• Journal of Educational Research in Mathematics
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• v.21 no.2
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• pp.105-120
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• 2011

This research intends to analyse how mathematically gifted 8th graders (age 14) discover and proof the properties on the sum of face angles of polyhedron. In this research, the problems on the sum of face angles of polyhedrons were given to 36 gifted students, and their discovery and proof processes were analysed on the basis of their the activity sheets and the researcher's observation. The discovery and proof processes the gifted students made were categorized, and levels revealed in their processes were analysed.

• 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.

• Communications of Mathematical Education
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• v.35 no.4
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• pp.425-444
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• 2021

In this study, under the assumption that the goal pursued in measurement area can be reached through the composition of the measurement activity considering the mathematical process, the method of summing the interior angles of a triangle using the measurement error was applied to the 4th grade class of the elementary school. Results of the study, first, students were able to recognize the possibility of measurement error by learning the sum of the interior angles of a triangle using the measurement error. Second, the discussion process based on the measurement error became the basis for students to attempt mathematical justification. Third, the manipulation activity using the semicircle was recognized as a natural and intuitive way of mathematical justification by the students and led to generalization. Fourth, the method of guiding the sum of the interior angles of a triangle using the measurement error contributed to the development of students' mathematical communication skills and positive attitudes toward mathematics.

• Communications of Mathematical Education
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• v.14
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• pp.61-70
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• 2001

수학은 추상적인 학문이다. '추상'은 몇 개 또는 무한히 많은 사물의 공통성이나 본질을 추출하여 파악하는 사고작용이다. 이렇게 추상된 것들을 모아 분류를 하고 그 다음에 이름을 붙이는 것이 바로 개념이 형성되는 과정이고 수학자가 수학을 하는 과정이다. 이 개념들은 여러 가지 모양으로 결합하여 스키마라고 부르는 개념 구조를 형성하게 되는데, 이 스키마는 수학적 사고를 하는데 매우 중요한 역할을 하여 수학을 개념적으로 이해하는데 도움을 주며, 새로운 지식을 얻는데 필요한 필수적인 도구가 된다. 본 논문에서는 연속적인 수열의 합의 공식에 대하여 학생들이 Skemp가 말한 '관계적 이해'를 할 수 있도록 스키마를 이용하여 문제를 해결할 수 있는 모델과 원주의 스키마를 이용한 생활 속의 문제를 제시하여 학생들이 공식을 암기하기보다는 수학의 구조를 파악하고 연계성을 이해함으로서 능동적인 구성활동을 유발하여 수학에 대한 흥미를 느낄 수 있도록 도움을 주고자 한다.

• Journal of the Korean School Mathematics Society
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• v.12 no.3
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• pp.247-265
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• 2009

In the 21C information-based society, there is an increasing demand for emphasizing communication in mathematics education. Therefore the purpose of this study was to research how properties of communication among small group members varied by mathematical problem types. 8 fourth-graders with different academic achievements in a classroom were divided into two heterogenous small groups, four children in each group, in order to carry out a descriptive and interpretive case study. 4 types of problems were developed in the concepts and the operations of fractions and decimals. Each group solved four types of problems five times, the process of which was recorded and copied by a camcorder for analysis, among with personal and group activity journals and the researcher's observations. The following results have been drawn from this study. First, students showed simple mathematical communication in conceptual or procedural problems which require the low level of cognitive demand. However, they made high participation in mathematical communication for atypical problems. Second, even participation by group members was found for all of types of problems. However, there was active communication in the form of error revision and complementation in atypical problems. Third, natural or receptive agreement types with the mathematical agreement process were mainly found for conceptual or procedural problems. But there were various types of agreement, including receptive, disputable, and refined agreement in atypical problems.

• Education of Primary School Mathematics
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• v.21 no.1
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• pp.75-91
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• 2018

This study examines the educational meaning of the sum of the angles of a triangle in elementary school mathematics and discusses the introduction and explanation methods to convey the meaning faithfully. First, we investigated how to introduce the sum of the angles of a triangle in the Korean national mathematics curriculums from the past to the present and surveyed the experiences and opinions of the teachers. The results of the survey are summarized and discussed in three parts: The context of 'arranging angles activities' and 'measuring angles activities', the methods to convey the meaning of the sum of the angles of a triangle as an invariance, and other details.

