• Communications of Mathematical Education
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• v.30 no.3
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• pp.335-351
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• 2016

The purpose of this study is to develop Project-Based Teaching-Learning materials for mathematically gifted students using a Fermat Point and apply the developed educational materials to practical classes, analyze, revise and correct them in order to make the materials be used in the field. I reached the conclusions as follows. First, Fermat Point is a good learning materials for mathematically gifted students. Second, when the students first meet the challenge of solving a problem, they observed, analyzed and speculated it with their prior knowledge. Third, students thought deductively and analogically in the process of drawing a conclusion based on observation. Fourth, students thought critically in the process of refuting the speculation. From the result of this study, the following suggestions can be supported. First, it is necessary to develop Teaching-Learning materials sustainedly for mathematically gifted students. Second, there needs a valuation criteria to analyze how learning materials were contributed to increase the mathematical ability. Third, there needs a follow up study about what characteristics of gifted students appeared.

• 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.

• Research in Mathematical Education
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• v.11 no.1
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• pp.33-51
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• 2007

The present study explores mathematics teachers' understanding of division by zero and their approaches to explaining the impossibility of division by zero. This study analyzes Chinese and Korean middle school mathematics teachers' responses to the teaching task of explaining the impossibility of dividing 7 by zero, and examples of teachers' reasoned explanations for their answers are presented. The findings from this study suggest that most Korean teachers offer multiple types of mathematical explanations for justifying the impossibility of division by zero, while Chinese teachers' explanations were more uniform and based less on mathematical ideas than those of their Korean counterparts. Another finding from this study is that teachers' particular conceptions of zero were strongly associated with their justifications for the impossibility of division by zero, and the influence of the teachers' conceptions of zero was revealed as a barrier in composing a well-reasoned explanation for the impossibility of division by zero. One of the practical implications of this study is those teachers' basic attitudes toward always attempting to give explanations for mathematical facts or mathematical concepts do not seem to be derived solely from their sufficient knowledge of the facts or concepts of mathematics.

• Education of Primary School Mathematics
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• v.15 no.3
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• pp.219-233
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• 2012

Practicality and value of mathematics can be verified when different problems that we face in life are resolved through mathematical knowledge. This study intends to identify whether the fraction teaching is being taught and learned at current elementary schools for students to recognize practicality and value of mathematical knowledge and to have the ability to apply the concept when solving problems in the real world. Accordingly, contextual problems and noncontextual problems are proposed around fractional arithmetic area, and compared and analyze the achievement level and problem solving processes of them. Analysis showed that there was significant difference in achievement level and solving process between contextual problems and noncontextual problems. To instruct more meaningful learning for student, contextual problems including historical context or practical situation should be presented for students to experience mathematics of creating mathematical knowledge on their own.

• Journal of the Korean School Mathematics Society
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• v.8 no.4
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• pp.481-494
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• 2005

In this study, the goal is to spread profound knowledge and theory through providing with accumulated methods in mathematics education to the students who are relatively neglected in educational benefits. The process is divided into 3 categories: mathematics for obtaining common sense and intelligence, practical math for application, and math as a liberal art to elevate their characters. Furthermore, it includes the reasons for studying math, improving problem-solving skills, machinery application learning, introduction to code(cipher) theory and game theory, utilizing GSP to geometry learning, and mathematical relations to sports and art. Based on these materials, the next step(goal) is to train graduate students to conduct researches in teaching according to the teaching plan, as well as developing interesting and effective teaching plan for the remote high school learners.

• 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.

