• School Mathematics
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• v.17 no.2
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• pp.223-239
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• 2015

This study focused on classroom dialogue for communicating spatial information which is supposed to be implemented through learning activities using building-blocks. Even though mathematics textbooks for $2^{nd}$ graders have activities which require abilities of explaining and understanding some spatial information, we know few about how mathematical communication between teacher and students or among students and which strategies are more effective. For this reason, two building-block lessons for $2^{nd}$ graders were observed. The characteristics of teachers' instruction and students' explanation were identified and the mathematical communication between teachers and students or among students was analyzed. As a result, mains factors of impeding students' explanation and understanding were induced and the types of their communication were classified. Based on these results, several teaching strategies for effective communication in buildingblock lessons were suggested.

• Education of Primary School Mathematics
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• v.1 no.1
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• pp.3-22
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• 1997

본 연구는 첫째로는 수학교육에서 패턴이 강조되는 이론적 근거를 찾고자 역사적 맥락에서 수학의 성격변화를 탐색하였다. 수학의 성격 변화를 통하여 수학은 수의 탐구, 기하의 탐구, 운동ㆍ변화ㆍ공간의 탐구, 수학 연구의 도구에 대한 탐구로 그 영역을 점차 확대하여 왔으며, '수학은 패턴의 과학이다'라는 정의는 수학이 폭넓어짐에 따라 수학이 무엇인가에 대한 수학의 본성에 접근하는 논의라고 할 수 있다. 이러한 수학에 대한 새로운 관점은 수학교육의 새로운 방향 모색에 시사하는 바를 살펴보고, 특히 수학교실의 변화에 따른 패턴의 강조를 살펴보았다. 둘째로는 수학적 패턴을 밝힘과 동시에 수학 교육에서 수학적 패턴 분석의 틀을 마련하고자 수학적 패턴의 유형화를 시도하였다. 패턴의 속성에 따른 유형화와 패턴의 생성 방식에 따른 유형화를 통하여 수학적 패턴의 유형을 마련하였다. 초등학교 수학에서 다루어지는 패턴은 어떠한 것인가를 현행 4학년 수학교과서 및 익힘책에 제한하여 유형화한 틀로서 조사 분석하였다. 셋째로는 수학적 패턴에 관한 지도 방안의 모색으로서, 지도의 기본 방향을 설정하고 수학적 패턴에 관한 교수 전략을 마련하였다. 교수전략은 크게 패턴에서의 규칙 찾기, 패턴을 변형ㆍ확장하기, 자신의 새로운 패턴 만들기, 패턴을 수학적으로 설명하기로 나누고, 각각에 3-4개의 세부 전략과 세부 전략에 따른 예를 제시하였다.

• Communications of Mathematical Education
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• v.33 no.4
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• pp.471-488
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• 2019

This paper aims to examine how mathematical history is used in $ textbooks according to the 2015-Revised Curriculum. We analyze the distribution and characteristics of making use of the mathematical history in the nine textbooks, using the framework suggested by Jankvist (2009) on the whys and hows of using historical tasks. First, the tasks related to mathematical history in the textbooks are mostly used as an affective tool, while few tasks are used as a cognitive tool. Second, most of the historical tasks of the type of an affective tool are introducing the anecdotes of mathematicians or in the history of mathematics, and only one case is trying to show human nature of mathematics by illuminating the difficulties mathematicians were faced with. Third, all the mathematical history tasks used as affective tools and goals are illumination materials, while only two out of the ten tasks in the category of a cognitive tool are illumination materials, yet eight others are modular ones. Considering the importance and value of using mathematical history in the math education, this paper recommends that more modular materials on mathematical history tasks in the category of cognitive tools and goals should be developed and their deployment in the textbooks or courses should be promoted. $

• Journal of Educational Research in Mathematics
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• v.13 no.2
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• pp.123-141
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• 2003

This study investigated the understanding level and the using level of mathematical language for middle school students in terms of Freudenthal' language levels. It was proved that the understanding level task developed by current study for geometric concept had reliability and validity, and that there was the hierarchy of levels on which students understanded mathematical language. The level that students used in explaining mathematical concepts was not interrelated to the understanding level, and was different from answering the right answer according to the sorts of tasks. And, the level of mathematical language that was understood easily as students' thought, was the third level of the understanding levels. Mathematics teachers should consider the students' understanding level and using level, and give students the tasks which students could use their mathematical language confidently.

