• 한국수학교육학회지시리즈A:수학교육
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• 제41권3호
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• pp.273-289
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• 2002

It tends to be emphasized that mathematics is the important discipline to develop students' mathematical reasoning abilities such as deduction, induction, analogy, and visual reasoning. This study is aimed for investigating the present state about mathematical reasoning in secondary school. We survey teachers' opinions and analyze the results. The results are analyzed by frequency analysis including percentile, t-test, and MANOVA. Results are the following: 1. Teachers recognized mathematics as knowledge constructed by deduction, induction, analogy and visual reasoning, and evaluated their reasoning abilities high. 2. Teachers indicated the importances of reasoning in curriculum, the necessities and the representations, but there are significant difference in practices comparing to the former importances. 3. To evaluate mathematical reasoning, teachers stated that they needed items and rubric for assessment of reasoning. And at present, they are lacked. 4. The hindrances in teaching mathematical reasoning are the lack of method for appliance to mathematics instruction, the unpreparedness of proposals for evaluation method, and the lack of whole teachers' recognition for the importance of mathematical reasoning

• 한국수학교육학회지시리즈C:초등수학교육
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• 제8권1호
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• pp.13-22
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• 2004

There were a lot of challenges to reform mathematics education. These challenges may include reforms of teaching and learning methods, development of mathematics curriculum and textbooks, innovative resources for teaching mathematics. Although there is considerable consensus that meeting these challenges will require that mathematics teachers have deep insights about mathematics, about students as learners of mathematics, and about teaching method, the teachers themselves may have little knowledge of them. The most of the professional development includes elective participation in reeducation course, workshop, and special lectures which designed to transmit a specific set of ideas, techniques, or materials to teachers. But such approaches treat mathematics teaching as routine and technical, and also provide limited opportunities for meaningful interactions within the teaching community. So, this paper suggests that what is needed to develop professional teachers of mathematics is community where teachers work with colleagues rather than working alone.

• 한국초등수학교육학회지
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• 제15권1호
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• pp.95-120
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• 2011

논술에서 요구되는 능력, 즉 논술 능력은 기본적으로 이해력, 논리적이고 창의적인 사고력, 표현력과 같은 고등사고능력이다. 그러나 이러한 논술 능력은 단기간에 신장되지 않는다. 더욱이 수학은 계열성이 강한 학문으로 이러한 능력의 신장을 위해서는 초등학교 저학년 때부터 차근차근 단계에 맞게 준비해야하는 것은 어찌 보면 당연한 일이다. 그러나 현재 초등 수리 논술에 대한 용어의 정의가 없어 사교육 시장을 중심으로 무분별하게 초등 수리 논술이라는 용어가 사용되고 있다. 초등학교는 1학년부터 6학년까지 다양한 발달단계의 학생들이 모여 있는 곳이다. 초등 논술이 입시논술과 그 성격과 지도방향이 다르듯 초등 수리 논술 또한 그 성격과 지도 방향이 달라야 한다. 논술 능력은 단기간에 완성되는 것이 아니므로 어릴 때부터 꾸준한 연습이 필요하며, 더욱 중요한 것은 흥미를 잃지 않도록 하는 것이다. 따라서 초등 수리 논술의 올바른 개념을 정립하고, 성격과 지도방향을 설정하여 후속연구를 활발히 해야 할 필요성이 있다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제18권2호
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• pp.103-128
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• 2014

This paper presents the Global van Hiele (GVH) questionnaire as a tool for mapping knowledge and understanding of plane and solid geometry. The questionnaire facilitates identification of the respondents' mastery of the first three levels of thinking according to van Hiele theory with regard to key geometrical topics. Teacher-educators can apply this questionnaire for checking preliminary knowledge of mathematics teaching candidates or pre-service teachers. Moreover, it can be used when planning a course or granting exemption from studying in basic geometry courses. The questionnaire can also serve high school mathematics teachers who are interested in exposing their students to multiple-choice questions in geometry.

• 한국수학교육학회지시리즈A:수학교육
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• 제60권4호
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• pp.555-580
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• 2021

본 연구의 목적은 수학 학습에 대한 상황적 흥미 요인을 탐색하고, 이 결과를 바탕으로 수학 수업 내의 교수·학습 방법과 교수·학습 활동 및 수업 외의 비교과 활동에 포함되어 있는 상황적 흥미 요인을 밝히는 것이다. 고등학생들을 대상으로 설문을 실시한 결과 수학 학습에 대한 상황적 흥미의 요인은 10개의 세부영역(즐거움, 호기심, 유능감/ 실생활, 타교과, 진로/ 사전 지식, 지식의 축적/ 변환, 해석), 4개의 일반영역(정서, 태도/ 지식, 이해), 2개의 고차영역(정의/인지)으로 추출되었다. 또한 교수·학습 방법과 교수·학습 활동 및 비교과 활동에는 상황적 흥미의 다양한 요인이 포함되어 있음을 밝혔다. 10개의 수학 학습에 대한 상황적 흥미 요인에 개인적 흥미로 발달에 필요한 요인이 공유되어 있었고, 이러한 연구 결과는 수학 학습 흥미 발달에 관한 연구로 확장될 수 있을 것이다.

