• Journal of Elementary Mathematics Education in Korea
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• v.10 no.2
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• pp.151-169
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• 2006

This study is to adjust the Theory in the Mathematics Education, apply it to learning mathematics and to analyse its effectiveness. The results of the study are summarized as follows. First, because learning mathematics is hierarchical, teachers must make and use a task analysis table classified by units. Second, development age and the retention of mathematics concepts are intimately associated with cognitive development theory. Third, learning mathematics through cognitive processes enhances a student's scholastic achievement. Fourth, students interests and self-confidence can be enhanced through the presentation of both examples and non-examples. We cannot understand the higher-order concepts of mathematics by only its definitions. The only way of understanding such concepts is to have experience through suitable examples.

• Communications of Mathematical Education
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• v.13 no.1
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• pp.381-408
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• 2002

본 논문에서는 테크놀로지를 활용해 본인이 직접 조작하고 시각화 할 수 있는 환경에서 함수와 그래프, 그를 이용한 문제해결에서 학생들이 수학적 개념 발달을 통해 어떠한 언어적 상호작용이 일어나는가에 관해 조사하고자 한다. 또한 이때 나타나는 언어적 상호작용을 분석하기 위한 분류 틀을 개발하여 언어적 상호작용의 양상을 밝히며, 컴퓨터가 학생들의 의사소통에 어떠한 역할을 하는가를 알아봄으로써 학생의 인지 발달은 어떻게 이루어지는 가를 파악하여 현장 수업에 기여하고자 한다.

• Communications of Mathematical Education
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• v.18 no.1 s.18
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• pp.211-222
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• 2004

신체적 체험은 인간의 사고를 형성하는 바탕이 된다. 문제해결 경험은 인간 사고를 한층 더 발전시킨다. 특히 사물의 형태와 움직임을 관찰하고, 그러한 환경에 감각-운동 신경을 발달시키는 체험에서 획득된 개념들은 추상적 사고에서 중심적 역할을 한다는 언어심리학의 가설이 흥미롭게 제기되어 연구되어 오고 있다. 개념체계로서 수학, 언어로서 수학, 의미 만들기로서 수학 , 문제 해결로서 수학 등 수학학습과 관련된 수학의 여러 모습에 대한 새로운 시각을 갖게 한다. Lakoff와 Johnson는 신체적 체험이 가져온 이러한 개념체계들 '메타포'라고 부른다. 메타포의 '개념' 수준으로의 확장은 analogy의 의미를 확장시켰다. 수학학습에 신체적 체험으로 존재하는 개념들은 수학적 개념에 이르는 학습을 새롭게 보게 한다. 본 연구는 metaphor와 analogy의 인지과학 및 언어과학에서 연구되고 있는 일반적 의미들을 제시하고 수학학습에서의 적용될 수 있는 방법들을 제시한다.

• Journal of Music and Human Behavior
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• v.7 no.1
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• pp.1-15
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• 2010

The purpose of this study is to inquire into the theoretical background of music therapy interventions for the improvement of mathematical concepts among young children with special needs. The researcher provides a basis of theoretical background about musical activities as an effective tool for young children to understand and promote their mathematical concepts, and the necessity of practical application in the field of mathematics education is suggested. Music, as a multi-sensory modality, has an ability to hold and maintain one's attention, and can be used as a memory aid and a powerful and effective motivator and reinforcer for young children. Therefore, musical activities can be used to facilitate mathematical concepts in the field of education for young children. Possible musical activities for promoting mathematical development are suggested, and the necessity for developing various musical activities is discussed.

• Journal of The Korean Association of Information Education
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• v.18 no.4
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• pp.559-566
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• 2014

This is to understand the neurological dynamic cognitive processes of math learning based on the abstract mappings( level A2), abstract systems(level A3), and single principles(level A4), which are principles of Fischer's cognitive development theory. Math learning requires flexibility to adapt existing brain function in selecting new neurophysiological activities to learn desired knowledge. This study suggests a general statistical framework for the identification of neurological patterns in different abstract learning change with optimal support. We expected that functional brain networks derived from a simple math learning would change dynamically during the supportive learning associated with different abstract levels. Task based patterns of the brain structure and function on representations of underlying connectivity suggests the possible prediction for the success of the supportive learning.

