• 대한수학교육학회지:학교수학
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• 제13권3호
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• pp.423-446
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• 2011

학교수학에서 정적분과 치환적분법의 개념은 확률밀도함수의 도입, 연속확률변수의 기댓값, 정규분포의 표준화와 관련하여 수학적 연결성을 가진다. 그러나 개정교육과정의 '미적분과 통계 기본', '적분과 통계' 과목의 교육과정해설서와 검인정 교과서 및 익힘책에서 적분단원과 통계단원 사이의 수학적 연결성 고려가 어려움을 발견하였다. 본 연구는 학교수학에서 확률밀도함수의 도입, 연속확률변수의 기댓값, 정규분포의 표준화에 대하여 적분단원과의 수학적 연결성을 고려한 지도방안 마련을 목적으로 한다. 세개념에 대한 학생대상 실태조사와 개정교육과정의 교육과정해설서, 교과서, 익힘책, 그리고 국내 외 통계학(확률론) 도서(국내 13종, 국외 22종)의 내용을 비교하였다. 이를 바탕으로 세 개념에 대한 지도내용을 개발하여 실제 수업에 적용해보았고, 교육과정개정이나 교과서의 내용구성 변화에 대한 시사점을 발견하여 그 결과를 제언하였다.

• 대한수학교육학회지:수학교육학연구
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• 제8권2호
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• pp.651-662
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• 1998

Mathematics is means for making sense of one's experiential world and products of human activities. A usefulness of mathematics is derived from this features of mathematics. Keeping the meaning of situations during the mathematizing of situations. However, theories about the development of mathematical concepts have turned mainly to an understanding of invariants. The purpose of this study is to show the possibility of computer in representing situation and phenomena. First, we consider situated cognition theory for looking for the relation between various representation and situation in problem. The mathematical concepts or model involves situations, invariants, representations. Thus, we should involve the meaning of situations and translations among various representations in the process of mathematization. Second, we show how the process of computational mathematization can serve as window on relating situations and representations, among various representations. When using computer software such as ALGEBRA ANIMATION in mathematics classrooms, we identified two benifits First, computer software can reduce the cognitive burden for understanding the translation among various mathematical representations. Further, computer softwares is able to connect mathematical representations and concepts to directly situations or phenomena. We propose the case study for the effect of computer software on practical mathematics classrooms.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제6권1호
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• pp.41-54
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• 2002

The purpose of this study is to find out what mathematical situation means, how to pose a meaningful situation and how situation-centered teaching could be done. The obtained informations will help learners to improve their math abilities. A survey was done to investigate teachers' perception on teaching-learning in mathematics by elementary teachers. The result showed that students had to find solutions of the textbook problems accurately in the math classes, calculated many problems for the class time and disliked mathematics. We define mathematical situation. It is artificially scene that emphasize the process of learners doing mathematizing from physical world to identical world. When teacher poses and expresses mathematical situation, learners know mathematical concepts through the process of mathematizing in the mathematical situation. Mathematical situation contains many concepts and happens in real life. Learners act with real things or models in the mathematical situation. Mathematical situation can be posed by 5 steps(learners' environment investigation step, mathematical knowledge investigation step, mathematical situation development step, adaption step and reflection step). Situation-centered teaching enhances mathematical connections, arises learners' interest and develops the ability of doing mathematics. Therefore teachers have to reform textbook based on connections of mathematics, other subject and real life, math curriculum, learners' level, learners' experience, learners' interest and so on.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제9권3호
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• pp.285-294
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• 2005

The author has been teaching with an instructional module consisting of many mathematical concepts, based on designs formed by personal names or words to arouse students' interesting in learning mathematics. This module has been growing since it was first used as a supplementary lesson for calculus students. Now it consists of concepts that connect with mathematical topics such as number sense, algebraic thinking, geometry, and statistical reasoning, as well as other subjects such as art and quilt design. With its content we can provide our students the basic mathematical knowledge needed for further study in their own fields. In this article, we will demonstrate the latest development of this instructional module, which makes connections between mathematical knowledge and the design of personal quilt patterns. We will exhibit a 'Quilt of Nations' which consists of the designed quilt blocks of different countries, such as USA, Japan, Taiwan, Korea and others, as well as a quilt design using the abbreviation of this seminar. Then we will talk about how the connections are built, and how to design these mathematically rich, uniquely created, beautifully designed, and personalized quilt block patterns.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제10권1호
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• pp.29-39
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• 2007

This paper is to give a brief introduction to a new discipline called 'conceptual metaphor' and 'mathematical metaphor(Lakoff & Nunez, 2000) from the viewpoint of mathematics education and to analyze the metaphors at 4th graders' mathematics classroom as a case of conceptual metaphors. First, contemporary conception on metaphors is reviewed. Second, it is discussed on the effects and defaults of metaphors in teaching and learning mathematics. Finally, as a case study of mathematical metaphors, conceptual metaphors on the concepts of triangles at 4th graders' mathematics classrooms are analyzed. Students may reason metaphorically to understand mathematical concepts. Conceptual metaphor makes mathematics enormously rich, but it also brings confusion and paradox. Digging out the metaphors may lighten both our spontaneous everyday conceptions and scientific theorizing(Sfard, 1998). Studies of metaphors give us the power of understanding the culture of mathematics classroom and also generate it.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제12권3호
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• pp.215-233
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• 2008

Deep comprehension of basic mathematical notions and concepts is a basic condition of a successful teaching. Some elements of algebraic thinking belong to the elementary school mathematics. The question "What stays the same and what changes?" link arithmetic problems with algebraic conception of variable. We have studied beliefs and comprehensions of future elementary school mathematics teachers on early algebra. Pre-service teachers from three academic pedagogical colleges deal with mathematical problems from the pre-algebra point of view, with the emphasis on changes and invariants. The idea is that the intensive use of non-formal algebra may help learners to construct a better understanding of fundamental ideas of arithmetic on the strong basis of algebraic thinking. In this article the study concerning arithmetic series is described. Considerable number of pre-service teachers moved from formulas to deep comprehension of the subject. Additionally, there are indications of ability to apply the conception of change and invariance in other mathematical and didactical contexts.

