• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.469-489
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• 2017

Teachers are the primary agent of didactic transposition. In the process of transposing mathematical knowledge presented in mathematics curriculum and textbooks to mathematical knowledge for teaching in a classroom, teachers are significantly influenced by not only teachers' personal factors but also circumstances and constraints existing inside and outside of classrooms. Therefore, to understand teachers' didactic transposition, we need to analyze influence of institutional and socio-cultural factors on teachers' didactic transposition process. Identifying factors and constraints influencing teachers' didactic transposition provides important opportunities to have a deeper understanding of teachers' didactic transposition and develop their classroom practices. This study analyzed secondary mathematics teachers' perspectives on didactic transposition by exploring factors influencing their didactic transposition process using their reflective journal about their classroom practices. As a result, we identified the five factors influencing participating teachers' didactic transposition. We also found that different teachers had different extent of influence of five factors on their didactic transposition. Based on the results, we discussed ways to help mathematics teachers' didactic transposition.

• The Mathematical Education
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• v.62 no.1
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• pp.95-115
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• 2023

Even the teachers who agree with the necessity of effective mathematical discussions find it difficult to orchestrate such discussions in the actual lessons. This study focused on analyzing the difficulties 15 elementary school teachers faced in applying "the five practices for orchestrating productive mathematics discussions" to their lessons. Specifically, this study analyzed the process of planning, implementing, and reflecting on the lessons to which three or four teachers as a teacher community applied the five practices. The results of this study showed that the teachers experienced difficulties in selecting and presenting tasks tailored to the student levels and class environment, monitoring all students' solutions, and identifying the core mathematical ideas in student solutions. In addition, this study revealed practical and specific difficulties that had not been described in the previous studies, such as writing a lesson plan for effective use, simultaneously performing multiple teacher roles, and visually sharing student presentations. This study is expected to provide practical tips for elementary school teachers who are eager to promote effective mathematical discussions and to provoke professional discourse for teacher educators through specific examples.

• The Mathematical Education
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• v.61 no.4
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• pp.539-557
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• 2022

A research field develops by experiencing several turns of paradigms. Mathematics education research have experienced those turns as well. Still, the dominant perspective is that mathematics education research should be scientific and objective. In this article, I suggest that this need not to be the prime rule to follow and that the mathematics education field will fertile by discussing extraordinary cases which may seem controversal to be recognized as valid research work. To this end, I first briefly describe the necessity of open discussions among researchers for a field to develop. Then, I introduce fiction writing, a resesarch method derived from arts-based research, as an extraordinary case for open discussions. The benefit of Arts-based research is on that it takes an holistic approach to how we know by embracing emotion and emphathy as means for knowing. Because of this trait, arts-based research holds a powerful potential for influencing a wide range of people, both inside and outside of the resesarch field. Following this, I present a fiction about a prospective teacher who participated in an activity for designing educative curriculum materials. By doing so, I sought to provoke discussions among mathematics education researchers about what to include as a valid research work, possible standards for reviewing arts-based resesarch.

• Journal of the Korean School Mathematics Society
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• v.4 no.2
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• pp.135-142
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• 2001

The selected questions for this study was their conversation in problem solving way of working together. To achieve its purpose researcher I chose more detail questions for this study as follows. $\circled1$ What is the difference of strategy according to its level \ulcorner $\circled2$ What is the mathematical ability difference in problem solving process concerning its level \ulcorner This is the result of the study $\circled1$ Difference in the strategy of each class of students. High class-high class students found rules with trial and error strategy, simplified them and restated them in uncertain framed problems, and write a formula with recalling their theorem and definition and solved them. High class-middle class students' knowledge and understanding of the problem, yet middle class students tended to rely on high class students' problem solving ability, using trial and error strategy. However, middle class-middle class students had difficulties in finding rules to solve the problem and relied upon guessing the answers through illogical way instead of using the strategy of writing a formula. $\circled2$ Mathematical ability difference in problem solving process of each class. There was not much difference between high class-high class and high class-middle class, but with middle class-middle class was very distinctive. High class-high class students were quick in understanding and they chose the right strategy to solve the problem High class-middle class students tried to solve the problem based upon the high class students' ideas and were better than middle class-middle class students in calculating ability to solve the problem. High class-high class students took the process of resection to make the answer, but high class-middle class students relied on high class students' guessing to reconsider other ways of problem-solving. Middle class-middle class students made variables, without knowing how to use them, and solved the problem illogically. Also the accuracy was relatively low and they had difficulties in understanding the definition.

