• 한국수학교육학회지시리즈A:수학교육
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• 제49권3호
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• pp.353-373
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• 2010

This research was to help slow learners to be motivated and to make their outcome productive, using GSP based on the mathematization theory for learning mathematics, as a way of encouraging the learner-centered approach. With 2 of the second graders in a high school, who had not yet understood trigonometric functions in their first grade period, 7 units of lesson plans were designed for the research. The results showed that first, understanding real life contexts and analyzing properties by observation, and experiment using GSP, to build the concept of trigonometric functions could be a foothold on which learner's organization and outcome from a horizontal mathematization led to vertical mathematization. Despite the delay during the level-up-stage for a while, the learners could attain the vertical mathematization stage and moreover the applicative mathematization through effective use of GSP and the interaction between the learners or a teacher and the learners. Second, using GSP was a vertical tool of connecting horizontal mathematization with vertical mathematization in forming the concept of trigonometric functions and its meaning could be understood by their verbalizing and presenting the outcomes through their active performance. Using GSP is helpful for slow learners to overcome learning difficulties, based on the instructional materials designed by Realistic Mathematics Education.

• 한국수학교육학회지시리즈A:수학교육
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• 제44권2호
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• pp.159-167
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• 2005

As the 7th mathematics curriculum reform in Korea was implemented with its goal based on Freudenthal's perspectives on mathematization theory, the research on the effect of mathematization has been become more significant. The purpose of this thesis is not only to find whether this foreign theory would be also applied effectively into our educational practice in Korea, but also to investigate how much important role teachers should play in their teaching students, in order that students accomplish the process of mathematization more effectively. Two case studies were carried out with two groups of middle-school students using qualitative-research method with the research instrument designed by the researcher. It was found that we could get the possibility of being able to apply effectively this theory even to our educational practice since the students engaged in their mathematization using the horizontal mathematization and the vertical mathematization in geometry. Also, it was mentioned that teachers' role was so important in guiding students' processes of mathematization, although mathematization is the teaching-learning theory, stimulating students' activities. Since the Freudenthal's mathematization applied in the thesis is so meaningful in our educational practice, we need more various research about this theory that helps students develope their mathematical thinking.

• 한국수학교육학회지시리즈A:수학교육
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• 제46권1호
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• pp.97-122
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• 2007

This article provides how to implement the use of Realistic Mathematics Education (RME) in a teaching a function at a school to improve students' mathematization for their mathematical thinking using technology, This study was planed to get research results using the mixed methodology with quantitative and qualitative methodologies. 120 middle school students participated in the study to bring us data about their mathematical achievement and disposition. Through the data analysis used ANCOVA, the students with the experiment of the mathematization and technology excelled the other groups of students who were not provided with technology or both of them. In analysis of the questions of the achievement test, the problems for vertical mathematization were presented harder for the students than the other problems for horizontal and applicative mathematization. The technology environment might have helped students manipulate the application of real-life problems easier. This means that teachers can put more careful assignment on vertical mathematization using technology. We also explored that learning and teaching under RME using technology encouraged students to refine and develop their informal functional concept and pursue higher thinking of formalization. The study results in a lot of resources for teachers to use into their teaching mathematics for improving students' mathematical thinking.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권3호
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• pp.345-365
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• 2006

This study, to effectively teach the concepts, principles and problem solving ability of the 2nd graders' learning of numbers and operations, offers realistic problem situation and focuses on the learning based on 'mathematization', one of the most important principles of RME (Realistic Mathematics Education) which is the mathematics education trend of Netherlands influenced by Freudenthal's theory. The instruction is applied to forty-one students of the 2nd grader for six weeks in twelve series in an elementary school, located in Seoul. To investigate the effects of the mathematising experience instruction for improving mathematical abilities, the group takes tests before and after the instruction. Also the qualitative analysis on the students' mathematising aspects through students' output at the instruction process is taken into account to evaluate the instruction's effects. The result shows that the mathematising experience instruction for improving mathematical abilities is proved to improve students' understanding of mathematical concepts and principles and their problem solving ability in learning numbers and operations after carrying out this instruction. Also the result indicates that students' mathematising aspects are mostly horizontal and vertical mathematization.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제23권2호
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• pp.297-312
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• 2009

다면체에 관한 연구 문제를 통해 수학사를 통한 문제 제기, 컴퓨터와 교구 등을 통한 수학실험, 추측, 그리고 정당화를 통한 수평적 수학화와 수직적 수학화의 과정을 다룬다. 구체적으로 본 논문에서는 아르키메데스 다면체와 카탈란 다면체를 중심으로, 수학사를 통해 등장하는 해밀턴 경로 문제, 다면체 색칠 문제, 그리고 다면체 전개도를 통한 구성 문제 등을 컴퓨터와 교구 등을 통해 수학실험으로 탐구하고, 추측과 정당화의 과정을 통해 얻어진 결과를 보고하며 또한 수학실험을 통해 발견된 미해결 문제를 제시한다.