• Education of Primary School Mathematics
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• v.14 no.1
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• pp.1-12
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• 2011

This paper provides an outline of mathematics education based on the classroom ecology. Ecology is the subject that concentrates on the relations of human and environment. As mathematics education consists of many factors, it is natural that mathematics education should be interest in the perspective of ecology. This paper examines the meaning of ecology and classroom ecology of mathematics education in the perspective of ecology. And it provides the directions of ecological mathematics education. In special, I set the frame of mathematics classroom in the perspective of ecology. The ecological structure divides microsystem(teacher, student, content), mesosysten(relations of microsystems), exosystem(school), and macrosystem(the objects of mathematics education). Lastly, I suggest the ways of mathematical learning and research of classroom ecology in mathematics education. For we should focus the improvement of students' mathematical ability, we must search for the various teaching and learning methods and the ares of research in the perspective of ecology classroom. Therefore, we should be interested in the classroom environments as well as teaching methods, contents based on the ecology classroom in mathematics education.

• Journal of the Korean School Mathematics Society
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• v.10 no.2
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• pp.149-171
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• 2007

This study is aimed at development of pedagogical content knowledge on fraction in the elementary school mathematics. Elementary students regard fraction as the difficult topic in school mathematics. Furthermore, fraction is the fundamentally important concept in studying mathematics. So it is important to develop the pedagogical content knowledge on fraction. The reason of attention to the pedagogical content knowledge is that improving the quality of teaching is the central focus of a high quality mathematics education. Shulman suggested that various knowledges are required for teacher to improve their classes. Of course, pedagogical content knowledge is the most valuable in teaching mathematics. Pedagogical content knowledge is related to the promotion of students' understanding about the learning. Pedagogical content knowledges are categorized by five factors in this study. These are understanding about curriculum, understanding about students and students' knowledge, understanding about teachers and teachers' knowledge, understanding about the methods, contents, and management of class, and understanding about methods of assessments. I develop the pedagogical content knowledge on fraction according to the these categories. I concentrate on the two types of pedagogical content knowledges in developing. That is, I present knowledges which teachers have to know for teaching fraction effectively and materials which teachers can use during the teaching fraction. Pedagogical content knowledges guarantee teachers as the professionalists. Teachers should not teach only content knowledges but teach various knowledges including the meta-knowledges which have relation to fraction.

• The Mathematical Education
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• v.63 no.1
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• pp.105-122
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• 2024

This study analyzed the research trends of 101 articles published in prominent international mathematics education journals over 24 years from 2000, when NCTM's recommendation emphasizing argumentation was released, until September 2023. We first examined the overall trend of argumentation research and then analyzed representative research topics. We found that students were the focus of the studies. However, several studies focused on teachers. More studies were examined in secondary school than in elementary school, and many were conducted in argumentation in classroom contexts. We also found that argumentation research is becoming increasingly popular in international journals. The representative research topics included 'teaching practice,' 'argumentation structure,' 'proof,' 'student understanding,' and 'student reasoning.' Based on our findings, we could categorize three perspectives on argumentation: formal, contextual, and purposeful. This paper concludes with implications on the meaning and role of argumentation in Korean mathematics education.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.3
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• pp.471-489
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• 2012

2007 Curriculum Revision adopted new Inquiry Activities in mathematical textbooks. So it is critical to analyze the problems of actual application of Inquiry activities in the classrooms. For this purpose, we analyzed the Inquiry activities of Measurement Area of the textbooks and find the appropriate solutions. Secondly, we develop the reorganization materials to fix and solve the existing problems found in the previous problem analysis, and apply the development materials and examine the effects afterwards. The results of the survey indicated that most of teachers are well aware of the importance of Inquiry Activities. However, many teachers answered that Inquiry activities does contain neither diverse strategic approaches nor solutions accommodating with various learning levels of students. The most difficult points to educate Inquiry Activities are that it is difficult to teach students based on individual learning level and that activities consist of mainly short answers that makes it difficult to do in-depth Inquiry Activities. Analyzing Inquiry Activities in the textbook shows that Inquiry Activities in some chapters were constructed as simple sentence questions or presented with the solving process in the questions themselves. The following application classes were implemented by partially taking advantage of the newly developed reorganization materials. Then, the effects were measured by before and after questionnaires, the survey to teachers, and the results of activities. The reorganization materials were effective at arousing the curiosity from students as well as enabling the natural ability-level driven classes.

