• 한국수학교육학회지시리즈A:수학교육
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• 제41권2호
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• pp.173-187
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• 2002

The purpose of this study through ethnographic inquiry is to describe how an elementary teacher teaches mathematics with understanding. The ways that teachers'beliefs affect instructional activities, what means understanding from the view of cognitive psychology, and ethnographic research tradition were reviewed to anchor theoretical background of this study. A third-grade teacher and his 45 students were selected in order to capture vivid and thick descriptions of the teaching and learning activities of mathematics. Three major sources of data, that is, participant-observation with video taping, formal and informal interviews with the teacher and his students, and a variety of official documents were collected. These data were analyzed through two phases: data analysis in the field and after the fieldwork. According to data analysis, ‘teaching mathematics with understanding’ was identified as the teachers central belief of teaching mathematics. In order to implement his belief in teaching practices, the teacher made use of three strategies: ⑴ valuing individual student's own way of understanding, ⑵ bring students' everyday experiences into mathematics classroom, and ⑶ lesson objectivies stated by students. It is suggested for future research that concrete and specific norms of mathematics classroom for the improvement of mathematics understanding are needed to be identified and that experienced and skillful teachers' practical knowledge should be incorporated with theories of teaching mathematics and necessarily paid more attention by mathematics educators.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제15권3호
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• pp.209-228
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• 2011

Many studies such as Pepin (1999a; 1999b), Kaiser (2002), and Park & Leung (2006) revealed that there is a strong dependence of mathematics teaching on cultural traditions in different countries. This study was set up as a detailed comparison between the intended curricula in Berlin and Hong Kong to explore how cultural tradition influenced the intended curriculum. In this study, the intended curriculum is what the (local, state or national) curriculum developers stipulate in the official documents. The German educational system is influenced by the curriculum tradition called Didaktik. Didaktik is a tradition about teaching and learning. Since 16th century, Didaktik has been the most important tool for planning, enacting, and thinking about teaching in most of northern and central Europe (Westbury, 1998). On the other hand, the education system in Hong Kong is influenced by both the Anglo-Saxon curriculum tradition and the Confucian heritage culture (CHC). It was found in this study that, although many studies revealed that there is a strong dependence on cultural traditions of mathematics teaching in different countries, other factors such as social factors or the education system also played an important part in shaping the intended mathematics curriculum. So a simplistic view of dependence of the curriculum on cultural traditions is not warranted. The formation of the curriculum is a much more complicated process encompassing various factors including needs of society, advancement of technology, and government policies at different levels.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제17권3호
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• pp.205-230
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• 2014

구성주의를 반영한 대표적인 교수 학습 이론인 학습자 중심 수학 수업이 이상적으로 실천되기 위해서는 구성주의 관점에 따른 교육과 관련된 유무형의 제 요소들(지식관, 학습자관, 교사의 역할, 평가, 수업 형식, 학습, 수업 자료 등)이 융합되어야 한다. 그 중 수업 자료는 학습자들이 스스로 지식을 구성할 수 있는 지적 능력이 있음을 전제로 개발되어야 하고, 지식의 통합성, 다양성 등이 반영되어야 할 것이며 개방형 속성을 지닌 자료이어야 한다. 이외에도 객관적 인식론을 적용할 때 갖던 특징과는 다른 특징들을 지녀야 하므로, 수업 자료가 그러한 특징들을 가지고 있는지 분석해 볼 필요가 있다. 이를 위해 2009 개정 교육과정 1-2 학년군 수학(3) 교과서의 스토리텔링이 처음 도입된 단원 중 수와 연산 영역에 해당되는 <1. 세 자리수>와 미국에서 사용되고 있는 구성주의 수학교실 2학년의 <3. 자릿값의 이해>를 비교하여 분석하였다.

• 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.

• Smart Structures and Systems
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• 제24권2호
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• pp.233-242
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• 2019

In this paper, an inverse approach based on uniform load surface (ULS) is presented for structural damage localization and quantification. The ULS is excellent approximation for deformed configuration of a structure under distributed unit force applied on all degrees of freedom. The ULS make use of natural frequencies and mode shapes of structure and in mathematical point of view is a weighted average of mode shapes. An objective function presented to damage detection is discrepancy between the ULS of monitored structure and numerical model of structure. Solving this objective function to find minimum value yields damage's parameters detection. The teaching-learning based optimization algorithm has been employed to solve inverse problem. The efficiency of present damage detection method is demonstrated through three numerical examples. By comparison between proposed objective function and another objective function which make use of natural frequencies and mode shapes, it is revealed present objective function have faster convergence and is more sensitive to damage. The method has good robustness against measurement noise and could detect damage by using the first few mode shapes. The results indicate that the proposed method is reliable technique to damage detection in structures.

• 한국수학교육학회지시리즈A:수학교육
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• 제59권2호
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• pp.185-199
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• 2020

이 연구의 목적은 수학에 인문학적 상상력을 접목하는 것이 수학교육에 주는 의미를 논의하고, 수학교육에 시사점을 제안하는 것이다. 전통적으로 수학은 추상적 사고를 대상으로 하기 때문에 우리의 삶의 문제와는 거리가 있다고 인식되었다. TIMSS나 PISA와 같은 국제 연구에 따르면, 우리나라 학생들의 수학학업성취도는 다른 선진 국가들의 학생들에 비하여 상대적으로 높으나, 수학에 대한 태도는 매우 부정적이고 삶에 대한 만족도도 낮은 편이다. 수학과 인문학적 상상력을 연계하여 학습하도록 하는 것은 학생들에게 인간의 삶의 문제에 대하여 인문학적인 관점으로 보도록 한다. 이 연구에서는 수학교육을 위한 수학과 인문학적 상상력을 접목의 의미를 생각해 보고, 학교의 수학교육에서 적용해 볼 수 있는 몇 가지 사례를 소개한다. 연구자는 수학을 배우는 궁극적인 이유는 학습자로 하여금 깨달음을 얻도록 하는 것이고, 모두가 보다 행복한 삶을 살아가기 위한 것이어야 한다고 주장한다.

