• Journal of Educational Research in Mathematics
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• v.16 no.1
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• pp.25-41
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• 2006

The purpose of this study was to analyze teachers' pedagogical content knowledge (PCK) about area of plane figure and how it was actualized in instruction. As an exploratory, qualitative, and comparative case study, 2 fifth-grade teachers were selected. Semi-structured interviews with the leachers were conducted in order to explore their PCK with regard to the area of plane figure. A total of 14 mathematics instructions were videotaped and transcribed. Teachers' PCK and classroom teaching practices were analyzed in detail into 3 categories: (a) knowledge of mathematics contents, (b) knowledge of students' understanding, and (c) knowledge of instructional methods. As such, this paper provided a detailed description on each teacher's PCK and her teaching practice. The results showed that teachers' PCK had a significant impact on instruction. The teacher who had rich knowledge about the area of plane figure was able to encourage students to understand the concept of area and to or explore the principles behind formula calculating various areas of plane geometry. The results demonstrated the importance of individual components of PCK as well as that of overall level of PCK. Different aspects of teaching practices were observed as to how the teachers had internalized PCK. On the basis of a close relationship between teachers' PCK and their teaching practice, this paper finally raised several implications for teachers' professional development for effective mathematics instruction.

• 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 Educational Research in Mathematics
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• v.26 no.2
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• pp.269-285
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• 2016

PCK(pedagogical content knowledge) has been frequently discussed in the field of subject matter education as well as education in general. Considering the fact that PCK characterizes teacher professionalism, and the distinction of mathematics education from neighboring disciplines, PCK is one of the core concepts in the discourse of mathematics education. This study focused on KCS(knowledge of content and students) among the areas of PCK. The purpose of this study to investigate the KCS of pre-service teachers attending a private university located in Seoul. An in-depth interview with 30 pre-service teachers was conducted in a semi-structured manner, using four questions dealing with common student errors, students' understanding of content, and student developmental sequences. The pre-service teachers gave mathematical answers while in others they gave priority to pedagogical considerations. The implication drawn from the interview data is that the teacher training program should fully reflect the complexity of mathematical concepts which appeared in school mathematics over several grade levels and content areas.

• The Mathematical Education
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• v.60 no.4
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• pp.555-580
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• 2021

The purpose of this study is to explore the factors of situational interest in math learning, and based on the results, to reveal the factors of situational interest included in teaching and learning methods, teaching and learning activities in mathematics class, and extracurricular activities outside of class. As a result of conducting a questionnaire to high school students, the factors of situational interest in learning mathematics were divided into 10 detail-domain(Enjoy, Curiosity, Competence / Real life, Other subjects, Career / Prior knowledge, Accumulation knowledge / Transformation, Analysis), 4 general-domain(Emotion, Attitude / Knowledge, Understanding), 2 higher-domain(Affective / Cognitive) were extracted. In addition, it was revealed that various factors of situational interest were included teaching and learning methods, teaching and learning activities and extracurricular activities. When examining the meaning of 10 situational interest factors, it can be expected that the factors for developing individual interest are included, so it can be expected to serve as a basis for expanding the study on the development of individual interest in mathematics learning. In addition, in order to maintain individual interest continuously, it is necessary to maintain situational interest by seeking continuous changes in teaching and learning methods in the school field. Therefore, it can be seen that the process of exploring the contextual interest factors included in teacher-centered teaching and learning methods and student-centered teaching and learning activities and extracurricular activities is meaningful.

• Journal of the Korean School Mathematics Society
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• v.12 no.1
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• pp.27-45
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• 2009

Recently there has been a high request for support for teachers' professional development and quality control to meet the demand of educational policy to introduce teacher evaluation, master teacher status, incentives for teacher competency, etc. It has been suggested that reeducation and support for professional development would be more effective to beginning teachers with a high developmental potential than to experienced teachers with routinized instruction. Since 2005 KICE-TLC has conducted research on the development of teacher supporting programs such as teaching consultation and pedagogical content knowledge(PCK) in school subjects. In line with the current education policy and previous research by KICE, this research has been conducted to meet the need for novice teacher induction by developing consulting program focused on PCK The goal of this research was to (1) explore the in light meaning of PCK in light of teaching consultation, (2) conduct a preliminary study on how to develop teaching consulting programs for secondary beginning teachers, (3) develop teaching consulting programs focused on pedagogical content knowledge(PCK), and (4) suggest implications for educational policy regarding pre-service and in-service teachers' continuing professional development and support.

