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ø¼ ðÅl”² °Æ¬¹˜°|· ÂYÕP!ÇÐÅÁ $Æœ· 0®¬ ÇÀÉ´´Å(Æ ÈµÑÈxÇ PÂ$ YÕµÂ )¼•¼ÐÅ ³\Õ ³HÅ<Ç\¸ ô¼ä² ˜°@Ç PÂ$ YÕµÂ )¼•¼DÇ ¨ºÉÀXÕ0® Ç\Õ XÕ˜°XÇ ÜÂÄ³\¸Á XÇXÇ¬ ˆÇ<Çpº, ø¼ ðÅl|¹ µÑtÕ 0®tÈXÇ PÂ·YÕµÂ à¬ÂÐÅÁ —¼´Å˜° PÂ$ YÕµÂ ¬ ÁDÇ Ç\Õ ä²‘Å\Õ ÜÂÄ³@Æ x±%¸tÇ DÕ”ÆXÕpº, ÈÀ\¸´Æ PÂ·YÕµÂ )¼•¼tÇ P!Ç Ö¥ÇÐÅ ¨Öü¬È<Ç\¸ È©Æ´0® ÇtÕ ä²‘Å\Õ ðÅl@Æ äÂœÌÈ x±%¸tÇ DÕ”ÆhÕDÇ ÜÂ¬ÀXÕà¬Ç \Õä².; In the 21st century of knowledge creation, the purpose of mathematics education can be called the improvement of the mathematical thinking ability. A mathematics lesson should made to provide students with a chance to independently think according to an era and an educational purpose, However, our mathematics lesson has maintain a traditional teaching method for acquiring knowledge and skills for a long time of period. Because the traditional teaching method is apt to implant fragmentary knowledge and forms student s passive learning attitude, it can not grow creative talented people. On the other hand, students in the learner-centered instruction based on constructionism can independently c< ompose knowledge, and apply composed knowledge to problems. In addition, as the learner-centered instruction is made based on student s leading and positive activity process, learners form a positive learning attitude.
Accordingly, this study suggests the learner-centered instruction as a countermeasure of the traditional teaching method, and selected following research problems so as to verify whether the mathematics lesson through the learner-centered instruction is appropriate as a teaching and learning method to improve mathematical thinking and a positive mathematics learning attitude.
Research Problem 1. What effects does the learner-centered mathematical activity give on student s mathematical thinking?
1-1. What differences occur to student s mathematical thinking level before and after the learner-centered mathematical activity?
1-2. What differences occur to student s mathematical thinking level in the learner-centered mathematical activity process?
Research Problem 2. What effect do the learner-centered mathematical activity give on student s mathematical learning attitude?
In order to acquire results of the research problems, a questionnaire was produced to test the mathematical thinking levels of research subjects. As for a pre and post questionnaire, graduate students in the master s course majoring in mathematics and in that majoring in mathematics education participated to judge the same questionnaire, and the produced items of the questionnaire were revised and supplemented through a preliminary examination. After production of the questionnaire, an activity paper was produced and the items of the activity paper were continuously revised and supplement during the activity. This study was conducted on 12 students of research subjects and legal representatives who agreed to this study out of applicants to participate in this study. After a pre questionnaire, an activity was divided into two groups for each 50 minutes and in the activity, voice and video recording was performed for analysis. After the students in the activity had time to think provided activity assignments for themselves, they had an interaction to talk about each other s thinking process and prepared for their own activity papers. This activity continued a total of 10 times and after 10 times activity, a pro questionnaire, interviews about student s mathematics learning attitude were performed. After the completion of research performance, based on a frame analysis, the items of a pre and pro questionnaire and the 10 times activity was analyzed. After the analysis, a total of 3 corders including me participated to secure reliability on the analysis result. The results of this study are as follows:
In Research Problem 101, there were differences in the mathematical thinking levels of the students before and after their participation in the learner-centered mathematical activity. There was no lower case of a mathematical thinking level and in general, the mathematical thinking levels were improved. However, the improvement levels of the mathematical thinking levels were different according to students, and as a result of the qualitative review of student s mathematical thinking levels, the levels of the mathematical thinking function and strategy were found to show various aspects as a mutually organic relation.
In Research Problem 1-2, student s mathematical thinking levels in the learner-centered mathematical activity process showed higher levels in the latter activity compared to the early activity. It was found that the more positively they participated in the interaction, the higher their mathematical thinking levels were, and particularly, the levels of the complicate thinking strategy were higher. It was found that students experience thinking at a level that they never thought by sharing reciprocal opinion through interactions, and based on it, their thinking expands to the next stage and the thinking level experience development even in the activity process.
In research problem 2, the students showed positive attitudes in<V all self-concept about the mathematics subject, attitudes about the mathematics subject and learning habits about the mathematics subject after the learner-centered mathematical activity.
Below conclusions and implications could be derived from the above research results. It was found that the learner-centered mathematical activity had positive effects on not only student s cognitive aspect but also affective aspect. According to the 2009 Revised Mathematics Curriculum, the goal of mathematics education is to grow the ability to solve mathematical problem situations, and improve the affective area such as interest, pride in and a positive attitude toward mathematics through mathematical and logical thinking (Ministry of Education, Science and Technology, 2011). In this aspect, the learner-centered mathematical activity can be called a learning type in compliance with the education goal that the mathematics education of our country is currently pursued.
This study is significant as an attempt to search for a better teaching and learning method as a substitute for the long preserved traditional teaching and learning method in our mathematics education, and various attempts and efforts for improving teaching and learning are required to avoid the existing teaching and learning through this study, and a variety of studies and practical efforts are suggested to apply new teaching and learning methods to the education field.~http://dspace.ewha.ac.kr/handle/2015.oak/212876;
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