• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.295-308
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• 2007

The purpose of this paper was to investigate the pedagogical content knowledge of a middle school mathematics teacher manifested in his mathematics instruction by identifying the components of the pedagogical content knowledge of the teacher. For the purpose of the study, I conducted an interpretive case study by collecting qualitative data. The results showed that the pedagogical content knowledge of the teacher was characterized by: (a) knowledge of mathematics including connection among topics and various ways of solving problems; (b) knowledge of students' understanding involving students' misconceptions, common errors, difficulties, and confusions; and (c) knowledge of pedagogy consisting of his efforts to motivate his students by providing realistic applications of mathematical topics and his use of materials.

• School Mathematics
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• v.10 no.4
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• pp.573-581
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• 2008

School geometry takes various approaches such as deductive, analytic, and vector methods. Especially, the mathematical connections between these methods are closely related to the mathematical connections between geometry and algebra. This article analysed the geometric consequences of vector algebra from the viewpoint of teacher's subject-matter knowledge and investigated the connections between the geometric proof and the algebraic proof with vector and inner product.

• Journal of Korean Elementary Science Education
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• v.42 no.1
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• pp.47-63
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• 2023

In this study, we analyzed the PCK components in the materials units of the third and fourth grades of the Korean government-authorized teacher's guides for elementary school, developed in the 2015 revised national curriculum. The results showed that the PCK components were presented in a relatively balanced manner compared to the teacher's guides for middle school. Knowledge of the subject matter accounted for the highest proportion, and knowledge of instructional strategies in science accounted for a higher proportion than knowledge of the science curriculum. The knowledge of assessment in science showed the greatest deviation among publishers, and knowledge of students tended to show the lowest. By subcomponents, experiments and inquiries had a higher proportion than concepts and theories. The ratio of horizontal articulation was lower than that of vertical articulation or lesson objectives, and lesson objectives were presented in various ways, such as in core competencies and achievement standards for science. As questioning was emphasized, teaching strategies and questioning appeared at a similar rate. Motivation and interest, misconceptions were linked to teaching strategies and questioning. In some cases, assessment items and assessment criteria were presented at each level, and various PCK components were linked to these two components. Components with relatively large differences among publishers were supplementary or in-depth concepts, inquiry in textbooks, instruction sequence and method, subject-specific strategies, and assessment items. From the results, the implications for the development of teacher's guides were discussed.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2008.05a
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• pp.17-28
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• 2008

이 논문은 중학교 기하 영역의 수업에 대한 학생들의 성취도가 낮은 것을 관찰하고, 그에 대한 고민으로 교육과정을 분석하고, 수학교육의 질적 접근을 위한 교수 실험을 통해 실제 중학교 과정에서 운용되는 논증기하 교육의 문제점과 그 대안을 탐색하고자 하였다. 본 연구에서는 교사가 반드시 갖춰야 할 지식으로 Shulman(1986)이 제시한 교과 내용 지식과 교수학적 내용 지식, 그리고 교육과정 관련 지식을 받아들였으며, 중학교 기하 영역에서 이런 지식을 갖추기 위해 교사가 폭넓은 고민을 하여 수업의 개선점을 찾는 과정을 보여주고 있다. 연구를 통해서 학생들에게 명제를 지도할 때 주의할 점과 학습자에게 증명을 하도록 제시하는 방법상의 문제점, 그리고 이등변삼각형의 지도에서의 그 증명이 갖는 의미를 잘 이해하여 학생들에 증명 학습에 진정한 도움이 될 수 있는 방향을 탐색하였다. 그리고 절차만을 학습시키는 현행 작도 수업을 개선하기 위한 여러 시도와 등변사다리꼴의 학습에서와 같이 학생들이 수학 용어를 되돌아보는 수업이 필요성을 탐색하여, 많은 교수 실험을 통한 교육과정의 바람직한 개정을 제안하였다.

• Journal of Educational Research in Mathematics
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• v.20 no.1
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• pp.57-71
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• 2010

Similarity between concept and concept, principle and principle, theory and theory is known as a strong motivation to mathematical knowledge construction. Metaphor and analogy are reasoning skills based on similarity. These two reasoning skills have been introduced as useful not only for mathematicians but also for students to make meaningful conjectures, by which mathematical knowledge is constructed. However, there has been lack of researches connecting the two reasoning skills. In particular, no research focused on the interplay between the two in didactic transposition. This study investigated the process of knowledge construction by metaphor and analogy and their roles in didactic transposition. In conclusion, three kinds of models using metaphor and analogy in didactic transposition were elaborated.