• 한국정보교육학회:학술대회논문집
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• 2004.08a
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• pp.272-280
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• 2004

전통적인 수학교육은 간단한 수학적 사실을 이해하고 활용하는 측면에 있어서는 효과적일 수도 있지만, 수학적 개념, 원리, 법칙을 학생 스스로 탐구, 발견하고 창조하는 능력을 기르는 데는 적절하지 않다. 이러한 능력을 기르기 위해서는 학생들 스스로가 관찰, 조작, 분석, 종합하는 활동을 강화할 필요가 있다. 구체적 조작물을 학습도구로 활용하는 경우, 수학 학습에 대한 흥미와 자신감을 길러 주고, 자신의 수준에 맞는 내용을 자기 주도적 학습을 통하여 성취감을 가지게 하며, 학생 스스로 탐구 활동을 활발히 하는데 도움이 된다. 삶의 질이 급격히 향상되는 정보사회에서는 사이버 공간의 등장으로 공간감각 기능의 필요성이 더욱 절실한 바, 현행 수학교과서에서 제공되는 각종 공간 도형들은 3차원 공간에서 이루어지지 않고 평면도형으로 처리함으로써 아동의 도형인지 능력 향상에 큰 효과를 기대하기 어렵다. 이에 본 연구에서는 아동의 인지발달 단계를 고려, 도형인지능력 향상을 위한 선 및 점대칭 관련 동기유발, 선수, 기본, 보충, 심화, 평가, 도움말 관련 프로그램을 개발, 적용한 결과 학습자의 동기가 유발되고, 도형 인지능력 향상에 유의미한 결과를 얻었다.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.3
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• pp.387-408
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• 2015

The purpose of this research is to analyze the mathematical tasks of length measurement in two different perspectives, the level of cognitive demands and learning trajectories, and restructure the mathematical tasks so that the students' conceptual learning is promoted and students are able to have opportunities to think more broadly. Ten lessons with the restructured mathematical tasks were implemented for a class of 2nd grade elementary students. Also a qualitative and in-depth study was conducted with 4 students of the target group. The study shows that firstly, the restructured tasks requiring high level of cognitive skills, had positive effects in increasing the students' level of thinking and reasoning. Secondly, the tasks modified according to the learning trajectories of Szilag, Clements & Sarama(2013) in length measurement, have proven to promote students' concept learning and elaborate the students' level of thinking.

• Communications of Mathematical Education
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• v.24 no.4
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• pp.891-907
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• 2010

This study analyzed the Fundamental Theorem of Calculus from the historical, mathematical, and instructional perspectives. Based on the in-depth analysis, this study suggested an alternative way of teaching the Fundamental Theorem of Calculus.

• Education of Primary School Mathematics
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• v.26 no.4
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• pp.317-332
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• 2023

Mathematical modeling activities hold the potential for diverse applications, involving the transformation of real-life situations into mathematical models to facilitate problem-solving. In order to assess the cognitive, affective, and social dimensions of students' engagement in mathematical modeling activities, this study conducted sessions with ten groups of fifth-grade elementary school students. The ensuing processes and outcomes were thoroughly analyzed. As a result, each group effectively applied mathematical concepts and principles in creating mathematical models and gathering essential information to address real-world tasks. This led to notable shifts in interest, enhanced mathematical proficiency, and altered attitudes towards mathematics, all while promoting increased collaboration and communication among group members. Based on these analytical findings, the study offers valuable pedagogical insights and practical guidance for effectively implementing mathematical modeling activities.

• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.727-745
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• 2017

This study investigated the Aristotle's continuity and the historical development of continuity of function to explore the differences between the concepts of mathematics and students' thinking about continuity of functions. Aristotle, who sought the essence of continuity, characterized continuity as an 'indivisible unit as a whole.' Before the nineteenth century, mathematicians considered the continuity of functions based on space, and after the arithmetization of nineteenth century modern ${\epsilon}-{\delta}$ definition appeared. Some scholars thought the process was revolutionary. Students tended to think of the continuity of functions similar to that of Aristotle and mathematicians before the arithmetization, and it is inappropriate to regard students' conceptions simply as errors. This study on the continuity of functions examined that some conceptions which have been perceived as misconceptions of students could be viewed as paradigmatic thoughts rather than as errors.