• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.33-36
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• 2002

최근 수학구조 및 교수-학습과 관련된 연구에 지식공간 이론을 응용하고자하는 논문들이 많이 나오고 있다. 실제로 유의미 학습과 관련된 수행평가와 수학문제를 푸는 능력에 관한 평가를 연구하는데 지식구조가 응용되고 있지만 이를 활용하는데는 많은 애로사항이 있으며 이를 보완하기 위한 여러 가지 방법이 연구되어오고 있다. 특히, Schrepp교수는 스피드문제의 경우로 제한하여 지식공간론을 응용한 일반화된 수학구조의 연구방법을 제시하였다. 본 논문에서는 주관적 지식의 평가를 하게되는 수학구조 및 공간에 관한 연구를 하는데 효과적으로 응용될 수 있는 퍼지지식공간론에 관한 전반적인 기초 이론을 정의하고 그 성질들을 연구하고자한다.

• The Mathematical Education
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• v.30 no.3
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• pp.71-89
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• 1991

• Journal of the Korean School Mathematics Society
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• v.10 no.1
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• pp.129-148
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• 2007

Recent reform movement in mathematics education has focused not only on the curriculum development but also on teachers' learning or professional development. Whereas various theoretical paradigms call for different programs of professional development for teachers, one of the common emphases is on the pedagogical content knowledge [PCK] which encompasses contents and methods to teach. Against this background, this study developed comprehensive instructional materials for the purpose of fostering PCK in mathematics for elementary school teachers with 17 essential learning themes such as fraction, plane geometry, and area. Each loaming theme was first summarized on the basis of literature reviews and surveys in terms of knowledge in mathematics contents, knowledge in teaching methods, and knowledge in students' mathematical understanding and learning. Each theme was then analyzed in detail on how it was represented in the national curriculum and its concomitant textbooks along with workbooks. Finally, this report included a reconstruction of one unit in textbooks per each learning theme, followed by teaching notes and suggestions from classroom implementation. This was intended for teachers to apply what they might loam from this material to their actual mathematics instruction. Given the page limit, this paper dealt only with the learning theme of ratio.

• Communications of Mathematical Education
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• v.10
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• pp.505-517
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• 2000

수학 학습에서 컴퓨터와 계산기의 활용은 시각화의 강화로부터 직관력과 사고력의 향상을 가져왔다. 컴퓨터 대수체계(Computer Algebra System)가 탑재된 수학 학습용 컴퓨터 프로그램과 계산기가 활발히 사용되고 있으며, 교수매체로서의 활용은 지식 정보전달 체계와 학습자의 지식 구성방법에 새로운 패러다임을 형성하였다. 특히 수학학습용 그래픽 계산기(Graphing Calculator)는 휴대형(Hand-held Technology)으로 학습공간의 이동(Mobil Education)이 가능하며, 수학학습 전용기라는데 의미를 둘 수 있다. Symbolic Graphing Calculator를 활용한 수업에서 학습자는 계산기를 가지고, 기호연산 실행 조작을 통해 자신의 사고과정을 표현하고, Symbolic Graphing Calculator는 실행 조작에 즉각적으로 과정과 결과를 제공하며, 다른 표상과 상호작용을 함으로써 학습자 스스로의 규제가 강화된 과정을 통해 지식을 구성하게 된다. 이때 교사는 지식 정보전달 체계인 대화형 실행매체(IMTs)를 작성하여 학습자의 지식 형성에 안내자의 역할을 하게 된다. 이번 워크샵에서는 CASIO fx 2.0을 활용한 교실 수업모형을 그래프 표상과 연계한 방정식의 풀이과정을 통해 알아본다.

• Journal of Elementary Mathematics Education in Korea
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• v.9 no.1
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• pp.19-38
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• 2005

There are differences in manner to be shown according to a basic point of view about knowledge in division which is traditional algorithm. The 1st and 2nd stage show didactic transpositions less systemic. The 3rd stage, which were influenced by the new math, uses logical mechanism. The 4th stage shows conceptual knowledge of the division independently. The 5th and 6th stage use concrete models which shows a course. The 7th stage constitutes contents systematically and shows many chances which focus on the formation of knowledge. The suggestions derived from such transition should be considered in the practice class and an elementary mathematics textbooks for meaningful learning.