• Communications of Mathematical Education
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• v.8
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• pp.189-207
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• 1999

본 연구의 목적은 초 ${\cdot}$ 중학생들의 수학적 신념을 알아보고, 그러한 신념을 형성하는 요인들을 수학 교실의 상호작용에서 찾아보는 것이었다. 이를 위해, 초등학교 5, 6학년과 중학교 1, 2, 3학년 학생들의 수학적 신념을 질문지로 조사하였으며 각급 학교의 수학 교실에서 벌어지는 교수-학습 과정을 비디오로 촬영하여 각 교실의 사회적 규범들을 비교 분석하였다. 그 결과로서, 학생들은 수학은 이미 만들어진 규칙과 용어들로 이루어졌고 그 규칙에 따라 주어진 문제를 풀어 답을 구하는 것이 수학적 활동이라고 인식하고 있었다. 한편, 이러한 신념은 각급 교실에 형성된 사회수학적 규범과 일치했으며, 특히 개념설명과 새로운 전략 및 오류에 대한 반응과 관련된 사회수학적 규범이 학생들의 수학적 활동을 제한함으로써 그들의 신념을 결정하고 있었다.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.163-183
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• 2009

The purpose of this study was to provide useful information for teachers by analyzing mathematical communication emphasized through 'exploratory activity' and 'story corner' in elementary textbooks based on the revised curriculum. Two classrooms from the first grade and second grade respectively were observed and videotaped. Mathematical communication of each classroom was analyzed in terms of questioning, explaining, and the sources of mathematical ideas. The results showed that only one classroom focused on students' thinking processes and explored their ideas, whereas the other classrooms focused mainly on finding answer. Particularly, this tendency often appeared when implementing 'story corner' than 'exploratory activity'. The reason for this was inferred that teachers were not familiar with teaching mathematics in stories and that teachers' manual did not include concrete questions and students' expected responses. This paper included implications on how to promote mathematical communication specifically in lower grades in elementary school.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.63-63
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• 2004

기계류는 대개 부정형의 형상을 지니고 있으며, 또 표면이 모두 연결되어 있으므로, 진동하는 물체 표면상에서의 소음원 특성을 세밀히 파악하는 일은 매우 어려운 일이다. 음향 인텐시티나 공간 푸리에 변환을 이용하는 홀로그래피 기법 등의 어레이 마이크에 의한 기법들이 제안되었고 또 활용되고 있으나, 이는 어디까지나 음원에서 가까운 음장을 가상적인 음원면이라 보고 재구성하는 것이어서 실제 음원의 특성을 파악하는데 어려움이 있다. 이러한 문제점을 해결하기 위해 음원표면을 경계요소화 모델링을 하고, 어레이 마이크로 측정될 음장의 지점과 표면간의 관계를 수학적으로 정리한 후, 마이크에서 측정된 신호를 이용해 역으로 경계요소해석 계산을 수행하여 음원 특성을 파악하는 기법이 제안되었다. 본 발표에 있어서는 이와 같은 취지에서 ‘개발된 Inverse BEM을 이용한 NAH 기법’에 관한 개괄적인 내용을 설명하고, 그 적용 가능성 및 이 기법의 미래에 대해 설명하며, 다음과 같은 내용의 순서대로 설명된다: $\textbullet$ 각종 음원 파악 기법들의 특성과 이 방법이 필요한 이유 $\textbullet$일반 음향 holography 기법 (STSF)과의 차이점 $\textbullet$ 이론적 배경 개괄 $\textbullet$ 실제 적용 순서에 따른 방법의 설명 $\textbullet$ 후처리 결과물 $\textbullet$ 본 기법의 향후 과제 및 적용 방법의 개선

• Communications of Mathematical Education
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• v.28 no.4
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• pp.513-528
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• 2014

This study is intended to examine 36 in-service secondary school mathematics teachers' conceptions of proof in the context of mathematics and mathematics education. The results suggest that almost teachers recognize the role as justification well but have the insufficient conceptions about another various roles of proof in mathematics. The results further suggest that many of teachers have vague concept-images in relation with the requirement of proof and recognize the insufficiency about the actual teaching of proof. Based on the results, implications for revision of mathematics curriculum and mathematics teacher education are discussed.

• Communications of Mathematical Education
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• v.25 no.3
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• pp.577-591
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• 2011

In this study, in order to use computer in mathematical learning effectively, we investigate application of computer shown textbooks in geometry unit of middle school mathematics. First, we analyzed about status of computer application and method of computer application in 27 textbooks. We presented concrete example of mathematics activity using computer that can be used by teachers. Also, we tried to find out the direction to use computer more effectively in teaching and learning geometry. Through this process, we do not simply use computer to play for interest but to use it more meaningfully.

• Education of Primary School Mathematics
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• v.14 no.2
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• pp.135-145
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• 2011

When mathematicians solve the new problems, they present the solutions to their colleagues for getting the approval. If the solution is accepted, it will be theorems. This phenomenon also happens to classrooms in elementary and secondary school. That is main reason to emphasize mathematical communication activities in mathematics education. This study is aimed to develop teaching and learning model for the improvement of mathematical communication ability, applicate the teaching and learning model to two groups and analyze for mathematical thoughts. This study is a case study of 3rd grader's activities. Eight students, four are group applied the teaching and learning model and four are traditional group. The results have been drawn as follows: First, students in the teaching and learning model group induced richer interactions for student's understanding and investigation when we compare to those of traditional group. Second, students in the teaching and learning model group have the chance to explain their thoughts. And we can observe students to clear on their thought through speaking and discussing. This model makes students to enhance organizing, forming and clearing in their mathematical thoughts and is effective to estimate of students thought for teacher.