• Journal of Elementary Mathematics Education in Korea
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• v.18 no.2
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• pp.189-209
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• 2014

This study designed and developed a model of ill-structured problem solving and ill-structured problems for the 4th, 5th, and 6th graders. In addition, two sets of ill-structured problems has been explored to 23 4th graders, 33 5th graders, and 23 6th graders in elementary schools in order to investigate their problem solving, creative personality, and mathematical reasoning. The model of ill-structured problem solving was suggested ABCDE (Analyze-Browse-Create-DecisionMaking-Evaluate) model and analyzed participants' problem solving procedure. As results, participants showed improvement between pretest and posttest in problem solving and the high graders showed the greater creative personality.

• Journal of the Korean School Mathematics Society
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• v.11 no.2
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• pp.159-175
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• 2008

The purpose of this study is to investigate the educational effects of pre-service mathematics teacher's teaching experiment on problem solving process and to give some suggestions in teacher training curriculum. The central theoretical background of this study is Palya's mathematical problem solving theory. In this study, we selected 21 pre-service mathematics teachers as research subject. And we conducted classroom activity that is constructing their problem-solving teaching design. We collected research data as observation materials, documents, video-service records etc. From these research data, we analysed that pre-service mathematics teacher's teaching experiment on problem solving process showed many significant educational effects. Therefore, we proposed that we need to serve many opportunities of teaching experiment on problem solving process to pre-service mathematics teacher in teacher training curriculum.

• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.167-189
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• 2005

본고에서는 영재교육에서 실제 학습자료의 부족과 이산수학의 중요성이 부각되고 있는 최근의 동향을 감안하여, 초등학교 영재교육에 적용 가능한 이산수학 프로그램을 개발하고자 한다. 우선 프로그램의 개발에 선행하여 관련 이론에 대한 고찰을 하였으며 제 7차 초등학교 수학과 교육과정의 이산수학 관련 내용을 분석하석 교육과정의 내용을 심화 ${\cdot}$ 발전할 수 있는 방안에 초점을 두었다. 특히 이산수학과 관련된 기존의 수학학습 프로그램들은 대부분 순수 수학적 이론을 제시하고 그에 따른 문제를 풀어보는 형식으로 구성되어 있는데, 본고에서는 이산수학의 이론을 중심으로, 문제해결에서 알고리즘적으로 사고하는 능력을 키울 수 있도록 하는 것에 초점을 두어 프로그램을 개발하고자 한다. 즉, 프로그램 자체가 하나의 수학적 원리를 탐구해 가는 과정이 되는 것이다. 또한 이산수학이 수학적 문제해결 학습과 연관됨에 착안하여 프로그램은 Polya의 문제해결학습을 바탕으로 구성하고자 한다.

• Korean Journal of Logic
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• v.10 no.1
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• pp.25-64
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• 2007

본 논문에서 필자는 수학에 대한 구조주의적 해석들은 수학의 객관성을 설명하는 문제인 비공허성의 문제를 해결하지 못하고 있음을 보이고자 한다. 제거적 구조주의가 비공허성의 문제를 해결하지 못한다는 것은 대부분의 수학철학자들 사이에서 공유되는 견해이며, ante rem 구조주의는, 케래넨의 논증을 수정한 필자의 강한 논증에 의하면, 수학적 대상들에 대한 적절한 동일성 설명을 결코 제공할 수 없기 때문에, 결국 비공허성의 문제를 해결하지 못한다. 또한, 양상 구조주의자인 헬만의 경우에는, 비공허성의 문제에 대한 양상 구조주의적 해결을 가능케 해주는 주장(산수와 관련하는 경우, "${\omega}$-순서열 체계가 논리적으로 가능하다")에 이르는 그의 증명이, 필자의 판단에 따르면, 논점 선취의 오류를 저지르고 있다.