• Journal of the Korean School Mathematics Society
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• v.24 no.4
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• pp.327-348
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• 2021

This study examines the effects of mathematics learning mentoring activities on mathematical knowledge for teaching (MKT) of pre-service mathematics teachers. We choose six pre-service mathematics teachers in the department of mathematics education at M University. The pre-service mathematics teachers conducted 1:1 mathematics learning mentoring for two hours at a times and twice a week for 15 weeks. The pre-service mathematics teachers submitted the mentor log, which recorded weekly learning and emotional observations. We collected the mentor log and the reflection log of pre-service mathematics teachers and the interviews with pre-service mathematics teachers. Based on the collected data, we analyzed the effects of MKT, the understanding of students, and pre-service mathematics teachers' introspection by mathematics learning mentoring. We obtained conclusions as follows. First, mathematics learning mentoring provides an opportunity for pre-service mathematics teachers to apply the theory of mathematical education to schools. Thus pre-service mathematics teachers express theoretical knowledge as practical knowledge. Second, mathematics learning mentoring helps pre-service mathematics teachers have the ability to understand students and provide opportunities to reflect on their attitudes as learners. Third, mathematics learning mentoring helps advance teaching activities by providing pre-service mathematics teachers with opportunities to reflect on their teaching activities. Finally, mathematics learning mentoring has positively influenced the change in pre-service mathematics teachers' beliefs and teaching intuition.

• Journal of Educational Research in Mathematics
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• v.24 no.3
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• pp.311-331
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• 2014

For preservice teachers' instrumental-to-relational pedagogical content knowledge transformations, this research designed several didactical tasks based on Kinach's cognitive strategies. The researcher identified preservice teachers' understanding about what is a definition and how to teach it. By challenging their fixed ideas about definitions, the researcher could motivate them to embrace the new teaching approach which guides reinvention of definitions. The PCK development was not the simple process of filling their tabular rasa PCK with theories of mathematics education, but the dialectical process of identifying, challenging, changing and extending preservice teachers' existent PCK. This research will contribute to explore new directions of mathematics teachers' PCK development and the method of teacher education.

• Education of Primary School Mathematics
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• v.17 no.1
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• pp.1-16
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• 2014

The purpose of this study is to analyze whether analogy distance and mathematical knowledge affect on transfer problems solving with different analogy distance. To conduct the study, transfer problems were classified into multiple categories: mathematical word problem based on rates, science word problem based on rates, and real-life problem based on rates with different analogy distance. Then analysed there are differences in participants' transfer ability and which mathematical knowledge contributes to the solution on over the three transfer problem. The study demonstrated a statistical significant difference(.05) in participants' three transfer problem solving and a gradual decrease of the participants' success rates of on transfer problems solving. Moreover, conceptual knowledge influenced transfer problem solving more than factual knowledge about rates. The study has an important implications in that it provided new direction for study about transfer of learning, and also show a good mathematics instruction on where teachers will put the focus in mathematical lesson to foster elementary students' transfer ability.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.381-405
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• 2015

The nature of school mathematics has not been asked from the epistemological perspective. In this paper, I compare two dominant perspectives of school mathematics: ethnomathematics and didactical transposition theory. Then, I show that there exist some examples from Old Babylonian (OB) mathematics, which is considered as the oldest school mathematics by the recent contextualized anthropological research, cannot be explained by above two perspectives. From this, I argue that the nature of school mathematics needs to be understand from new perspective and its meaning needs to be extended to include students' and teachers' products emergent from the process of teaching and learning. From my investigation about OB school mathematics, I assume that there exist an intrinsic function of school mathematics: Linking scholarly Mathematics(M) and everyday mathematics(m). Based on my assumption, I suggest the chain of ESMPR(Educational Setting for Mathematics Practice and Readiness) and ESMCE(Educational Setting For Mathematical Creativity and Errors) as a mechanism of the function of school mathematics.

• The Mathematical Education
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• v.36 no.1
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• pp.11-22
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• 1997

교육의 목적은 창조적인 인간상(creativity), 유용성 있는 인간상(utilitarian), 심미감 있는 인간상(esthetic)의 구현으로서, 이에 따르는 수학교육의 목적은 크게 두 가지로 나누어 생각할 수 있다. 하나는 수학 지식의 습득, 기능의 습득과 같은 직접적인 것으로 그것들의 응용 및 적용이며, 다른 하나는 간접적인 것으로 수학적 사고의 신장과 수학적 태도의 함양이다.(중략)