• East Asian mathematical journal
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• 제27권4호
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• pp.381-389
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• 2011

The flexible mathematical thinking - the ability to generate and connect various representations of concepts - is useful in understanding mathematical structure and variation in problem solving. In particular, the flexible mathematical thinking with the inventive mathematical thinking, the original mathematical problem solving ability and the mathematical invention is a core concept, which must be emphasized in all branches of mathematical education. In this paper, the author considered a case of flexible mathematical thinking with an inventive problem solving ability shown by his student via real analysis courses. The case is on the proofs of the equivalences of three different definitions on the concept of limit superior shown in three different real analysis books. Proving the equivalences of the three definitions, the student tried to keep the flexible mathematical thinking steadily.

• 한국수학교육학회지시리즈A:수학교육
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• 제41권2호
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• pp.157-172
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• 2002

The purpose of this study is to improve middle students'mathematical communication ability. We designed the mathematics instruction model based on Vygotsky's ZPD to develop the mathematical communication ability, and applied to 2nd grade students in Middle School. And we investigated the significant differences between the group which was instructed with mathematical communication and the group which was instructed with teacher's traditional explanation in aspects of learning achievement, mathematical disposition, and mathematical communication abilities. The results of the study are as follows : 1. There is no significant difference in learning achievement within significance level .05 between the group which was instructed with mathematical communication and the group which was instructed with teacher's traditional explanation by t-test. 2. There is a significant difference in reflection within significance level .01 and in self-confidence within significance level .10 by MANCOVA. 3. There is a significant difference in mathematical communication ability within significance level .01 between two groups by covariance analysis. In particular, there is a significant difference in reading within significance level .01 and in speaking within significance level .05 by t-test.

• East Asian mathematical journal
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• 제36권2호
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• pp.173-201
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• 2020

Mathematical modeling has been emphasized because it offers important opportunities for students to both apply their learning of mathematics to a situation and to explore the mathematics involved in the context of the situation. However, unlike its importance, mathematical modeling has not been grounded in typical mathematics classes because teachers do not have enough understanding of mathematical modeling and they are skeptical to implement it in their lessons. The current study analyzed the data, such as video recordings, slides, and surveys for teachers, collected in four lessons of teacher education in terms of mathematical modeling. The study reported different kinds of tasks that are authentic with regards to mathematical modeling. Furthermore, in teacher education, teachers' identities have separated a mode as learners and a mode as teachers and conflicts and intentional transition were observed. Analysis of the surveys shows what teachers think about mathematical modeling with their understanding of it. In teacher education, teachers achieved different kinds of modeling tasks and experience them which are helpful to enact mathematical modeling in their lessons. However, teacher education also needs to specifically offer what to do and how to do it for their lessons.

• 한국수학교육학회지시리즈A:수학교육
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• 제46권4호
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• pp.483-492
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• 2007

The purpose of this study was to investigate the relation between the cognitive processes and the mathematical achievement of the 4th grade students. And according to the several studies, there were significant relation between cognitive processes and achievement. Based on the PASS(Planning-Attention-Simultaneous-Successive Processes) Model presented by Das and Naglieri, four cognitive process variables were selected. The results of this study as follows. First, there was not significant relation between attention and mathematical achievement. Second, there was significant relation between planning and mathematical achievement. Third, there was significant relation between simultaneous/successive processes and mathematical achievement. Fourth, the students who got higher scores in the two types (simultaneous/successive)of information processing had more mathematical achievement. Specially, the students who got higher scores in the type of simultaneous information processing had higher scores in mathematical achievement. These results indicated that planning and simultaneous information processing had influence on the mathematical achievement.

• 한국수학교육학회지시리즈A:수학교육
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• 제59권3호
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• pp.237-254
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• 2020

본 논문은 수업을 위한 수학적 지식과 수업의 질에 대한 상관관계를 보고하는 연구이다. 선다형 평가 문항 유형의 설문지를 이용하여 교사들의 수업을 위한 수학적 지식을 수집하였고, 촬영된 그 교사들의 수업을 수학 수업 분석 도구를 이용하여 수업의 질을 평가하였다. 두 점수들의 상관관계를 통계적으로 분석하여, 유의미한 양적 상관관계가 있음을 보고한다. 또한, 수집된 수업 영상과 교사들의 인터뷰 자료의 분석을 통해 수업을 위한 수학적 지식이 중재하지 못하는 수업의 질과 관련된 요소를 찾아내었다. 이러한 결과를 기반으로 수학 교사 교육에 대해 논의한다.

• 영재교육연구
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• 제25권4호
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• pp.581-605
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• 2015

본 연구에서는 유아들을 대상으로 수학적 과정 중심 교수학습법을 통한 수학적 사고 변화에 대하여 관찰하고 그 내용을 분석하였다. 이를 위해 설문조사와 현장 관찰을 통한 상황분석을 실시하여 구성한 수학적 과정 중심 교수학습법을 서울에 위치한 유치원에 재원중인 만 5세, 12명을 대상으로 적용하여 질적 연구를 시행하였다. 연구 결과는 문제해결하기, 추론과 증명하기, 연계하기, 표상하기, 의사소통하기의 다섯 가지 수학적 과정이 교사-유아, 유아-유아의 상호작용을 통해 구체화되어 유아의 수학적 사고를 자극하고 변화를 창출하였다. 또한 수학적 지식이 내재되고 통합된 문제 상황을 교사가 제시하고 수학적 과정에 중점을 두어 유아들이 또래와 협력적으로 문제를 해결하면서 수학적 과정과 수학적 태도에 변화가 일어났다. 즉 유아의 수학적 사고는 수학적 지식이 내재된 수학적 과정을 통해 수학적 태도의 긍정적인 변화과정 안에서 통합되어 증진되었다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제12권4호
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• pp.271-281
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• 2008

Quarter a century ago, I founded the Colorado Mathematical Olympiad. The Colorado Mathematical Olympiad is the largest essay-type in-person mathematical competition in the United States, with 600 to 1,000 participants competing annually for prizes. In this article, I explain what it is, how it works, give examples of problems and solutions, and share with the reader careers of some of the Olympiad's winners.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제7권2호
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• pp.69-72
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• 2003

Editor's Note: On the occasion of the publication of the 100th issue (Vol. 42, Number 2) of the Journal of the Korea Society of Mathematical Education Series A: "The Mathematical Education", Professors Hyman Bass (President of the International Commission on Mathematics Instruction) and Bernard R. Hodgson (Secretary-General of ICMI) together send a message of congratulation to the Korea Society of Mathematical Education(KSME).

• 한국수학교육학회지시리즈A:수학교육
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• 제41권1호
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• pp.35-44
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• 2002

The purpose of this study is to estimate teachers'conceptions of mathematics through the conception on compositions of mathematical knowledge, the conception on structure of mathematical knowledge, the conception on status of mathematical knowledge, the conception on mathematical activity, and the conception of mathematics learning. This study reached the following conclusions: Most of teachers has more internal viewpoint than external viewpoint on the compositions, structures and status of mathematical knowledge, mathematical activity and mathematics learning.

• 한국수학교육학회지시리즈A:수학교육
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• 제42권1호
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• pp.57-67
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• 2003

In this paper we analyze educational aspects of a mathematical problem. As a result of the analysis, we extract five meaningful mathematical knowledge and ideas. Corresponding with these we suggest some chains of mathematical problems that are expected to activate student's self-oriented mathematical investigation.