• Education of Primary School Mathematics
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• v.13 no.1
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• pp.37-48
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• 2010

In this paper we analyze a concept 'didactical unit', and some concrete methods of expanding didactical unit studied by P.M.Erdniev. Erdniev studied the concept for a long time, wrote mathematics textbooks from 1st grade to 9th grade. In these textbooks he tried to embody his ideas related with expanded didactical unit. We analyze Erdniev's mathematics textbook of 3rd grade.

• Journal for History of Mathematics
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• v.17 no.4
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• pp.87-100
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• 2004

There is great enthusiasm among many mathematics educators to seek to understand how mathematical history can be employed to emphasize the usefulness of mathematics and to make it even more useful. This study focused on reviewing the history of mathematics to provide a 'source of insight.' In this study, the reasons for including the history of mathematics in the mathematics curriculum were divided into three domains: cognitive, affective, and sociocultural. Each domain included the followings: mathematical thinking and understanding; development of a positive attitude and increase motivation; and last, humanistic facets and sociocultural experience. At the same time, we need to develope a pedagogical approach that allows educators to use history properly. Furthermore, we must integrate the historical topics into regular curricula including the syllabus historically-informed grounds.

• Journal of Christian Education in Korea
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• v.69
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• pp.45-75
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• 2022

The purpose of this study is to explore the implementation of Bibliodrama on the metaverse platforms. In other words, to create interesting and effective Bible education for modern learners, this study took a didactical approach to the implementation of Bibliodrama through the metaverse. The main reason to be enthusiastic about using the metaverse for education is because users, who have been only content consumers, now able to experience and create values. As a Bible didactical approach, Bibliodrama is a an emphatical and communicative learning method in the form of role play. Bibliodrama seeks to interact with the world of the learner and the world of the Bible through improvisational acting, to study the Bible. Through the Bible didactical approach, the meeting of Bibliodrama and the metaverse can have a positive effect on modern learners, in terms of improving learning environment and, above all else, increasing learning interest. In terms of biblical didactics, implementing Bibliodrama in the metaverse has the following advantages. First, it helps to construct a dramatic situation and environment so that the meaning of the biblical text can be proved relevant to today's learners, not something belonging to the past. Second, in the metaverse, the historical space and characters of the Bible can be realized in virtual reality to produce a 'situational play'. Demonstrating freedom, imagination and creativity in the metaverse learners play in Bibliodrama. This way they also become aware of the hidden meaning of the blank pages in the Bible. Third, the metaverse environment is not static but dynamic and interactive; Bibliodrama pursues an interpretation that harmonizes spirit and body. Therefore, through the dynamic activities of discovering the meaning and significance of the Bible, it is possible to form a holistic faith in which spirit and body act as one.

• Journal of the Korean Chemical Society
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• v.68 no.4
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• pp.205-220
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• 2024

This study aims to explore characteristics of pedagogical reasoning and action of beginning science teachers that naturally and spontaneously occurs in a professional learning community. Three novice middle school science teachers who majored chemistry education in A college of education, passed the examination for selecting secondary school chemistry teachers, and had a common goal of designing 8^th grade science lesson plan voluntarily created a professional learning community and had weekly meetings over a year. Main data sources included transcribed audio-recording of 11 meetings of three science teachers in a professional learning community. Data was analyzed using Shulman's pedagogical reasoning model that includes comprehension, transformation, instruction, evaluation, reflection, and new comprehension to identify characteristics and features of pedagogical reasoning in a professional learning community. Data analysis revealed that pedagogical reasoning in a professional learning community comprises not only preparation, representations, instructional selections, and adaptation but also evaluation, reflection, and new comprehension in transformation stage. Reflection in transformation stage leads teachers to be actively engaged in discussion and get new comprehension on each sub-component(preparation, representations, instructional selections, adaptation, and evaluation) of transformation stage.

• 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.

• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.315-334
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• 2005

The purpose of this study is to find out the implications on when and how the correlation concept can be taught. we investigate the development time and method of the concept in a statistical perspective those initially have discussed in psychology by Piaget. We first reviewed the 1958 research by Inhelder and Piaget. It was the first one which researched the development of the correlation and has become the foundation of psychological perspective. According to them, the correlation concept needs proportional and probability concept ahead of its development and argued on the coefficient of correlation based on formal and logical position. However, from a statistical perspective, the correlation concept is a part of the distribution concept. So, the level of the correlation concept grows from the comparison of conditional distributions to the conditional probability distribution where the proportional concept and probability concept are applied. As reviewed through the literature, we found that 11-12 years old students in early formal operation stage reasoned about correlation through the comparison of conditional distributions. In our study, we argue that we need to consider the possibility of beginning didactic mediation for correlation concept earlier and the method approaching it in a distribution perspective.

• School Mathematics
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• v.9 no.1
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• pp.119-139
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• 2007

The purpose of this study is to analyze students' misconception in the teaming of the conic sections with the cognitive and pedagogical point of view. The conics sections is very important concept in the high school geometry. High school students approach the conic sections only with algebraic perspective or analytic geometry perspective. So they have various misconception in the conic sections. To achieve the purpose of this study, the research on the following questions is conducted: First, what types of misconceptions do the students have in the loaming of conic sections? Second, what types of errors appear in the problem-solving process related to the conic sections? With the preliminary research, the testing worksheet and the student interviews, the cause of error and the misconception of conic sections were analyzed: First, students lacked the experience in the constructing and manipulating of the conic sections. Second, students didn't link the process of constructing and the application of conic sections with the equation of tangent line of the conic sections. The conclusion of this study ls: First, students should have the experience to manipulate and construct the conic sections to understand mathematical formula instead of rote memorization. Second, as the process of mathematising about the conic sections, students should use the dynamic geometry and the process of constructing in learning conic sections. And the process of constructing should be linked with the equation of tangent line of the conic sections. Third, the mathematical misconception is not the conception to be corrected but the basic conception to be developed toward the precise one.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.511-536
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• 2017

The present study aims to investigate ways in which pre-service secondary mathematics teachers anticipate 1) students' responses to specific mathematical tasks which are chosen or devised by the participating pre-service teachers as requiring students' higher cognitive demand and, 2) their roles as math teachers to scaffold students' mathematical thinking. To achieve the goal, we had our pre-service teachers to engage in an adapted version of Spangler & Hallman-Thrasher(2014)'s Task Dialogue writing activity whose focus was to develop pre-service elementary teachers' ability to orchestrate mathematical discussion. 14 pre-service teachers who were junior at the time enrolled in the Mathematics Teaching Method Course were subjects of the current study. In-depth analysis of both Task Dialogues which pre-service secondary mathematics teachers wrote and audiotapes of the group discussions while they wrote the dialogues suggests the following results: First, the pre-service secondary teachers anticipated how students would approach a task based on their own teaching experiences. Second, they were challenged not only to anticipate more than one correct students' responses but to generate questions for the predicted correct-responses to bring forth students' divergent thinking. Finally, although they were aware that students' knowledge should be the crucial element guiding their decision-making process in teaching, they tended to lower the cognitive demands of tasks by providing students with too much guidance which brought forth the use of procedural knowledge. The study contributes to the field as it provides insights as to what to attend in designing teacher education course whose goal is to provide a foundation for developing pre-service teachers' ability to effectively orchestrate mathematical discussion.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.19-37
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• 2004

In school mathematics, polygon and polyhedron are defined by vague terms such as "surrounded" or "formed" Moreover, the inclusion of boundary and interior in the definition of polygon and polyhedron is varied according to the context. Polygon and polyhedron are considered as "context-dependent concept" in school mathematics. Elementary school mathematics introduces a surface only in the context of solid, yet secondary school mathematics explains a surface as the trace of the line movement. From the perspective of fallabilism, it is possible and desirable to lead students to revise and improve their conceptions on polygon, polyhedron, and surface. It is more appropriate to name a face, an edge, and a vertex rather than to express a face of polyhedron, an edge of polyhedron, and a vertex of polyhedron in textbooks. The term "surface as a polygon" in secondary mathematics textbooks shows a conflict between intuitive approach in elementary school and logical approach in secondary school.

• 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.