生提供这样的补充“模块材料”，帮助他们通过自学来克服上述困难。另一方面，藤田教授和寺田教授主持的两个关于高中数学教育的研究项目，提出了一种新的数学课程制定理念，即“核心选项模块”课程。本课程由两部分组成，一部分是所有学生必须学习的核心部分，另一部分是选修部分，以学习模块的形式按内容单独安排。通过核心模块和选修模块的结合，学生的多样性将得到解决。本项目拟采用的模块材料与那些学习选修模块基本相同，以使核心部分更加丰富或高级。与此同时，那些在高中阶段没有学习过某些主题的大一新生也可以利用这些模块独立学习这些主题。为了实现上述理念，通过对在职教师的问卷调查和项目成员的讨论，选择了一系列的主题，并在选定的主题中绘制了以下四个模块的大纲。integer2的性质。指数函数和对数函数图与方程在大纲的起草中，强调了两个原则，即通过丰富的数值实验帮助直观和（或）归纳理解，积极使用计算器和微型计算机的动态图形表示，并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.