• School Mathematics
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• v.8 no.2
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• pp.139-160
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• 2006

It seems that North Korea has been trying to reorganize its educational system as well as its economic system on a large scale since July 1, 2002. There has been a decrease in quantity of math textbooks by about 30% decrease. Until the 1990's, geometry and algebra had been kept apart from each other in North Korea, but they are put together now. Moreover many changes have been made in both contents and methods of teaching. For example, an area model is used in North Korea to teach operation of fraction, which makes the learning period shorter. This idea will provide us with many implication when we need to ready for decreasing the quantities in the future. Moreover teaching methods of division algorithms need to be reconsidered since the visual algorithm of division could help save the thinking in problem solving.

• Education of Primary School Mathematics
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• v.27 no.2
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• pp.155-171
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• 2024

This study compared and analyzed students' reasoning processes and justification methods when introducing the concept of "the sum of angles in a triangle" in mathematics classes with a focus on both measurement and geometric aspects. To confirm this, the research was conducted in a 4th-grade class at H Elementary School in Suwon, Gyeonggi-do, South Korea. The conclusions drawn from this study are as follows. First, there is a significant difference when introducing "the sum of angles in a triangle" in mathematics classes from a measurement perspective compared to a geometric perspective. Second, justifying the statement "the sum of angles in a triangle is 180°" is more effective when explained through a measurement approach, such as "adding the sizes of the three angles gives 180°," rather than a geometric approach, such as "the sum of the angles forms a straight angle." Since elementary students understand mathematical knowledge through manipulative activities, the level of activity is connected to the quality of mathematics learning. Research on this reasoning process will serve as foundational material for approaching the concept of "the sum of angles in a triangle" within the "Geometry and Measurement" domain of the Revised 2022 curriculum.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.245-263
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• 2013

Mathematical learning via projects, which enables the reconstruction of curriculum through integration and emphasizes the process of solving problems by posing questions, has attracted the attention of the department of mathematics. This research is aimed at exploring the link between mathematics and project learning by analyzing an example of student-oriented project 'the secrets of pyramid' focused on understanding 'triangle' specifically designed for forth graders. From 115-hour process of subject-oriented project, this study reinterpreted the mathematical meaning of only 24 hours directly related to mathematics, especially to figure exploration. Consequently, this problem solving involved a variety of geometric activities as a process, such as measuring an angle, constructing a triangle, etc. Thus students attempt to actively participate in the process, thereby allowing them to learn how to measure things more accurately. Moreover, project learning improved students' understanding on not only plane figures but solid figures. This indicates that by project learning, learning from given problems or contents can be extended to other mathematical areas.

• 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 Educational Research in Mathematics
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• v.11 no.1
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• pp.123-136
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• 2001

우리나라 중학교 2학년 학생들은 제3차 수학.과학 국제비교연구인 TIMSS와 그 반복연구인 TIMSS-R의 수학 검사에서 최상위권의 성취 수준을 보임으로써 국내외 연구자들의 관심의 초점이 되어 왔다. 이 논문은 우선 우리나라 학생들이 높은 성취 수준을 기록할 수 있는 원인을 $\circled1$ 체계적인 수 세기 방식, $\circled2$ 상급 학교 진학을 위한 시험의 대비, $\circled3$ 수학 교사 의 능력, $\circled4$ 교육과정과 검사와의 관련성, $\circled5$ 검사에 대한 태도라는 다섯 가지 측면에서 탐색하였다. 또한 높은 성취 수준 이면에 드리워진 부정 적인 측면을 조망하여 $\circled1$ 공학적 도구 의 이용에 대한 소극성, $\circled2$ 실생활 관련 문장제에 대한 저조한 성취 수준, $\circled3$ 지역에 따른 성취 수준의 차이, $\circled4$ 수학에 대한 부정적인 태도의 네 가지로 요약하였다. 또한 TIMSS-R 의 수학 성취 수준에 대한 성별 차이를 $\circled1$ 친숙함/생소함, $\circled2$ 대수/기하, $\circled3$ 자유반응형/선택형이라는 세 가지 측면에서 분석하였다. 마지막으로 국제비교 연구의 결과는 국가별 평균성취 수준의 양적인 비교에 초점을 두기보다는, 성취도 이면에 깔린 다양한 요소에 대한 복합적인 고려와 깊이 있는 분석을 통해 수학교육의 현 상태를 점검하는 하나의 잣대로 이용해야 한다는 점을 지적하였다.

