• Korean Journal of Logic
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• v.10 no.2
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• pp.47-107
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• 2007

나는 이 글에서 프레게 제한에 대한 라이트의 해석이 옳지 않다는 것을 보인다. 우선 나는 그가 산수 개념의 적용에 대한 반성을 통해 그 개념에 대한 선천적 지식을 얻을 수 있다고 여긴 사례를 검토한다. 이 검토를 기초로 나는 산수 개념의 적용을 지배하는 원리가 있고, 프레게 제한은 바로 그런 원리가 성립하도록 해당 개념을 정의하라는 요구임을 보인다. 둘째로 나는 라이트의 해석은 수학의 적용에 대한 아주 좁은 견해에 의존한다는 것을 보인다. 나는 산수의 적용에 대한 프레게의 견해를 살펴본 후에 실수가 적용될 수 있는 양을 산수량, 순수 공간량 및 물리량 세 부류로 나눈다. 나는 실수 적용 원리는 순수 공간량만 아니라 물리량에 대해서도 성립한다는 것을 보인다. 이에 근거해서 나는 실수 이론을 확립하는 데에도 여전히 프레게 제한은 유효하다고 결론짓는다.

• Journal of the Korean School Mathematics Society
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• v.15 no.3
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• pp.395-410
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• 2012

When planning lessons and developing materials about mathematical teaching and learning, we should condignly change and reconstruct contents and orders in light of ranks and connections between subject materials. Moreover teachers should teach mathematical concepts so that students might understand then not only independently and disjunctively but also relationally and reflectively. For this, teachers have to prepare thoroughly. By analyzing advanced research for mathematical connections, this study categorizes them according to two conditions: internal-external and content-formality. Through this, tactical aspect similarity and indistinguishability between mathematical external connections and mathematical internal connections have been identified. Based upon this fact, this study proposed the principles and the examples of tactical aspect on mathematical Internal Connetions.

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.493-506
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• 2014

This study is to seek access to a way of learning of the discipline of mathematics education, one of several knowledge is required to pre-service mathematics teachers. First, by selecting the key topics and researchers in mathematics education learning materials were produced by the relevant classification information by keyword. This applies to pre-service teachers in the curriculum, and looked to clarify the theoretically connectivity among the researchers and concepts and principles of the discipline of mathematics education. And as a result, investigate whether there is any effect to the pre-service teacher education.

• Journal of the Korean School Mathematics Society
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• v.14 no.2
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• pp.143-161
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• 2011

Mathematics PBL, which has recently attracted much attention, is a teaching and learning method to increase mathematical ability and help learning mathematical concepts and principles through problem solving using mathematical knowledge the students have. In spite of the attention, however, the implementations are yet significant. In this study, we worked to find the needs of mathematics teachers for mathematics PBL implementation. The methods of this study are taxonomic analysis and componential analysis by using cards depth interviewing. As a result, mathematics teachers' needs are to consider how to develop the mathematics PBL problems and how to make progress.

• Journal for History of Mathematics
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• v.16 no.4
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• pp.79-90
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• 2003

This paper aims to consider the genesis of irrational numbers and to suggest a method for teaching the concept of irrational numbers. It is the notion of “incommensurability” in geometrical sense that makes Pythagoreans discover irrational numbers. According to the historica-genetic principle, the teaching method suggested in this paper is based on the very concept, incommensurability which the school mathematics lacks. The basic ideas are induced from Clairaut's and Arcavi's.

• Honam Mathematical Journal
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• v.1 no.1
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• pp.11-14
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• 1979

S^{**}를 S의 subclass로서$f(z)=z+a_zz^2+{\cdots}\;{\cdots}\;{\cdots}\;{\cdots}$가 $Re\{zf^'(z)[f(z)-f(-z)]^{-1}\}$>0, ${\left|z\right|}$<1을 만족하는 함수족(函數族)이라 하자. M.S. Robertson은 1961년에 subordination의 원리를 이용하여 $f(z)=z+a_zz^2+{\cdots}\;{\cdots}\;{\cdots}$가 S^{**}에 속하기 위한 충분조건을 구하였다. 본(本) 논문(論文)은 Robertson의 조건에 약간의 수정을 가해서 f(Z)가 S^{**}에 속하기 위한 필요 충분 조건을 만들고, 그것을 증명하였다.