• Journal of Educational Research in Mathematics
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• v.19 no.4
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• pp.545-564
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• 2009

TPACK (Technological Pedagogical Content Knowledge) adds the technological knowledge to PCK (Shulman 1986), completing the combination of three kinds of knowledge, i.e. teacher's content knowledge (CK), pedagogical knowledge (PK), and technological knowledge (TK). In this study, I seek to design methodological ways to improve TPACK for preservice mathematics teachers by developing and analyzing team project-based classes with technology in a class of the first semester 2009 in a teacher's college in Seoul, South Korea. The goal of the team project is to design classes to teach mathematics with technology by selecting technology tools suitable for specific mathematical concepts or mathematics sections. In the early stage of the class in the college, the confidence levels among the preservice mathematics teachers were relatively low but increased in the final stage their mathematics teaching efficacy up to from 3.88 to 4.50. Also, the pre service mathematics teachers answered the team project was helpful or very helpful in developing TPACK; this result proves that lectures with technology which based on team project are excellent tools for the teacher to design classes with technology confidently. Considering the teacher's TPACK is one of the abilities to achieve the goals required in the information technology era, the preservice mathematics teachers are asked to plan and develop the lectures with technology, rather than just taught to know how to use technology tools or adapt to specific cases. Finally, we see that national-wide discussion and research are necessary to prepare customized standards and implementable plans for TPACK in South Korea.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.1
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• pp.39-65
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• 2013

This study intended to draw some suggests for the development of mathematics teachers' expertise through the comparison research of pre-service and in-service teachers' PCK about questioning in elementary mathematics class. For this purpose, questionnaire survey was conducted to some pre-service and in-service teachers about the PCK concerning the way how questioning during mathematics class. This survey revealed the following implications. First, from the perspective of mathematics classroom, it is still more important the practical knowledge about how to teach which is evolutionally developed passing through the experience and currier of teaching than theoretical knowledge itself. Comparing the teachers' PCK about the two related knowledge types of mathematics contents, in case of procedural knowledge related PCK it was more asked of teachers' expertise than the case of conceptual knowledge related PCK. Thirdly, in case of learners' incorrect answer, for the desirable teaching it should be a questioning focused on whether there being or not the systematic among the learners' incorrect answer, and in case of appreciating the learners' understanding about the presently taught contents the questioning should be constructed considering the relevant contents early learned.

• The Mathematical Education
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• v.45 no.1 s.112
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• pp.105-121
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• 2006

The purpose of this study is to investigate preservice secondary mathematics teachers' knowledge about graphical representation and provide implications for better mathematics teaching and learning in our schools. For this purpose, sixty-three preservice teachers were selected and given diverse graphical representation problems of y=1, y=x, x=0, $x^2+y^2=1$. All preservice teachers completed two types of questionnaires. First type is about constructing the graphs of the above each equation, and the second one is to make them find the appropriate graphs from given examples of the each equation. The results indicated that all the participant pre service teachers were unable to construct graphs in terms of various dimensions and various direction of coordinate axis. All of the participants represented the graph of each equation on only two-dimensional coordinate system. In addition, some preservice teachers believed that the axis of coordinates have to be x-axis on horizontal line and y-axis on vertical line. From this study, it is implicated that pre service teacher education program needs to provide the experience of representing the graphs of equation in terms of various dimensions and various direction of coordinate axis so as to develop their future students the flexibility and creativity in mathematical thinking especially in the area of space perception.

• Journal of the Korean School Mathematics Society
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• v.13 no.4
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• pp.619-633
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• 2010

To offer insights in organizing professional development programs to promote teachers' substantial ongoing learning, this paper provides an overview of situative perspectives in terms of cognition as situated, cognition as social, and cognition as distributed. Then, it describes research findings on how mathematics teachers can enhance their knowledge and thus improve their instructional practices through participation in a professional development program that mainly provides opportunities to learn and analyze students' mathematical thinking and to perform mathematical tasks through which they interpret the understanding of students' mathematical thinking. Further, it shows that a knowledge of students' mathematical thinking is a powerful tool for teacher learning. In addition, it suggests that teacher-researcher and teacher-teacher collaborative activities influence considerably teachers' understanding and practice as such collaborations help teachers understand new ideas of teaching and develop innovative instructional practices.