• Journal for History of Mathematics
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• v.25 no.2
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• pp.97-111
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• 2012

This paper aims to identify the area of knowledge required for constructing test items by comparing the consulting contents with the area of MKT(Mathematical Knowledge for Teaching). This paper collects the consulting results by the consulting group of A provincial office of education from 2007 to 2009, and analyzes and categorizes the results. The knowledge for constructing test items are known by the analysis on the consulting contents. Training and consulting for teachers are necessary to enable them to recognize the importance of these categories and improve the quality of test items.

• Journal of Educational Research in Mathematics
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• v.26 no.2
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• pp.173-188
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• 2016

Research on didactic transposition in mathematics education has about 25-year and about 35-year long history in and out of Korea, respectively. This study attempts to investigate in trends of those research and to suggest tasks needed to be tackled. Major findings are followed. First, studies done in Korea tended to focus on the application of the didactic transposition theory for proving its effectiveness in understanding mathematics textbooks and mathematics lessons in-depth. It is suggested to conduct meta-analysis of the accumulated results or analysis of further applications of the didactic transposition theory to improve theoretical aspects of didactic transposition. Second, new categories for extreme teaching phenomenon were found and new typology in knowledge to be considered in the didactic transposition was developed in a few studies done in other subject matter education. Application of these to mathematics education may enhance research in didactic transposition of mathematical knowledge. Third, praxeology or a complex of praxeology for Korean school mathematics should be explored as did in other countries. Fourth, there have been rich attempts to link perspectives in didactic transposition to other perspectives or fields such as anthropology, human and education in technology era, praxeology theory in economics, epistemology in other countries but not in Korea. It is suggested to extend the scope of discussion on didactic transposition and to relate various concepts given in other disciplines. Fifth, clarification or negotiation of meaning for the main terms used in the discussion on didactic transposition such as personalization, contextualization, depersonalization, decontextualization, Topaze Effect, Meta-Cognitive Shift is suggested by comparing researchers' various descriptions or uses of the terms.

• Education of Primary School Mathematics
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• v.11 no.2
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• pp.141-159
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• 2008

The purpose of this study id to delve into how elementary mathematics textbook deal with the quadrilaterals from a view of Didactic Transposition Theory. Concerning the instruction period and order, we have concluded the following: First, the instruction period and order of quadrilaterals were systemized when the system of Euclidian geometry was introduced, and have been modified a little bit since then, considering the psychological condition of students. Concerning the definition and presentation methods of quadrangles, we have concluded the following: First, starting from a mere introduction of shape, the definition have gradually formed academic system, as the requirements and systemicity were taken into consideration. Second, when presenting and introducing the definition, quadrilaterals were connected to real life. Concerning the contents and methods of instruction, we have concluded the following: First, the subject of learning has changed from textbook and teachers to students. Second, when presenting and introducing the definition, quadrilaterals were connected to real life. Third, when instructing the characteristics and inclusive relation, students could build up their knowledge by themselves, by questions and concrete operational activities. Fourth, constructions were aimed at understanding of the definition and characteristics of the figures, rather than at itself.

• Communications of Mathematical Education
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• v.26 no.1
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• pp.137-154
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• 2012

Approximation' is one of central conceptions in calculus. A basic conception for explaining 'approximation' is 'tangent', and 'tangent' is a 'line' with special condition. In this study, we will study pedagogically these mathematical knowledge on the ground of a viewpoint on the teaching of secondary geometry, and in connection with these we will suggest the teaching program and the chief end for the probable teaching. For this, we will examine point, line, circle, straight line, tangent line, approximation, and drive meaningfully mathematical knowledge for algebraic operation through the process translating from the above into analytic geometry. And we will construct the stream line of mathematical knowledge for approximation from a view of modern mathematics. This study help mathematics teachers to promote the pedagogical content knowledge, and to provide the basis for development of teaching model guiding the mathematical knowledge. Moreover, this study help students to recognize that mathematics is a systematic discipline and school mathematics are activities constructed under a fixed purpose.

• Journal of the Korean School Mathematics Society
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• v.19 no.3
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• pp.261-275
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• 2016

Many students have dualistic beliefs about mathematics and its learning- for example, there is always just one right answer in mathematics and their role in the classroom is receiving and absorbing knowledge from teacher and textbook. This article investigated some epistemic implications and limitations of common mathematics teaching practices, which often present mathematical facts(or procedures) and treat students' errors in a certain and absolute way. Langer and Piper's (1987) experiment and Oliveira et al.'s (2012) study suggested that presenting knowledge in conditional language which allows uncertainty can foster students' productive epistemological beliefs. Changing the focus and patterns of classroom communication about students' errors could help students to overcome their dualistic beliefs. This discussion will contribute to analyze the implicit epistemic messages conveyed by mathematics instructions and to investigate teaching strategies for stimulating students' epistemic development in mathematics.