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

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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.