• 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 the Korean School Mathematics Society
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• v.16 no.2
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• pp.459-478
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• 2013

Didactic transposition refers to an adaptive treatment of mathematical knowledge into knowledge to be taught. This study intends to investigate how mathematical knowledge was modified in mathematics textbooks and lessons. This study identified examples of didactic transposition in mathematics textbooks and lessons in Korea and those in the U.S., The examples identified were FOIL method, trigonometry using s, c, t in writing style, order of operations(PEMDAS), area of a circle and circumference, order of prefixes in the metric system, trigonometry(SOH, CAH, TOA), operations on integer, and regular polyhedra. These examples were classified into the two categories, one for mnemonics, and one for concreteness and intuitiveness. Then a survey was conducted for in-service teachers in Korea and those in the U.S. to evaluate the appropriateness and the necessity of didactic transposition. Lastly, the potential didactic phenomena, meta-cognitive shift which may occur with these examples were discussed.

• The Korean Journal of Community Living Science
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• v.22 no.4
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• pp.519-533
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• 2011

The objective of this study was to follow up changes in knowledge related to the mathematics education field work of preliminary early childhood teachers. The subjects of this research were 28 students who were taking mathematics education courses in early childhood education departments at various universities. This research ran for 15 weeks and was conducted through field work relating to mathematics education. The study collected data from pre-service teachers' knowledge, the diagram of concept, writing journals, interviews, and materials from the internet. Through this procedure, pre-service teachers' knowledge for mathematics education could later be expanded, ordered, and integrated. In addition, pre-service teachers not only understood the importance of contents and levels of lesson plans, but also learned how to utilize educational media to make effective lessons. Furthermore, pre-service teachers realized that the mathematical concepts of students could be expanded depending on the contents and methods of pre-service teachers' lesson plans and students could then apply these concepts into daily situations.

• Communications of Mathematical Education
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• v.25 no.4
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• pp.681-691
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• 2011

Mathematics curriculum according to 2009 Revised National Curriculum suggests that school mathematics must cultivate interest and curiosity about mathematics in addition to creative thinking ability of students, and ability and attitude of observing and analyzing many things happening around. Centroid of a triangle in 2007 Revised National Curriculum is defined as 'an intersection point of three median lines of a triangle' and it has been instructed focusing on proof study that uses characteristic of parallel lines and similarity of a triangle. This could not teach by focusing on the centroid itself and there is a problem of planting a miss concept to students. And therefore this writing suggests centroid must be taught according to its essence that centroid is 'a dot that forms equilibrium', and a justification method about this could be different.

• The Mathematical Education
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• v.60 no.3
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• pp.265-279
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• 2021

In this study, by analyzing of types and functions of questions presented in Data and Chance area of the mathematics textbooks for grades 1-6 of the 2015 revised curriculum, the characteristics of the questions presented in the textbook were identified, and implications for teaching and learning related to the questions in this textbook were obtained. Types and functions of the presented questions showed different proportions of appearance according to the grade clusters, and this seems to be related to the learning contents for each grade clusters and the characteristics of grade clusters. In addition, it can be seen that the functions of questions are related to the types of questions. Teachers should have pedagogical content knowledge about Data and Chance area as well as developmental characteristics for each grade clusters. In addition, the teacher should present an suitable question for the level of grade clusters and the nature of the content to be taught so that effective learning can be achieved based on the understanding of the characteristics and functional characteristics of each type of questions. The results of this study can contribute to statistical teaching in a progressive direction by providing a foundation for textbook writing and teaching/learning.

• Education of Primary School Mathematics
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• v.25 no.4
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• pp.297-312
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• 2022

Word problems can lead learners to more meaningfully learn mathematics by providing learners with various problem-solving experiences and guiding them to apply mathematical knowledge to the context. This study attempted to provide implications for the textbook writing and teaching and learning process by examining the word problem of elementary mathematics textbooks from the perspective of practical context. The word problem of elementary mathematics textbooks was examined, and elementary mathematics textbooks in the United States and Finland were referenced to find specific alternatives. As a result, when setting an unnatural context or subject to the word problem in elementary mathematics textbooks, artificial numbers were inserted or verbal expressions and illustrations were presented unclearly. In this case, it may be difficult for learners to recognize the context of the word problem as separate from real life or to solve the problem by understanding the content required by the word problem. In the future, it is necessary to organize various types of word problems in practical contexts, such as setting up situations in consideration of learners in textbooks, actively using illustrations and diagrams, and organizing verbal expressions and illustrations more clearly.