• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.69-96
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• 2008

The purpose of this paper is to perceive the problems of current geometry education in the middle school mathematics, to develop some learning materials fitted for the mathematising activities based on Freudenthal's learning theories and to analyze the mathematising process followed by teaching-learning activities. For this purpose, we design activity-oriented learning materials for geometry based on Freudenthal's learning theories, and appropriate teaching-learning models are established for the middle school geometry at the 8-NA stage level according to the theory of van Hiele's geometry learning steps. After applied to the practical lessons, the effects of mathematical activities are analyzed.

• Communications of Mathematical Education
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• v.18 no.2 s.19
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• pp.427-440
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• 2004

Freudenthal의 수학화 이론에 대한 지금까지의 대부분의 연구는 이론의 탐색에 집중하고 이에 따른 학습 지도 방안과 자료개발에만 역점을 두었던 것이 그 한계점으로 지적되어져 왔다. 이에 본 연구자는 실제 이 이론이 어떻게 학습 현장에 적용될 수 있는지에 대해 첫째, Freudenthal의 수학화에 의한 도형 지도에서 학생이 어떻게 수학화를 이루어 가는지를 조사하였고, 둘째, 학습의 주체자인 학생들의 능동적인 활동을 강조한 수학화 과정에서 교수의 주체자인 교사는 학생들의 수학화가 원만히 이루어지게 하기 위하여 어떤 역할을 수행하게 되는지를 중학교 1학년 학생을 대상으로 사례연구를 실시하여 조사하였다.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.95-116
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• 2013

Though the term "mathematical modeling" has no single definition or perspective, it is pursued commonly by groups from various perspectives who emphasize the activities of understanding and representing real phenomenon mathematically, building models to solve problems, and reinterpreting real phenomenon to make an attempt to understand the real world and related mathematical models more deeply. The purpose of this study is to identify how mathematization arises and find difficulties of mathematization in mathematical modeling process that share common features with the mathematical modeling activities as presented here. As a result of this research, we confirmed that the students mathematized real phenomena by building various representations, and interpreting them with regard to relationships and contexts inherent real phenomena. The students' communication fostered interplay between iconic representations and indexical representations. We also identified difficulties of mathematization in mathematical modeling process.

• Communications of Mathematical Education
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• v.20 no.3 s.27
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• pp.391-405
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• 2006

In this paper we study on administration system and student's activities in whole-day club activities. As a result of this study we propose teaching methods, mathematical program for the year, and concreate teaching-learning materials for mathematical circle in whole-day club activities.

• Journal of Educational Research in Mathematics
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• v.16 no.4
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• pp.297-312
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• 2006

As research on the instruction method of the concept of irrational numbers, this thesis is theoretically based on the Freudenthal's Mathematising Instruction Theory and a conducted case study in order to find an introduction method of irrational numbers. The purpose of this research is to provide practical information about the instruction method ?f irrational numbers. For this, research questions have been chosen as follows: 1. What is the introducing method of irrational numbers based on the Freudenthal's Mathematising Instruction Theory? 2 What are the Characteristics of the teaming process shown in class using introducing instruction of irrational numbers based on the Freudenthal's Mathematising Instruction? For questions 1 and 2, we conducted literature review and case study respectively For the case study, we, as participant observers, videotaped and transcribed the course of classes, collected data such as reports of students' learning activities, information gathered through interviews, and field notes. The result was analyzed from three viewpoints such as the characteristics of problems, the application of mathematical means, and the development levels of irrational numbers concept.

• Communications of Mathematical Education
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• v.12
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• pp.1-19
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• 2001

유치원과 초등학교 1학년 아동은 그들의 발달특성과 학습의 효율성 측면을 고려할 때, 일상생활 경험과 놀이 활동 등을 이용한 활동중심 교육방법으로 상호 연계성있게 수학을 학습하는 것이 바람직하다. 이러한 필요성에서, 본 연구는 현행 교육과정 상에 제시된 수학교육의 성격과 목표, 내용, 교수방법, 평가 면에서 유치원과 초등학교 1학년 간에 얼마나 연계되어 있는 지를 분석해 보았다. 분석 결과, 유치원과 초등학교 1학년 수학 교육과정 간에는 수학교육의 방향 및 목표, 내용 영역, 교수학습 방법, 평가 면에서 대체로 높은 연계성을 보였다. 그러나 교과 편제나 명칭, 세부적인 내용 구성에서 차이가 있었으므로 이를 해결하기 위한 교육과정 상에서의 연계 실천 방안을 제시해 보았다. 그리고 실제 수학 교육 활동측면에서의 실천 방안으로서 활동중심 교수학습 자료의 개발, 수학 영역 설치를 통한 개별화 교육의 실천, 가정과의 협력 방안 등을 제시해 보았다.

• School Mathematics
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• v.16 no.3
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• pp.409-444
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• 2014

There have been many discussions of teaching and learning mathematics through modeling activities in mathematics education research community. Although there has been some agreement regarding modeling activity as an alternative way to support mathematics teaching and learning, there is still no clear consensus on these issues. This paper reports a case study which aims to identify ways to design modeling tasks and instruction to foster meta-level learning, and investigate how modeling activities can facilitate meta-level learning. From the results of teaching experiment, this study examines the potential of modeling activities in mathematics teaching and learning.

• School Mathematics
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• v.14 no.1
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• pp.151-163
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• 2012

In 2006 with the revised national curriculum, Elementary mathematics teaching and learning methods are presented in the following ways. Learners explore the way through the operational activities of the teachers and students with learning and learners' active learning activities, etc., and an active learning based on the principle of attention to learning how to maximize the effectiveness are required. In this study, from first grade through sixth grade elementary school mathematics textbooks for all learning activities presented in 10 different types were investigated This result of 5 contents area of number and operation, geometry, probability and statistics, measurement and patterns and problem solving and divided into low, middle, and hight three were intentional. In addition, teachers are looking forward to this result was compared with the type of activity.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.701-722
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• 2010

Students have to investigate, experiment and inquire using the manipulative materials and real-world thing for studying Geometry. Manipulative materials activities encourage to understand mathematical concept and connection of symbol. Experiment activities using the computer focused the student's intuitive and inquisitive activities because of visualization of an abstract mathematics concept. This study developed a workbook through the use of manipulative materials and computer for operating and experimenting, and suggested a method for inquiry of geometrical properties and proved an effect. Manipulative materials-experiment activities was proven effective to middle level and lower level students in understanding the geometrical properties, and was proven effective to high level and lower level students when it comes to mathematical communication ability. When students operate, at first, they have to know about the feature and information of the materials, and the teacher has to make an elaborate plan and encourages the students to discuss about this.

• Journal of Educational Research in Mathematics
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• v.13 no.4
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• pp.463-483
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• 2003

In the learning of mathematics, students experience the semiotic activities of representing and interpreting mathematical signs. We called these activities as the representing and interpreting of mathematical signs. On the foundation of Peirce's three elements of the sign, we analysed that students constructed the representamen to interpret the concept of correlation as for the object, "as one is taller, one's size of foot is larger" 4 middle school students who participated the gifted center in Seoul, arranged the statistical data, constructed their own representamen, and then learned the conventional signs as a result of the whole class discussion. In the process, students performed the detailed representing and interpreting of signs, depended on the templates of the known signs, and interpreted the process voluntarily. As the semiotic activities were taken place in this way, it was needed that mathematics teacher guided the representing and interpreting of mathematical signs so that the representation and the meaning of the sign were constructed each other, and that students endeavored to get the negotiation of the interpretants and the representamens, and to reach the conventional representing.