• 대한수학교육학회지:수학교육학연구
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• 제12권3호
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• pp.409-424
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• 2002

The historico-genetic principle has been advocated continuously, as an alternative one to the traditional deductive method of teaching and learning mathematics, by Clairaut, Cajori, Smith, Klein, Poincar$\'{e}$, La Cour, Branford, Toeplitz, etc. since 18C. And recently we could find various studies in relation to the historico-genetic principle. Lakatos', Freudenthal's, and Brousseau's are representative in them. But they are different from the previous historico- genetic principle in many aspects. In this study, the previous historico- genetic principle is called as classical historico- genetic principle and the other one as modern historico-genetic principle. This study shows that the differences between them arise from the historical views of mathematics and the development of the theories of mathematics education. Dewey thinks that education is a constant reconstruction of experience. This study shows the historico-genetic principle could us embody the Dewey's psycological method. Bruner's discipline-centered curriculum based on Piaget's genetic epistemology insists on teaching mathematics in the reverse order of historical genesis. This study shows the real understaning the structure of knowledge could not neglect the connection with histogenesis of them. This study shows the historico-genetic principle could help us realize Bruner's point of view on the teaching of the structure of mathematical knowledge. In this study, on the basis of the examination of the development of the historico-genetic principle, we try to stipulate the principle more clearly, and we also try to present teaching unit for the logarithm according to the historico- genetic principle.

• East Asian mathematical journal
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• 제28권4호
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• pp.383-401
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• 2012

The purpose of mathematics education includes two important areas; cognitive area that emphasizes mathematical knowledge and understanding and affective area that stresses mathematical interest and attitude. The purpose of mathematics education is not only in acquiring the contents and knowledge but also rousing up interest and attention toward mathematics. Therefore, effort to accomplish this affective purpose has to be made. Introducing history of mathematics to teaching can be a important method for the students to arouse interest and attention toward mathematics. History of mathematics can help the students who are familiar to only manipulation of the symbols to develop a new way of thinking and mathematical thoughts arousing reflective thinking. According to the survey, although the effect of using mathematics history has been recognized, the mathematics history has neither been developed as teaching materials nor reflected in the courses of study. The purpose of this research is to develop the reading materials into suit for the mathematics curriculum to extract contents of the mathematics valuable in using in elementary mathematics teaching, and to investigate the effect of reading materials using the history of mathematics on learning attitude in elementary school. The way of developing materials in this study is as follows. First, to select the interesting and instructive subject for the elementary students such as the story and life of a mathematician, developmental stages of mathematical theory and calculation currently used and finding the patterns of the rules that requires mathematical thoughts. Second, to classify the selected items according to mathematics curriculum. Third, to reorganize the classified items of the appropriate grade with the reading materials of dialogue pattern in order to draw attention and interest from the students I developed 18 kinds materials in accordance with the above procedure and applied 5 materials among them to one class in 4th grade. Analysing the student's responses, First, using history of mathematics helps the students to arouse interest and confidence on mathematical learning attitude. And the students became better attitude of studying by oneself and attention on class. Second, as know by opinions after lesson, most students have a chance refresh one's thinking of mathematics, want to know the other content of history of mathematics and responded to study hard in mathematics. As a result, the reading materials on the basis of the history of mathematics motivates students for mathematics and helps them become confident in mathematics. If the materials are complemented properly, they will be useful and effective for students and teachers.

• 한국수학교육학회지시리즈A:수학교육
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• 제50권3호
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• pp.355-365
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• 2011

The purpose of this study is to provide mathematical knowledge for supporting the didactical knowledge on circular measure and radian in the high school curriculum. We show that circular measure related to arcs can be mathematically justified as an angular measure and radian is a well defined concept to be able to reconcile the values of trigonometric functions and ones of circular functions, which are real variable functions. Radian has two-fold intrinsic attributes of angular measure and arc measure on the unit circle, in particular, the latter property plays a very important role in simplifying the trigonometric derivatives. To improve students's low academic achievement in trigonometry section, the useful advantage and the background over the introduction of radian should be preferentially taught and recognized to students. We suggest some teaching plans to practice in the class of elementary and middle school for enhancing teachers' and students' understanding of radian.

• East Asian mathematical journal
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• 제28권2호
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• pp.135-158
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• 2012

The ideals of the rings of integers are used to induce rational number system as operators(=group homomorphisms). We modify this inducing method to be effective in teaching rational numbers in secondary school. Indeed, this modification provides a nice model for explaining the equality property to define addition and multiplication of rational numbers. Also this will give some explicit ideas for students to understand the concept of 'field' efficiently comparing with the integer number system.

• 대한수학교육학회지:수학교육학연구
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• 제16권2호
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• pp.95-113
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• 2006

본 연구는 학교 수학에서 추론 지도의 수준을 보다 상세히 구분해 보고자 한 것이다. 수학의 특징으로부터, 대상에서 분리된 순수한 형식적 관점은 새로운 지식의 창안에서 한계를 지닌다는 점을 알 수 있으며, 수학교육에서도 이를 반영할 필요가 있다고 본다. 이런 점에서 귀납 추론과 형식적 연역 추론의 매개 단계로서 구체적 조작이나 감각 경험과 관련된 직관적 증명의 수준을 설정하는 것이 적절할 것으로 생각되며, 이 수준의 핵심적인 활동은 경험으로부터 일반성을 통찰하는 것이다. 이 수준은 낮은 수준의 귀납 추론보다는 대상과 분리되며 보다 형식적인 논리의 개입을 필요로 하는 과정에 있다. 이와 같이 보다 점진적으로 대상으로부터 분리되고 형식적 논리를 학습할 수 있도록 추론 지도 수준을 구분하고, 이에 따라 수학적 추론을 지도하는 것이 필요할 것이다.