• 한국수학사학회지
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• 제30권2호
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• pp.101-119
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• 2017

This paper is a follow up study of [2]. In this paper we analyse the contents of middle school mathematics textbooks published in the 1st National Curriculum Period centered on the concept 'straight line' and discuss how they are different from contemporary mathematics textbooks in view of connectedness of contents, mathematical terms, textbook as a learning material vs. teaching material, relationship between contents of national curriculum and textbooks, and some topics related to direct proportion, function, method of equivalence as a method for solving simultaneous linear equations and so on. The results of our analysis and discussion suggest implications for reforming mathematics curriculum and developing mathematics textbooks.

• 한국수학교육학회지시리즈A:수학교육
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• 제50권3호
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• pp.285-308
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• 2011

The objective of this study is to review how researches on mathematics education are being conducted currently in Korea and overseas and to examine the current state of domestic researches on mathematics education from a broader view. Although many efforts have been made to understand trends in researches on mathematics education, there have been few in depth studies on research trends in overseas or for comparison between domestic and overseas trends. Thus, this study classified and analyzed 181 domestic articles between 2005 and 2009 in the journals and and 201 overseas articles in the journals and according to year, research area, research contents, school level, research method, and key words using the PME classification system with some modification. Through these analysis, we examined research trends on secondary mathematics education in Korea and overseas. The research findings are as follows. First, 'teaching learning process' was a spotlight area both at home and overseas, and 'realistic mathematics' and 'social cultural subjects' were not covered much either at home or overseas. 'Mathematical communication' occupied a very small portion in Korea but was a highly interesting area in overseas research. Second, research contents of interest were different between Korea and overseas. Research on general area was the mainstream. But geometry and statistics were mainly studied in Korea and algebra and analysis in overseas. Third, research related to middle school was twice more than that related to high school in Korea, But, research related to middle school was the same as high school in overseas. Fourth, qualitative research was the absolute majority both at home and overseas, and philosophical didactical analysis was used only in Korea. Fifth, the order of key words were problem solving - teacher - curriculum - creativity - textbook in Korea, but teacher - teaching - semiotic - affective factor - proo f- problem solving - technology in overseas.

• 한국융합학회논문지
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• 제13권4호
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• pp.63-70
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• 2022

최근 교육시장의 변화와 코로나로 인해 과외 시장 및 온라인 학습시장으로 소비자들이 이동하여 대형 교육 프랜차이즈 사업이 매출액을 중시하는 입장에서 수익구조를 극대화하는 비즈니스 모델로 재편되고 있다. 교육환경의 변화로 교수자 중심에서 학생 중심으로 개별 맞춤 서비스를 제공하고, 학생들 스스로가 자기주도 학습이 가능할 수 있도록 학습동기를 부여하고 학습기술을 배양할 수 있는 새로운 학습균형 모델이 요구되고 있다. 본 논문에서는 수학 교육서비스 프랜차이즈 사업을 운영하는 가맹본부 입장에서 최근 교육 트렌드와 소비자의 욕구를 만족하면서 기업의 수익구조를 향상 시킬 수 있는 새로운 수학 프랜차이즈 모델(K-MODEL)을 제안한다. K-MODEL은 차별화 콘텐츠 및 서비스, 학습 및 운영 프로세스, 학습 성취도 향상을 위한 다양한 프로그램을 개발하여 가맹본부와 가맹사업을 진행하는 가맹점사업자들이 안정적인 수익구조를 가질 것으로 기대한다.

• 한국학교수학회논문집
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• 제12권2호
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• pp.309-325
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• 2009

본 연구의 목적은 미국의 개정 교과서(reform curriculum) 중 하나인 CPMP 교과서 (코스1-코스3)와 한국의 교과서(중3-고2)를 사전에 설정한 비교 준거를 토대로 비교분석하여 두 교과서 및 교수 학습 환경에서의 차이점을 토대로 한국의 수학과 교육과정 및 수학 교과서의 질적 수준을 향상시킬 수 있는 요인을 찾아보는 데 있다. 비교 준거는 두 교과서의 구성상의 특징인 내용의 위계 및 지도계열의 설정, 수업의 방법적 접근 방법, 교수 학습 환경으로 설정하였다. 연구 결과, 한국의 교과서는 수학의 구조 또는 계통성, 수학 내적 연결망을 강조하여 수학의 구조를 효율적으로 전달할 수 있는 교수 방법에 맞게 구성되어 있고, CPMP 교과서는 수학의 계통성과 더불어 수학외적 연결망과 통합 연결망을 강조하여 학생들이 수학적 개념을 보다 다양한 맥락 속에서 탐구 활동을 통하여 학습할 수 있도록 구성되었다. 또, 한국 교과서의 경우 엄격한 개념의 일반화를 중요하게 여겨 논리적이고 형식적인 내용 전개 과정을 강조한 반면, CPMP 교과서는 비형식적 사고 과정 또는 직관을 중요하게 여겨 실생활 소재를 포함한 다양한 맥락 속에서 수학적 개념의 탐구와 문제 해결을 보다 강조하였다. 각 교과서가 사용되는 교수 학습 환경은 한국의 경우 주로 유의미 설명 방법으로 수업이 진행되었고 보조 학습 도구로 교구 및 학습지가 활용되었다. 반면, CPMP 교과서를 사용하는 교실에서는 학생들의 의사소통 활동을 강조한 모둠 활동과 그래픽 계산기의 사용이 강조되었다.