• School Mathematics
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• v.5 no.4
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• pp.401-420
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• 2003

We have many problems in the teaching and learning of proof, especially in the demonstrative geometry of middle school mathematics introducing the proof for the first time. Above all, it is the serious problem that many students do not understand the meaning of proof. In this paper we intend to show that teaching the meaning of proof in terms of historic-genetic approach will be a method to improve the way of teaching proof. We investigate the development of proof which goes through three stages such as experimental, intuitional, and scientific stage as well as the development of geometry up to the completion of Euclid's Elements as Bran-ford set out, and analyze the teaching process for the purpose of looking for the way of improving the way of teaching proof through the historic-genetic approach. We conducted lessons about the angle-sum property of triangle in accordance with these three stages to the students of seventh grade. We show that the students will understand the meaning of proof meaningfully and properly through the historic-genetic approach.

• Journal of Educational Research in Mathematics
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• v.17 no.4
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• pp.395-418
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• 2007

The purpose of this study was to analyze the influence of mathematical tasks on mathematical communication. Mathematical tasks were classified into four different levels according to cognitive demands, such as memorization, procedure, concept, and exploration. For this study, 24 students were selected from the 5th grade of an elementary school located in Seoul. They were randomly assigned into six groups to control the effects of extraneous variables on the main study. Mathematical tasks for this study were developed on the basis of cognitive demands and then two different tasks were randomly assigned to each group. Before the experiment began, students were trained for effective communication for two months. All the procedures of students' learning were videotaped and transcripted. Both quantitative and qualitative methods were applied to analyze the data. The findings of this study point out that the levels of mathematical tasks were positively correlated to students' participation in mathematical communication, meaning that tasks with higher cognitive demands tend to promote students' active participation in communication with inquiry-based questions. Secondly, the result of this study indicated that the level of students' mathematical justification was influenced by mathematical tasks. That is, the forms of justification changed toward mathematical logic from authorities such as textbooks or teachers according to the levels of tasks. Thirdly, it found out that tasks with higher cognitive demands promoted various negotiation processes. The results of this study implies that cognitively complex tasks should be offered in the classroom to promote students' active mathematical communication, various mathematical tasks and the diverse teaching models should be developed, and teacher education should be enhanced to improve teachers' awareness of mathematical tasks.

• Communications of Mathematical Education
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• v.34 no.3
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• pp.355-372
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• 2020

The concept of infinite series is an important subject of major mathematics curriculum in college. For several centuries it has provided learners not only counter-intuitive obstacles but also central role of analysis study. As the understanding in concept on infinite series became foundation of development of calculus in history of mathematics, it is essential to present students to study higher mathematics. Most students having concept of infinite sum have no difficulty in mathematical contents such as convergence test of infinite series. But they have difficulty in organizing concept of infinite series of partial sum. Thus, in this study we try to analyze construct the concept of infinite series in terms of APOS theory and genetic decomposition. By checking to construct concept of infinite series, we try to get an useful educational implication on teaching of infinite series.

• The Mathematical Education
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• v.62 no.4
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• pp.551-567
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• 2023

Even and odd numbers are taught in elementary school mathematics, but the introductory activities, definitions, and properties of sum on even and odd numbers vary depending on which grade they are presented. The purpose of this study was to compare and analyze the activities related to even and odd numbers presented in Korean mathematics textbooks developed under the different curriculum revisions, and to further analyze the related activities in foreign textbooks to draw implications for the teaching of even and odd numbers. In Korean textbooks, from the time of the fourth mathematics curriculum until the 2007 revision, even and odd numbers were covered in the multiples and divisors unit of the fifth grade textbook, while since the 2009 revision, the first grade textbook has covered the topic along with teaching numbers up to 50 or 100. In addition, the definitions of even and odd numbers varied depending on the grade level and the nature of the unit being taught, and activities addressing the properties of sum were only presented in the mathematics textbook under the third curriculum along with a few mathematics workbooks. In foreign textbooks, even and odd numbers were introduced in Grades 1, 2, or 5, and their related activities varied accordingly. Based on these findings, this study discusses the implications for the teaching of even and odd numbers.