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The purpose of this study was to design models of CAI programs for the graphing of quadratic functions. In order to achieve this aim, I researched the relationship between mathematics educations computer programing, and theoretical approaches of CAI. The CAI program, which was developed based on my research was then positively applied to the mathematics education class in a middle school. First of all, I selected two classes -An experimental class and a comparative class. The experimental class was taught using the CAI program and the comparative class was taught by conventional methods of instruction. The results of this study are as follows: 1. The class taught by using the CAI program scored higher academic achievement than the class taught by conventional methods of instruction. 2. The analysis of the two classes' academic scores shows that the instruction using CAI program is more effective than that by conventional methods in improving students' academic achievement. The followings are suggestion for developing CAI programs and students' understanding through this study. 1. Non computer specialists will require a few months to develope an effect CAI program. Thus, development of easier, more clearly defined and flexible models must be constructed. 2. Teachers should be eager to use pre-existing models to motivate their students irregardless of their own development of programs. 3. School should provide computer rooms with a perfect net work in proportion to class size. 4. CAI programs can make students understand faster and more directly than blackboard examples. However, inconsideration of mathematical characteristics, arithmetic by hand is more effective for the students' memory retention. Computers is an effective tool of instruction. But it is most effective when used in conjunction with other methods that complement its use.