• Education of Primary School Mathematics
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• v.12 no.2
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• pp.81-97
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• 2009

Visual representations play an important role for students to understand the meaning of a given problem, devise problem-solving approaches, and implement them successfully. The purpose of this study was to investigate how 6th graders would use visual representations in solving mathematical problems and in what ways such use might affect successful problem solving. The results showed that many students preferred numerical expressions to visual representations. However, students who used visual representations, specifically schematic representations, performed better than those who employed numerical representations. Given this, this paper includes instructional implications to nurture students' use of visual representations in a way to increase their problem solving ability.

• School Mathematics
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• v.9 no.3
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• pp.397-408
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• 2007

This research intends to look into how mathematically gifted 6th graders (age12) who have not learned conditional probability before solve conditional probability problems. In this research, 9 conditional probability problems were given to 3 gifted students, and their problem solving approaches were analysed through the observation of their problem solving processes and interviews. The approaches the gifted students made in solving conditional probability problems were categorized, and characteristics revealed in their approaches were analysed. As a result of this research, the gifted students' problem solving approaches were classified into three categories and it was confirmed that their approaches depend on the context included in the problem.

• School Mathematics
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• v.18 no.3
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• pp.541-569
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• 2016

The purpose of the study is to investigate elementary school students' creativity-integrated thinking ability and problem solving ability of core ability in 2015 revision curriculum of mathematics department. In addition, the relation between students' creativity-integrated thinking ability and problem solving ability was analyzed on problem solving process. As result, students' both abilities showed moderate level. Furthermore, students' creativity-integrated thinking ability and problem solving ability showed positive correlation.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.55-69
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• 2016

The purpose of this study is to investigate statistical units of elementary school mathematics textbooks upon on the statistical problem solving process to provide useful information for qualitative improvement of developing curriculum and teaching materials. This study analyzed the statistical units from the textbooks of 1st to 6th year along the 2009 revised national curriculum. The analysis frame is based on the 4 phases of the statistical problem solving process: formulate questions, plan and collect data, present and analyze data and interpret data.

• Communications of Mathematical Education
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• v.9
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• pp.153-164
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• 1999

작도 문제는 역사적으로 아주 오래된 문제 중의 하나일 뿐만 아니라, 현재 우리 나라 기하 교육에 있어 매우 중요한 역할을 하고 있다. 즉, 평면 기하의 중심 정리들 중의 하나인 삼각형의 합동 조건들을 도입하기 위한 기초로 주어진 조건들(세 선분, 두 선분과 이들 사이의 끼인각, 한 선분과 그 양 끝에 놓인 두 각)에 상응하는 삼각형의 작도가 행해진다. 그러나, 현행 수학 교과서나 수학 교수법을 살펴보면, 작도 문제 해결 방법 및 지도에 대한 연구가 미미한 실정이다. 본 연구에서는 작도 문제의 특성, 작도 문제의 해결 방법 및 지도에 관한 접근을 모색할 것이다. 이를 통해, 학습자들이 다양한 탐색 활동 속에서 작도 문제를 탐구할 수 있는 이론적, 실제적 근거를 제시하고, 수학 심화 학습에 작도 문제를 이용할 수 있는 가능성을 제시할 것이다.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.113-130
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• 2009

It can be said that the teaching and learning of mathematical problem solving has been greatly influenced by G. Polya. His heuristics shows down the explicit process of mathematical problem solving in detail. In contrast, Polanyi highlights the implicit dimension of the process. Polanyi's theory can play complementary role with Polya's theory. This study outlined the epistemology of Polanyi and his theory of problem solving. Regarding the knowledge and knowing as a work of the whole mind, Polanyi emphasizes devotion and absorption to the problem at work together with the intelligence and feeling. And the role of teachers are essential in a sense that students can learn implicit knowledge from them. However, our high school students do not seem to take enough time and effort to the problem solving. Nor do they request school teachers' help. According to Polanyi, this attitude can cause a serious problem in teaching and learning of mathematical problem solving.