In the college mathematics learning activity, with the result of a great gap of the mathematics competence among the students according to their high school background (the high school for entering the university; human science and natural science, and the vocational high schools) and their departments in the college, I have got to begin this study because I felt the necessity for the proper instructional (teaching) methods for the students who have lost their interests in classroom activity. In this study, as a result of classifying what kind of elements has played key roles in the achievement test of college mathematics learning by giving marks to the mathematics classroom participation attitude, approaching method, classroom participation and homework habits, preparation habits for mathematics exam, the basic competence test of class activity evaluation sheets, the self-diagnosis method of instructional objective, prerequisite learning competence, the mathematics preference degree, and the mathematics achievement degree, there has been shown a meaningful difference in the fundamental competence, in the prerequisite competence, and in the learning achievement degree. Accordingly, this study is to suggest methods which are certainly helpful in learning the college mathematics and in acquiring the fundamental competence of taking lessons which is effective for the major subjects, major mathematics, in college as followings: First, after checking out the fundamental competence and the prerequisite competence, we should distinguish the students who can be in the group of college mathematics procedure from those who can be in the group of major mathematics procedure, prerequisite-learning procedure. Second, after applying the test to the students of two or three departments whom every professor is in charge of, we should divide them into the fundamental group and the high level group, college mathematics group according to their marks, and then lead individual lessons.(Orig.)