• School Mathematics
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• v.11 no.1
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• pp.111-129
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• 2009

This paper is about didactical transposition, which is to transpose academic knowledge into practical knowledge intended to teach. The research questions are addressed as follows. 1. Are the 13 mathematics textbooks of the 10-Na level indisputable regarding with the didactical transposition, in terms that the order of arrangement and the way of explaining the knowledge of trigonometric functions being analyzed and that its logical construction and students' understandings are considered? 2. Can some transpositions for easier use of didactical manipulative, for more practical and for more principle based be proposed? To answer these questions, this research examined previous studies of mathematics education, specifically the organization of the textbook and the trigonometric functions, and also compared orders of arranging and ways of explaining trigonometric functions from the perspective of didactical transposition of 13 versions of the 10-Na level reorganized under the 7th curriculum. The paper investigated what lacks in the present textbook and sought a teaching guideline of trigonometric functions(especially about sector and graph, period, characters of trigonometric function, and sine rule).

• Proceedings of the Korean Society of Computer Information Conference
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• 2015.07a
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• pp.137-138
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• 2015

학습 효과는 교사의 질을 능가할 수 없으므로 교사가 학습자를 어떻게 가르칠 것인가에 전략이나 방법은 학습자의 학습에 영향을 미치는 중요한 변인이 된다. 이러한 점에서 볼 때 교사는 교육학적 지식, 교과 내용학적 지식을 수업에 적절히 통합하는 능력을 갖추어야 한다. 특히 현대 사회는 테크놀로지가 발전하면서 수업에 테크놀로지를 활용하여 학습의 효과를 높이고자 하는 다양한 시도들이 이루어지고 있다. 테크놀로지라는 영역에 포함되는 것들을 살펴보면 주로 도구나 응용소프트웨어를 사용하는 것에 한정되어 있는 경우가 많다. 그러나 도구나 응용소프트웨어는 이들이 제공할 수 있는 기능 내에서만 활용 가능하다는 점에서 제약점이 있다. 따라서 본 연구에서는 TPACK의 테크놀로지 지식을 프로그래밍으로까지 그 범위를 확장하는 가능성에 대하여 논의하였다.

• Journal of Educational Research in Mathematics
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• v.15 no.4
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• pp.445-459
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• 2005

Statistics education is considered within the mathematics curriculum and, thus, can be integrated into other areas of mathematics. However, statistical concepts and thinking skills have to be considered as very different from those of other areas. It is possible to make statistics more meaningful for the learner by making definitions or explanations of concepts in textbooks more clear and consistent. In 'Math I' and 'Probability & Statistics' of the 7th curriculum, the definitions of sample standard deviation are different, which might confuse students. In this study, firstly, some issues relevant to sample standard deviation concept are discussed through the analysis in terms of didactical situation and curriculum. Secondly, the characteristics of sample standard deviation concept as a scholarly knowledge are examined. Finally, the characteristics of didactic transposition of sample standard deviation concept in Japanese, American, and British textbooks are investigated and some suggestions are elicited.

• Journal of the Korean School Mathematics Society
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• v.23 no.3
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• pp.239-257
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• 2020

This study analyzes the degree of freedom with three aspects: as academic knowledge, in the curriculum focused on textbooks, and students' understanding of the degree of freedom. The results provide five critical points. First, we need discussions on whether to include the degree of freedom in the curriculum. Second, we need to reconsider the current way textbooks are described. Third, there should be a didactical analysis to advance students' understanding of the concept of the degree of freedom. Fourth, there are limitations in learning the concept of the degree of freedom in the current textbook learning environment. Fifth, a didactical check of sampling distribution such as sample mean, sample variance, and sample standard deviation is required. The implications were drawn that the emphasis on statistical reasoning education in the curriculum and careful consideration of introducing the t-distribution curriculum was required.

• The Mathematical Education
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• v.43 no.3
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• pp.257-273
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• 2004

In this paper, we analyze what the components of mathematics teacher` knowledge are, and find that mathematics teacher need knowledge of three areas: subject matter knowledge, pedagogical knowledge, and pedagogical content knowledge. Studies of practicing teachers suggest that When teachers lack understanding in their respective disciplines, it inhibits them from providing students the best learning opportunities, but that a teacher possessing pedagogical content knowledge provides learners with multiple approaches into learning. Some teachers having sound knowledge of mathematics and students were able to respond appropriately to students' questions, design appropriate learning activities involving a variety of mathematical representations, and orchestrate mathematical discourse in the classroom. Thus, it appears that mathematics teachers' knowledge positively affect teaching and student learning..