• Journal of the Korean School Mathematics Society
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• v.23 no.4
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• pp.427-448
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• 2020

The purpose of this study is to confirm the MKT(Mathematical Knowledge for Teaching) of the pre-service mathematics teachers on the normal distribution through the comparative analysis between the sub-elements of the MKT. In addition, it is to examine the factors that cause the difference of the subjects' MKT. To accomplish this, by the subject of 24 secondary pre-service mathematics teachers, in this study the test items of the MKT on the normal distribution were developed and data were collected and analyzed. As a result of the analysis of the MKT test sheet, the CCK(Common Content Knowledge) of the preparatory mathematics teacher was confirmed as a high score, whereas the SCK(Specialized Content Knowledge) and KCS(Knowledge of Content and Students) were confirmed as low scores. In addition, through these results, it could be confirmed that the difference in MKT of preparatory mathematicians occurred.

• School Mathematics
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• v.11 no.3
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• pp.335-349
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• 2009

The purpose of this study is to explore how a mathematics teacher's beliefs about mathematics and teaching and learning and mathematics and how such beliefs are related to her knowledge manifested in her mathematics instruction. The study illustrates images of teaching practice of an American mathematics teacher in middle grades mathematics classrooms. Results suggest that the teacher seems consistent in teaching in terms of her beliefs about mathematics and learning and teaching mathematics in some degrees. In particular, the teacher's beliefs affected the ways in which mathematics teacher organized and structured her lessons.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.1
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• pp.1-24
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• 2018

This study included eleven elementary pre-service teachers who participated in the first and second teaching practices held by J Education College in 2015. After the pre-service teachers were encouraged to self-reflect on their mathematics teaching using a reflective survey sheet of mathematics teaching expertise, their uses of mathematics teaching expertise were analyzed according to the times of their mathematics practice instructions. The results are as follows: First, as the frequency of their mathematics teaching increased, the pre-service teachers' uses of mathematics teaching expertise increased, especially greatly with seven of them. However, the number of subcategories where the teachers' uses of mathematics teaching expertise increased was different from at least two to seven depending on the teachers. Second, the pre-service teachers who performed mathematics teaching practices four times used more of mathematics teaching expertise than those who did two times or three times. Third, some pre-service teachers who taught two or three times never reached 90% of the total score of any subcategory, even in the subcategory where they showed increase in their uses of mathematics teaching expertise. Fourth, the subcategory of 'reflection before class - teaching perspective - understanding of mathematics subject knowledge' was analyzed as the most difficult one for the study participants, and the reason is, they think, that there are not enough materials on the historical back grounds of mathematical concepts.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.137-156
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• 2008

This article discusses the purpose of mathematics education based on the epistemology of Michael Polanyi. According to Polanyi, studying is seeking after the truth and pursuing the reality. He opposes to separate humanity and knowledge on account that no knowledge possibly exists without its owners. He assumes tacit knowledge hidden under explicit knowledge. Tacit knowing is explained with the relation between focal awareness and subsidiary awareness. In the epistemology of Polanyi, teaching and learning of mathematics should aim for change of students' minds in whole pursuing the intellectual beauty, which can be brought about by the operation of their minds in whole. In other words, mathematics education should intend the cultivation of mind. This can be accomplished when students learn mathematical knowledge as his personal knowledge and obtain tacit mathematical knowledge.

• Korean Journal of Child Education & Care
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• v.17 no.3
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• pp.49-63
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• 2017

This study aims to investigate the effect of early childhood teachers' mathematical attitude on their mathematics teaching efficacy and to prove the moderating role of pedagogical content knowledge (PCK) in mathematics, which we selected based upon previous literatures. To explore the effect of early childhood teachers' mathematical attitude on their mathematics teaching efficacy and the moderating role of PCK in mathematics between them, This study randomly sampled 500 early childhood teachers who work at child care centers and kindergartens in Seoul, Kyunggi province and Kangwon province and collected their responses by questionnaires. Mathematics teaching efficacy was measured with mathematics teaching efficacy scale for early childhood teachers developed by Luo (2000) and translated by Jung (2001a). Mathematical attitude was measured with Smith (2000)'s scale which we translated for this study. To measure the pedagogical content knowledge in mathematics, we revised Hong(2012)'s scale to be applicable for early childhood teachers. Direct effect of mathematical attitude on mathematics teaching efficacy and the moderating effect of PCK in mathematics were analyzed by multiple regression analysis using IBM SPSS 21.0. Study results demonstrated the significant direct effect of mathematical attitude on mathematics teaching efficacy. Also, the moderating effect of PCK in mathematics was also proved to be significant. That is, if the teacher has high level of pedagogical content knowledge in mathematics, the positive effect of mathematical attitude on mathematics teaching efficacy was even more enhanced. This results supports the current finding where PCK in mathematics functions as a moderating variable between mathematical attitude and mathematics teaching efficacy. Thus, our study is expected to provide relevant contents that should be covered during teacher education, which aims to improve early childhood teachers' mathematics teaching efficacy.

