• Communications of Mathematical Education
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• v.27 no.3
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• pp.221-248
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• 2013

Among five types of the model textbook based on storytelling, the type of 'Inquiry into history of Mathematics' focuses on adapting the logic of mathematical discovery to the organization of mathematical contents. It enables students to recognize that mathematics has been developed by human needs and creativity while they are engaged in the story about knowledge formation. Moreover the textbook offers the context in which students are able to understand mathematical insights and logics hidden in the subject matter, so that they can reinvent and develop mathematical knowledge. In this study, we found the principles for development of the textbook based on storytelling for 'Inquiry into History of Mathematics' by analyzing the chapter about 'Complex number and Quadratic Equations' of the model textbook. The chapter was implemented in classroom environment and students' understanding of the subject matter and their perception on the textbook based on storytelling were surveyed before and after the implementation. The results showed the possibilities of adapting the textbook based on storytelling and we suggested some implications for further development.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.611-626
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• 2010

The purpose of this study is to explore the composite properties of linear functions using CAS calculators. The meaning and processes in which technological tools such as CAS calculators generated to instrument are reviewed. Other theoretical topic is the design of an exploring model of observing-conjecturing-reasoning and proving using CAS on experimental mathematics. Based on these background, the researchers analyzed the properties of the family of composite functions of linear functions. From analysis, instrumental capacity of CAS such as graphing, table generation and symbolic manipulation is a meaningful tool for this exploration. The result of this study identified that CAS as a mediator of mathematical activity takes part of major role of changing new ways of teaching and learning school mathematics.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.1
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• pp.63-81
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• 2014

Korean students have shown high achievements on the cognitive domain of mathematics in a range of international assessment tests. On the affective domain, however, significantly low achievements have been reported. Among the factors in the affective domain, this article discusses on the value of mathematics in the perspective of Michael Polanyi's philosophy, which centers personal knowledge and tacit knowing. Polanyi emphasizes abstractness and generalization in mathematics accompanied by intellectual beauty and passion. In his perspective, therefore, utilitarian aspects and usefulness of mathematics imparted through linguistic representations have limits in motivating students to learn mathematics. Students must be motivated from recognition of the value of mathematics formed through participating authentic mathematical problem solving activity with immersion, tension, confusion, passion, joy and the like.

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.113-135
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• 2017

The purpose of the research was to develop an analysis framework for Korean mathematics textbooks from a critical mathematics education perspective. For this, we conducted a comprehensive literature review regarding critical theory, critical education, and critical mathematics education. Based on the literature review, we derived a preliminary framework for textbook analysis. To validate the preliminary framework delphi survey was carried out twice with 21 expert panelists in the field of mathematics education and multicultural education. The first delphi survey was conducted with open-ended questions to investigate diverse opinions regarding educational goals, contents, and teaching methods of critical mathematics education. The second delphi survey was conducted with Likert-type scale and it was analyzed using Mean, Contents Validity Ratio, Degree of Consensus. As the result of the whole research procedures, the final analysis framework was developed consisting of four categories: classical knowledge, community knowledge, communicative knowledge, and political knowledge. A development of the analysis framework from a critical mathematics education perspective could give a significant impact on the mathematics curriculum or mathematic teacher education in the Korea and a meaningful initial step for the effort of practicing critical mathematics education. It is expected that this study could not only incite consideration for the better mathematics education but also expand the prospect of research and practice in mathematics education. This study would provide a new paradigm of future mathematics education with which to teach and guide students to become members of world civil society with mathematical power and critical competency.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.163-178
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• 2012

The efforts to represent the numbers based on the decimal system give us fundamental understanding to construct and teach the concept network on the related knowledge of elementary and secondary school mathematics. In the process to represent natural numbers, integers, rational numbers, real numbers as decimal system, we will classify the extended decimal system. Moreover we will obtain the view to classify real numbers. In this paper, we will study the didactical significance of mathematical knowledge, which arise from process to represent real numbers as decimal system, starting from decimal system representation of natural numbers, and provide the theoretical base about the classification of real numbers. This study help math teachers to understand school mathematics in critical inside-measurement and provide the theore tical background of related knowledge. Furthermore, this study provide a clue to construct coherent curriculum and internal connections of related mathematical knowledge.

