• Communications of Mathematical Education
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• v.29 no.3
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• pp.533-551
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• 2015

Problem posing in school mathematics is generally regarded to make a new problem from contexts, information, and experiences relevant to realistic or mathematical situations. Also, it is to reconstruct a similar or more complicated new problem based on an original problem. The former is called as problem generation and the latter is as problem reformulation. The purpose of this study was to explore the co-relation between problem generation and problem reformulation, and the educational effectiveness of each problem posing. For this purpose, on the subject of 33 pre-service secondary school teachers, this study developed two types of problem posing activities. The one was executed as the procedures of [problem generation${\rightarrow}$solving a self-generated problem${\rightarrow}$reformulation of the problem], and the other was done as the procedures of [problem generation${\rightarrow}$solving the most often generated problem${\rightarrow}$reformulation of the problem]. The intent of the former activity was to lead students' maintaining the ability to deal with the problem generation and reformulation for themselves. Furthermore, through the latter one, they were led to have peers' thinking patterns and typical tendency on problem generation and reformulation according to the instructor(the researcher)'s guidance. After these activities, the subject(33 pre-service teachers) was responded in the survey. The information on the survey is consisted of mathematical difficulties and interests, cognitive and affective domains, merits and demerits, and application to the instruction and assessment situations in math class. According to the results of this study, problem generation would be geared to understand mathematical concepts and also problem reformulation would enhance problem solving ability. And it is shown that accomplishing the second activity of problem posing be more efficient than doing the first activity in math class.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.297-312
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• 2009

We study the process of horizontal and vertical mathematization on the polyhedron problems through the history of mathematics, computer experiments, problem posing, and justifications. In particular, we explore the Hamilton cycle problem, coloring problem, and folding net construction on the Archimedean and Catalan polyhedrons. In this paper, we present our mathematical results on the polyhedron problems, and we also present some unsolved problems that we found. We found that the history of mathematics and mathematical experiments are very useful in such R&E exploration as polyhedron problem posing and solving project.

• School Mathematics
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• v.17 no.4
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• pp.531-553
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• 2015

This study discussed a sketch map and planar figure, classical contents in math curriculum of Korea. Two problems were posed. One was the degree of difficulty and ambiguous intentions of some contents in 5th grade math textbook of 2009 revised curriculum. The other was the status of sketch maps and planar figures in more general view. We looked into elementary mathematics textbooks of former Korean national curriculums and other countries to discuss the problems. The reason why the present Korean textbook has such contents was considered, based on the result of searching former Korean and foreign textbooks. The suggestions in view of expression and building of 3D shapes were also talked.

• Korean Journal of Logic
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• v.1
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• pp.117-138
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• 1997

• Communications of Mathematical Education
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• v.18 no.1 s.18
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• pp.211-222
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• 2004

신체적 체험은 인간의 사고를 형성하는 바탕이 된다. 문제해결 경험은 인간 사고를 한층 더 발전시킨다. 특히 사물의 형태와 움직임을 관찰하고, 그러한 환경에 감각-운동 신경을 발달시키는 체험에서 획득된 개념들은 추상적 사고에서 중심적 역할을 한다는 언어심리학의 가설이 흥미롭게 제기되어 연구되어 오고 있다. 개념체계로서 수학, 언어로서 수학, 의미 만들기로서 수학 , 문제 해결로서 수학 등 수학학습과 관련된 수학의 여러 모습에 대한 새로운 시각을 갖게 한다. Lakoff와 Johnson는 신체적 체험이 가져온 이러한 개념체계들 '메타포'라고 부른다. 메타포의 '개념' 수준으로의 확장은 analogy의 의미를 확장시켰다. 수학학습에 신체적 체험으로 존재하는 개념들은 수학적 개념에 이르는 학습을 새롭게 보게 한다. 본 연구는 metaphor와 analogy의 인지과학 및 언어과학에서 연구되고 있는 일반적 의미들을 제시하고 수학학습에서의 적용될 수 있는 방법들을 제시한다.

• 대학교육
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• s.149
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• pp.83-87
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• 2007

우리 사회의 고령화와 저출산이 심각한 사회문제로 제기되면서 경제활동인구의 감소에 대비해 입직연령 하향의 필요성이 강하게 제기되기 시작했다. 이를 위해 취학연령의 하향, 수학년한의 단축 등과 같은 학제개편 논의가 제기되고 있으나 학자들이나 이해단체 간의 이견이 분분하고, 관련 종사자들간의 이해관계가 얽혀 단기간에 합의를 도출하기는 어려운 상황이다. 따라서 현 제도적으로 가능한 조기졸업 활성화에 대한 진지한 논의는 하나의 대안이 될 수 있다. 여기에서 입직연령 하향과 대학경쟁력, 그리고 조기졸업제의 효과적인 활용방안에 대해 살펴보기로 하자.

• 발명특허
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• v.5 no.7 s.53
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• pp.20-22
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• 1980

중세과학자가 크롬비(A.C Crombie)에 따르면 중세는 과학과 기술, 그리고 과학의 방법에서 모두 진전을 보였다. 먼저 합리적 설명의 개념, 특히 수학의 이용의 회복은 어떻게 이론을 세우고 검증 또는 반증하는 가의 문제를 제기했다. 이 문제는 스콜라적인 귀납이론과 실험적 방법에 의해 해결되었다. 그 예는 13, 14세기의 광학과 자기학에서 볼 수 있다.

• Education of Primary School Mathematics
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• v.19 no.1
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• pp.19-30
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• 2016

This study examined pre-service teachers' pedagogical content knowledge of fraction division in a context where they were asked to write a story problem for a symbolic expression illustrating a whole number divided by a proper fraction. Problem-posing is an important instructional strategy with the potential to create meaningful contexts for learning mathematical concepts, especially when real-world applications are intended. In this study, story problems written by 135 elementary pre-service teachers were analyzed with respect to mathematical correctness. error types, and division models. Patterns and tendencies in elementary pre-service teachers' knowledge of fraction division were identified. Implicaitons for teaching and teacher education are discussed.

• Korean Journal of Logic
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• v.18 no.1
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• pp.39-64
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• 2015

The most difficult problem for mathematical Platonism is the epistemological problem raised by Paul Benacerraf and Hartley Field. Recently, Mark Balaguer argued that his version of mathematical Platonism, Full Blooded Plantonism (FBP), can solve the epistemological problem. In this paper, I show that there are serious problems with Balaguer's argument. First, I analyse Balaguer's argument and reveal a formal defect in his argument. Then I raise an objection based on an analogical argument. Finally, I disarm some potential moves from Balaguer.

• The Mathematical Education
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• v.44 no.3 s.110
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• pp.361-374
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• 2005

I analyzed the effect of problem posing teaching and teacher-centered teaching on mathematical problem-solving ability and creativity in order to know the efffct of problem posing teaching on mathematics study. After we gave problem posing lessons to the 3rd grade middle school students far 28 weeks, the evaluation result of problem solving ability test and creativity test is as fellows. First, problem posing teaching proved to be more effective in developing problem-solving ability than existing teacher-centered teaching. Second, problem posing teaching proved to be more effective than teacher-centered teaching in developing mathematical creativity, especially fluency and flexibility among the subordinate factors of mathematical creativity. Thus, 1 suggest the introduction of problem posing teaching activity for the development of problem-solving ability and mathematical creativity.