• Journal of Elementary Mathematics Education in Korea
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• v.9 no.2
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• pp.181-200
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• 2005

The purpose of this thesis was to analyze communicational means of mathematical communication in perspective of languages and behaviors. Research questions were as follows; First, how are the characteristics of mathematical languages in communicating process of mathematical small group learning? Second, how are the characteristics of behaviors in communicating process of mathematical small group learning? The analyses of students' mathematical language were as follows; First, the ordinary language that students used was the demonstrative pronoun in general, mainly substituted for mathematical language. Second, students depended on verbal language rather than mathematical representation in case of mathematical communication. Third, quasi-mathematical language was mainly transformed in upper grade level than lower grade, and it was shown prominently in shape and measurement domain. Fourth, In mathematical communication, high level students used mathematical language more widely and initiatively than mid/low level students. Fifth, mathematical language use was very helpful and interactive regardless of the student's level. In addition, the analyses of students' behavior facts were as follows; First, students' behaviors for problem-solving were shown in the order of reading, understanding, planning, implementing, analyzing and verifying. While trials and errors, verifying is almost omitted. Second, in mathematical communication, while the flow of high/middle level students' behaviors was systematic and process-directed, that of low level students' behaviors was unconnected and product-directed.

• School Mathematics
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• v.9 no.1
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• pp.99-117
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• 2007

In this paper it is discussed how children develop their logical reasoning beyond difficulties in the process of making sense of division with decimals in the classroom setting. When we consider the gap between mathematics at elementary and secondary levels, and given the logical nature of mathematics at the latter levels, it can be seen as important that the aspects of children's logical development in the upper grades in elementary school should be clarified. This study focuses on the teaching and learning of division with decimals in a 5th grade classroom, because it is well known to be difficult for children to understand the meaning of division with decimals. It is suggested that children begin to conceive division as the relationship between the equivalent expressions at the hypothetical-deductive level detached from the concrete one, and that children's explanation based on a reversibility of reciprocity are effective in overcoming the difficulties related to division with decimals. It enables children to conceive multiplication and division as a system of operations.

• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.95-111
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• 2015

The purpose of this study is to analyze cases on teaching solutions exploration of Wythoff's game through using the analogy for the gifted elementary students, to suggest useful teaching methods. Students recognized structural similarity among problems on the basis of relevance of conditions of problems. The discovery of structural similarity improves the ability to solve problems. Although 2 groups-NIM game with surface similarity is not helpful in solving Wythoff's game, Queen's move game with structural similarity makes it easier for students to solve Wythoff's game. Useful teaching methods to find solutions of Wythoff's game through using the analogy are as follow. Encoding process helps students make sense of the game. It is significant to help students realize how many stones are remained and how the location of Queen can be expressed by the ordered pair. Inferring process helps students find a solution of 2 groups-NIM game and Queen's move game. It is necessary to find a winning strategy through reversely solving method. Mapping process helps students discover surface similarity and structural similarity through identifying commonalities between the two games. It is crucial to recognize the relationship among the two games based on the teaching in the Encoding process. Application process encourages students to find a solution of Wythoff's game. It is more important to find a solution by using the structural similarity of the Queen's move game rather than reversely solving method.

• Journal of Educational Research in Mathematics
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• v.15 no.1
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• pp.57-74
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• 2005

The aim of this study is to reflect Vygotsky's theory of Zone of Proximal Development and other scholars' scaffolding theories emboding the theory and to examine the effects of mathematics instruction by scaffolding. The subjects of this study consist of 8 fifth graders attending S elementary school which is located in San-Chung county. The teaching-learning processes were videotaped and analysed according to scaffolding components. The results between pretest and posttest regarding to fraction were compared and the responses of students to a questionnaire on the mathematical attitude before and after the teaching experiment. It concludes that mathematics instruction by scaffolding was effective to improve students' mathematical learning ability and positive mathematical attitude.

• Proceedings of the Korea Contents Association Conference
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• 2014.11a
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• pp.391-392
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• 2014

지식과 정보가 다양하고 급속하게 변하는 정보화 시대를 살아가는 우리에게 필요한 것은 주어진 상황에 빠르게 대처하는 창의적인 사고이다. 이런 능력을 신장하기 위해서는 교육과정에도 창의력 신장을 위한 방법들이 모색되어야 한다. 본 연구는 초등학교 수학과 교육 과정의 한 부분인 '도형' 영역의 내용을 컴퓨터를 이용해 수업할 수 있도록 교육 지원 도구로 구현하였다.

• School Mathematics
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• v.17 no.1
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• pp.47-63
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• 2015

In this study, we will develope and apply the education program for mathematical creativity, with the open-ended problems about development figure. The purpose of this study is to categorize the elements of the mathematical creativity in consideration of the real class, and is to design a education program that reflects this. To do this, from 2006 through 2014, by targeting 205 gifted students in the sixth grade until eighth grade of Busan, Gyeongnam, Gyeongbuk were carried out in class. Also in this study, we will examine the process and the results of its application. As a result, students' outcomes and behavioral reactions brought about a qualitative development of the program, and students became aware of the participants in the development of the program. These results suggest the aim of developing a education program for mathematical creativity, as well as the effectiveness of this education program.