• Communications of Mathematical Education
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• v.29 no.4
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• pp.687-698
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• 2015

This research is based on Jungian psychology. The founder psychoanalysist Jung introduced the notion of unconsciousness. This researcher made Mandala figures as an intermediary between consciousness and unconsciousness, and then took Mandala figures a research starting point. Until now, Mandala has been used therapy tool for emotional stability. But, this researcher tried Mandala coloring to develope cognitive and emotional abilities for early childhood. This paper is a result of experiment to recognize geometric and spacial conceptions for early childhood.

• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.607-622
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• 2014

The purpose of this paper is that it analyzes the historical development of the concept of trigonometric functions and discuss some didactical implications. The results of the study are as follows. First, the concept of trigonometric functions is developed from line segments measuring ratios to numbers representing the ratios. Geometry, arithmetic, algebra and analysis has been integrated in this process. Secondly, as a result of developing from practical calculation to theoretical function, periodicity is formalized, but 'trigonometry' is overlooked. Third, it must be taught trigonometry relationally and structurally by the principle of similarity. Fourth, the conceptual generalization of trigonometric functions must be recognized as epistemological obstacle, and it should be improved to emphasize the integration revealed in history. The results of these studies provide some useful suggestions to teaching and learning of trigonometry.

• East Asian mathematical journal
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• v.32 no.4
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• pp.483-500
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• 2016

Ancient Greek mathematician Euclid left three books about mathematics. It's 'The elements', 'The data', 'On divisions of figure'. This study is based on the analysis of Euclid's 'On divisions of figure'. 'On divisions of figure' is a book about the construction of the shape. Because, there are thirty six proposition in 'On divisions of figure', among them 30 proposition are for the construction. In this study, based on the 'On divisions of figure' we explore the direction for construction education. The results were as follows. First, the proposition of 'On divisions of figure' shall include the following information. It is a 'proposition presented', 'heuristic approach to the construction process', 'specifically drawn presenting', 'proof process'. Therefore, the content of textbooks needs a qualitative improvement in this way. Second, a conceptual basis of 'On divisions of figure' is 'The elements'. 'The elements' includes the construction propositions 25%. However, the geometric constructions contents in middle school area is only 3%. Therefore, it is necessary to expand the learning of construction in the our country mathematics curriculum.

• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.529-546
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• 2010

This study aims to analyze and criticize the definition of the similarity concept in mathematical texts by investigating mathematical history. At first, we analyzed the definition of Pythagoras, the definition of Euclid's ${\ll}$Elements${\gg}$, the definition of Clairaut's ${\ll}$Elements of geometry${\gg}$, the postulate of Brkhoff's postulates for plane geometry, the definition of Birkhoff & Beatly의 ${\ll}$Basic Geometry${\gg}$. the definition of SMSG ${\ll}$Geometry${\gg}$. and the definition of the similarity concept in current mathematics texts. Then we criticized the definition of the similarity concept in current mathematics texts based on mathematical history. We critically discussed three issues and gave three suggestions.

• Education of Primary School Mathematics
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• v.20 no.1
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• pp.53-68
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• 2017

Although the table, as one of the representations for helping mathematics understanding, steadily has been shown in the mathematics textbooks, there have been little studies that focus on the table and analyze how the table may be used in understanding students' functional thinking. This study investigated the elementary school 5th graders' abilities to design function tables. The results showed that about 75% of the students were able to create tables for themselves, which shaped horizontal and included information only from the problem contexts. And the students had more difficulties in solving geometric growing pattern problems than story problems. Building on these results, this paper is expected to provide implications of instructional directions of how to use the table as 'function table'.