數學 學習에서의 意思疏通 能力 效果에 관한 硏究

Abstract

The purpose of this study is to investigate both students' improvement in mathematical communication and the impact on their mathematics-learning when the teaching-learning method that emphasizes communication skill is applied to students in a mathematics class. For this study, two questions are considered. 1. What effect does mathematical communication class, which includes speaking, listening, writing, and reading, have on learning of mathematics? 2. What difference in the ability of mathematical communication is there between two groups?: group one shows a better and more aggressive attitude to learning mathematics than group two, and also achieves a higher score in mathematics than the other. A case study is carried out so as to get the answers for the above two questions. Fifteen out of the first-year students of a middle school in Jeolla Namdo region are picked up randomly for this study. They are all involved in a mathematical communication class in two groups, and among them, six students are closely investigated. The conclusions from the results of the case study are like these: The answers to the first question are shown as follows. The mathematical communication class that consists of speaking, listening, writing, and reading has the following effects on the participants. First of all, there happen such great things as good and constructive relationship among the students and active learning-attitude, when they get fully involved in mutual communication to resolve mathematic problems. Therefore, the method can make a great contribution to the students' learning. Second, mathematical communication helps students to collaborate in finding a way out and diminishing stress, in particular, when the math problem is too complicated and difficult to solve due to their lack of sufficient mathematical knowledge. Third, it also helps students enhance their understanding of mathematics and, at the same time, remember for a long time what they learn through collaboration with others if they are trained through mathematical communication to compare various ideas of their friends, to correct and to make a note of it neatly. The answers to the second question are shown as follows. First, both two groups show the far low capability of speaking expression, though they are rather active only in their own groups, when they explain how to solve a mathematical problem to all other students. It is because of their lack of confidence and concentration, and because of a hitch in mathematical communication. But, as a member of the group, one makes a breakthrough in communication, the group members improve gradually the way of expressing, compared with the other group which does not make any stride in mathematical communication. Second, the two groups do not have great difficulties in writing how to solve mathematics problems. However, the first group consisted of students who have more positive attitudes toward mathematics and better abilities to learn mathematics gives clearer and more logical procedures of working out the problems than the other group, the second group specifically, in proposing their creative ideas and delineating the process of how to solve the problem with drawings. Last, in the two groups, the parts of listening and reading in which students understand and analyze a mathematical problem, though it is less satisfactory than the part of writing, go well, while the part of speaking expression does not. Unlike the second group, the students of group one learned efficiently not only listening and comparing their ideas but also correcting them. Moreover, they figured out a given problem easily and used mathematical signs correctly. On the other hand, the members of the second group has difficulties in comparing other methods for solving the problem and focusing on teacher's explanation, though they understood that there are a variety of ways of expressing the mathematical topics. They also read the contents in the mathematics textbook to the letter, but not to make it out clearly and interpret it rigidly. As shown in the above, the results of the case study, the students who carry active attitude to mathematics and the higher capability of learning mathematics succeed in mutual mathematic-communication, and they make good progress in using mathematic signs properly and of the ability to understand and express, that is, of the parts of speaking, listening, writing, and reading. The results also show that the mathematical communication is efficient in mathematics class in terms of intimacy and companionship that they get by communicating mutually and in terms of knowledge or intelligence achieved in class. In conclusion, the method of teaching-learning which focuses on communicating one another mathematically in class gives many advantages to mathematics education