• Journal of Educational Research in Mathematics
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• v.19 no.3
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• pp.355-369
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• 2009

Though there is no agreement on the definition of analogical reasoning, there is no doubt that analogical reasoning is the means of mathematical knowledge construction. Mathematicians generally have a tendency or desire to find similarities between new and existing Ideas, and new and existing representations. They construct appropriate links to new ideas or new representations by focusing on common relational structures of mathematical situations rather than on superficial details. This focus is analogical reasoning at work in the construction of mathematical knowledge. Since analogical reasoning is the means by which mathematicians do mathematics and is close]y linked to measures of intelligence, it should be considered important in mathematics education. This study investigates how mathematicians used analogical reasoning, what role did it flay when they construct new concept or problem solving strategy.

• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.429-442
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• 2014

In this study we reviewed the backgrounds, main claims, and teaching and learning of STEAM education, and analysed STEAM education on the viewpoint of didactics of mathematics. The core competences of STEAM are creativity, communication, convergence, and caring. We found that the theoretical background of caring among these competences is relatively very weak, and the main principles for teaching and learing are mainly included the theories of didactics of mathematics and of creativity. We need to approach very carefully and progressively to creativity education through STEAM, and also need to study on the background of the mathematical creativity.

• The KIPS Transactions:PartB
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• v.8B no.5
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• pp.429-440
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• 2001

To achieve a computer tutor framework with high learning effects as well as practicality, the goal of this research has been set to developing an intelligent tutor for problem-solving in mathematics domain. The maine feature of the CyberTutor, a computer tutor developed in this research, is the facilitation of a learning environment interacting in accordance with the learners differing inferential capabilities and needs. The pedagogical information, the driving force of such an interactive learning, comprises of tutoring strategies used commonly in various domains such as phvsics and mathematics, in which the main contents of learning is the comprehension and the application of principles. These tutoring strategies are those of testing learners hypotheses test, providing hints, and generating explanations. We illustrate the feasibility and the behavior of our propose framework with a sample problem-solving learning in geometry. The proposed tutorial framework is an advancement from previous works in several aspects. Firstly, it is more practical since it supports handing of a wide range of problem types, including not only proof types but also finding-unkown tpes. Secondly, it is aimed at facilitating a personal tutor environment by adapting to learners of varying capabilities. Finally, learning effects are maximized by its tutorial dialogues which are derived from real-time problem-solving inference instead of from built-in procedures.

• Communications of Mathematical Education
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• v.36 no.4
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• pp.469-486
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• 2022

Counting occupies a fundamental and important position in mathematical learning due to its relation to number concepts and numeral operations. In particular, counting up to large numbers is an essential learning element in that it is structural counting that includes the understanding of place values as well as the one-to-one correspondence and cardinal principles required by counting when introducing number concepts in the early stages of number learning. This study aims to derive didactical implications by investigating the possibility of and the strategies for counting large numbers that is expected to have no students' experience because it is not composed of current textbook activities. To do this, 89 second-grade elementary school students who learned the three-digit numbers and experienced group-counting and skip-counting as textbook activities were provided with questions asking how many penguins were in a picture where 260 penguins were irregularly arranged and how to count. As a result of analyzing students' responses in terms of the correct answer rate, the strategy used, and their cognitive characteristics, the incorrect answer rate was very high, and the use of decimal principles, group-counting, counting by one, and partial sum strategies were confirmed. Based on these analysis results, several didactical implications were derived, including the need to include counting up to large numbers as textbook activities.