• Proceedings of the Korean Society of Computer Information Conference
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• 2013.01a
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• pp.309-312
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• 2013

현대사회는 지식정보의 사회로서 이러한 사회에서는 지식을 단순히 암기하는 것보다 주어진 지식과 정보를 이용하여 새로운 지적 가치를 창출할 수 있는 자율적이고 창의적인 인재가 필요하다. 창의성 신장의 측면에서 볼 때, 수학은 문제 해결의 다양성, 사고의 유연성을 길러주므로 매우 중요한 과목이다. 하지만 많은 학생들이 수학의 가치와 필요성을 인식하지 못하고 흥미를 잃어가고 있다. 이에 자발적인 학습을 유도할 수 있는 PBL학습을 도입하고자 한다. 그리고 컴퓨터 프로그래밍은 수학 학습에서 학습자의 알고리즘적 사고력을 향상시킨다. 따라서 본 연구자는 수학 흥미도를 향상시키기 위해 스크래치를 활용한 PBL기반의 수학 학습 컨텐츠 개발을 제안한다.

• School Mathematics
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• v.17 no.4
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• pp.613-632
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• 2015

In this study, we hope to reveal teacher knowledge necessary to address student errors and difficulties about ratio and rate. The instruments and interview were administered to 3 in-service primary teachers with various education background and teaching experiments. The results of this study are as follows. Specialized content knowledge(SCK) consists of profound knowledge about ratio and rate beyond multiplicative comparison of two quantities and professional knowledge about the definitions of textbook. Knowledge of content and students(KCS) is the ability to recognize students' understanding the concept and the representation about ratio and rate. Knowledge of content and teaching(KCT) is made up of knowledge about various context and visual models for understanding ratio and rate.

• 한국정보교육학회:학술대회논문집
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• 2008.01a
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• pp.198-205
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• 2008

오늘날과 같은 지식 정보화 사회는 지식과 정보를 기초로 한 사회활동이 주를 이루고 있다. 그래서 교육현장에서도 학습자는 컴퓨터를 이용하여 정보를 수집하고 처리하는 정보의 주체로 인식되어지고 있다. 특히 수학 교과 내용 중 도형 영역은 컴퓨터를 이용하여 다양한 시각적 경험과 탐구 기회를 제공하는 것이 매우 중요하다. 이를 실현하기 위한 방법으로써 여러 가지 방법이 있지만, 본 논문에서는 Sketchup이라는 상용 소프트웨어를 활용하여 도형 영역에 적용시켜 활용하는 방안에 대해 연구하였다. 학생들이 수학을 재미있고 쉽게 생각할 수 있는 방안을 내세우기란 쉽지 않지만, 이 연구의 결과로부터 수학과목의 도형영역에 대한 수학적 사고력과 성취도를 높이고 Sketchup과 같은 탐구형 소프트웨어의 효과적 활용 방안을 마련하고, 이를 통해 수학에 대한 긍정적인 인식을 마련할 수 있는 기틀이 되고자 한다.

• Journal of Gifted/Talented Education
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• v.25 no.4
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• pp.581-605
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• 2015

The purpose of this study is to build an instruction method focused on the mathematical process and apply it to 12, 5-year-olds from Kindergarten located in Seoul with a view to explore the changes in their mathematical thinking. In addition, surveys with parents and teachers, as well as those conducted in the field of early childhood education, were conducted to analyze the current situation. The effects focused on the five mathematical processes, namely problem solving, reasoning and proof, connecting, representing and communication was found to help the interactions between teacher-child and child-child stimulate the mathematical thinking of the children and induce changes. The mathematical process-focused instruction aimed to advance mathematical thinking internalized mathematical knowledge, presented an integrated problematic situation, and empathized the mathematical process, which enabled the children to solve the problem by working together with peers. As such, the mathematical thinking of the children was integrated and developed within the process of a positive change in the mathematical attitude in which mathematical knowledge is internalized through mathematical process.

• The Mathematical Education
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• v.47 no.1
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• pp.91-106
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• 2008

Interviews with 24 pupils in grade 1-2 were used to investigate awareness of the relation between situation and computation in simple quotitive and partitive division problems as informally experienced. Then it was suggested how to connect children's informal knowledge and formal knowledge of division. Most subjects counted cubes or made drawing, and related these methods to the situation described in the problems. In result, quotitive division was experienced as a dealing situation, where the number of items represented by the divisor was repeatedly taken from the whole number. And estimate-adjust was the most frequently displayed way of experiencing partitive division. Therefore, partitive division with its two measurement variables can be related to a measurement model. And children should be taught column algorithms for division with estimated-adjust which pupils used for partitive division problems.