• 대한수학교육학회지:수학교육학연구
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• 제20권3호
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• pp.293-303
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• 2010

이 연구의 목적은 인식론 분석을 통해 수학사의 세 가지 역할을 분류하는 것이다. 무한과 극한에 대한 수학사를 바탕으로 네 가지의 다른 인식론들을 통해 "잠재적 무한"과 "실제적 무한" 담화를 묘사한다. 무한과 극한 개념의 상호 의존성을 또한 제시한다. 이러한 분석들을 이용하여 무한과 극한에 대한 수학사의 세가지 다른 사용을 보이고자 한다 : 과거, 현재, 그리고 미래사용.

• 대한수학교육학회지:학교수학
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• 제14권4호
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• pp.469-493
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• 2012

본 연구는 증명을 성공적으로 구성하는 학생들은 수학적 개념을 어떻게 이해하고 있으며, 증명을 어떻게 구성하는 지를 살펴보고 이를 통해 증명을 구성하는 다양한 방식과 개념 이해의 관련성을 분석하는 데 목적이 있다. 증명 구성에 도움이 되는 수학 학습에 제언을 얻기 위해서는 증명을 구성하는 과정과 그 과정에서 개념이 어떻게 반영되고 이용되는 지를 살펴볼 필요가 있다. 이를 위하여 4명의 수학교육과 학생들을 대상으로 사례연구를 실시하였다. 그 결과 구문론적 증명을 하는 학생들은 형식적 개념의 내용을 정확하게 알고 있을 뿐만 아니라 그 개념이 담겨있는 명제는 어떠한 방식으로 증명하는 지 그 방법까지 알고 있었다. 실제 증명에서도 평소 증명 경험을 통하여 학습한 증명 전개 방법을 이용하여 증명하는 것을 볼 수 있었으며, 이로부터 증명 방법에 대한 절차적 지식이 구문론적 증명에는 중요한 요소라는 결론을 얻을 수 있었다. 의미론적 증명을 하는 학생들은 형식적 개념의 내용을 정확하게 알고 있고 그 내용과 의미를 본인만의 언어나 그림으로 표현한 개념 이미지를 가지고 있었다. 구문론적 증명을 하는 학생들의 개념 이미지와 비교해보았을 때, 의미론적 증명을 하는 학생들의 개념 이미지는 구문론적 증명을 하는 학생들의 개념 이미지보다 형식적 개념의 내용을 잘 반영하고 있었다. 이러한 개념 이미지는 개념 이미지를 활용하여 증명의 아이디어를 생각하고, 생각한 아이디어를 증명의 형식에 맞게 표현하는 데 사용된다는 점에서 의미론적 증명에 필요한 요소라는 것을 발견할 수 있었다.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제21권3호
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• pp.527-540
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• 2007

수학적 지식들이 참으로 인정되기 위해서는 많은 시간과 노력이 필요하다. 수학적 지식들은 추가되거나, 수정되거나, 혹은 거짓인 것으로 밝혀져왔다. 수학적 지식들은 수학적 언어, 명제, 추론, 질문, 메타수학적 관점으로 이루어져있다. 이것들은 수학자들의 연구과 반박에 의해, 반박을 고려한 증명의 수정에 의해, 새로운 개념의 소개에 의해, 새로운 개념에 대한 질문의 추가에 의해, 새로운 질문에 대한 답변을 찾기 위한 노력에 의해, 이전의 연구들을 현재에 적용하려는 시도에 의해 끊임없이 변화되어왔다. 본 연구에서는 Kitcher가 제시한 수학적 지식의 변화를 소개하고, 그 변화의 다양한 예에 대하여 살펴본다.

• East Asian mathematical journal
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• 제38권4호
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• pp.463-496
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• 2022

The purpose of this study is to analyze the mathematical creativity and computational thinking of mathematically gifted elementary students through a convergence class using programming and to identify what it means to provide the convergence class using Python for the mathematical creativity and computational thinking of mathematically gifted elementary students. To this end, the content of the nine sessions of the Python-applied convergence programs were developed, exploratory and heuristic case study was conducted to observe and analyze the mathematical creativity and computational thinking of mathematically gifted elementary students. The subject of this study was a single group of sixteen students from the mathematics and science gifted class, and the content of the nine sessions of the Python convergence class was recorded on their tablets. Additional data was collected through audio recording, observation. In fact, in order to solve a given problem creatively, students not only naturally organized and formalized existing mathematical concepts, mathematical symbols, and programming instructions, but also showed divergent thinking to solve problems flexibly from various perspectives. In addition, students experienced abstraction, iterative thinking, and critical thinking through activities to remove unnecessary elements, extract key elements, analyze mathematical concepts, and decompose problems into small components, and math gifted students showed a sense of achievement and challenge.