• Communications of Mathematical Education
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• v.15
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• pp.207-214
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• 2003

수학교육에서 학생들이 학습을 통하여 습득하여할 중요한 주제는 수학 지식과 수학을 다루는 인지적 조작 기술일 것이다. 특히 수학지식과 지식의 활용은 문제해결을 통한 학습에서 의미 있게 학생에게 나타나며 이를 통하여 수학 학습 동기를 강화하고 수학의 가치를 느끼게 한다는 점에서 중요한 의의를 갖는다. 대학수준의 수학교육과정에서도 문제해결은 중요한 수학교육의 중심 수단으로서 목적으로서 선언되어 있지만 실제 수업에서 잘 다루고 있지 못하다. 문제해결 지도에 대한 접근 방식으로 1950년대의 문제해결전략을 다룬 Polya, 1990년대의 메타인지적 접근을 강조한 Schoenfeld 및 최근의 여러 연구자들의 활발한 연구가 이어지고 있다. 본 논문에서 대학 수준의 문제해결 수업의 접근 방법을 소개함으로 문제해결 수업을 구현할 수 있는 지식을 제공한다. 특히 Schoenfeld의 문제해결 수업 모델은 수학 교육의 교실 수업으로의 구현 측면에서 갖는 다양한 함의를 제시한다.

• School Mathematics
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• v.15 no.4
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• pp.995-1013
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• 2013

The purpose of this paper was to investigate mathematics teachers' mathematical content knowledge about quadratic curves. Three components of mathematical knowledge are needed for teaching: (i) knowing school mathematics, (ii) knowing process of school mathematics, (iii) making connections between school mathematics and advanced mathematics. 24 mathematics teachers were asked to perform 10 questions based on mathematics curriculum. The results showed that mathematics teachers had some difficulties in conic section definitions and eccentricity definitions of ellipse and hyperbola. And they also got difficulty in Dandellin sphere proof of the equivalence of conic section definitions and quadratic curve definitions. Especially, no one answered correctly to the question about the definition of eccentricity. The ratio of correct answer for the question about constructing tangent lines of quadratic curves is less than that for the question about the applications of the properties of tangent lines. These findings suggests that it is needed that to provide plenty of opportunities to learn mathematical content knowledge in teacher education programs.

• Communications of Mathematical Education
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• v.19 no.2 s.22
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• pp.389-407
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• 2005

수학은 위계적이고 구조적인 특성을 가지고 있어서 학생들이 적절하게 학습하면 내적 동기유발이 가능하고 흥미 있게 학습해 나갈 수 있는 반면 단편적인 지식들로 학습하려 한다면 그 양이 방대해지고 제대로 이해하기가 어렵다. 그러므로 교사는 수학적 지식의 구조를 깨달아 지식의 본체가 내적으로 어떻게 조직되고 상호 관련되어 있는지 알아야 하고 학생들이 수학적인 아이디어와 절차를 획득하고 탐구하게 하는 적절한 문제를 제시하여 문제해결을 통해 가르쳐 가는 방법을 생각해야 할 것이다. 이 때에 학생들은 문제해결 과정에서 능동적인 역할을 하면서 자신이 학습하고 있는 것의 핵심을 인식하고 호기심을 갖고 유의미한 기능들을 이끌어내는 학습을 해야 하는데, 이는 오랜 전통의 탐구 학습과 그 맥락을 같이 하는 것이다. 수학교과 고유의 특성을 살려 지식의 구조를 가르침에 있어서 교수 방법으로의 문제해결을 통한 지도와 학습 방법으로의 탐구학습 과정은 잘 조화될 수 있다. 이러한 조화된 모습을 드러나게 하고자 초등학교 5학년 가 단계에서 '평면도형의 넓이와 둘레 사이의 관계'를 탐구하게 하는 문제해결을 통한 탐구학습 과제를 제시해 보았다. 30-40년을 거슬러 올라가는 역사를 갖는 지식의 구조나 탐구학습, 문제해결에 대한 관심은 오늘날에도 여전히 시사하는 바가 크다고 하겠다. 수학교육에 관한 연구들은 완전히 새로운 것이기보다는 이전의 것들이 주는 의미를 되새기고 오늘의 상황에 비추어 해석할 때 수학교육은 한 단계 올라서게 된다.

• School Mathematics
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• v.15 no.2
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• pp.443-457
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• 2013

This study investigated the perceptions of beginning teachers about teacher knowledge. Reflections and improvement of their class knowledge have been perceived as the most important factors by beginning teachers. In terms of utilization of actual classes, teacher knowledge, mathematical concepts and correlations such as connection linked to class contents and hierarchy have been used the most. Among the needed teachers knowledge, knowledge of student understanding and mathematics content knowledge was the most essential knowledge that could be mainly formed through classroom experience and teacher training program. On the other hand, knowledge about technology and assessment was not necessary or useful factor for beginning teachers. To facilitate formation of beginning teachers' knowledge, teacher introductory program, mentoring program, interactive relationship with teacher education institutes, curriculum improvement for teacher education institute and the development and dissemination of various teachers training program would be required.

• Communications of Mathematical Education
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• v.14
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• pp.27-41
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• 2001

인지적으로 안내된 교수(CGI)는 학생들의 수학적 사고(특히, 비형식적 지식)의 발달; 그러한 발달에 영향을 미치는 교수; 교수 실제에 영향을 미치는 교사의 지식과 신념들; 교사의 지식, 신념들, 실제들이 학생들의 수학적 사고에 대한 이해에 의해 영향을 받는다는 점에 초점을 둔 통합된 연구 프로그램이다. 본 논문에서는 아동의 비형식적인 지식을 중시하는 최근의 연구들을 고찰하고, CGI를 위한 수업을 어떻게 조직하며, 그러한 교수법이 수업을 어떻게 진행할 것인지에 대한 구체적이고 명확한 지침을 제공하지 않으므로 CGI를 적용하는 교실들의 유사점을 살펴본다. 그리고, 마지막으로 최근의 연구들을 고찰함으로써 CGI의 효과를 알아본다.