• Journal of Educational Research in Mathematics
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• v.20 no.1
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• pp.57-71
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• 2010

Similarity between concept and concept, principle and principle, theory and theory is known as a strong motivation to mathematical knowledge construction. Metaphor and analogy are reasoning skills based on similarity. These two reasoning skills have been introduced as useful not only for mathematicians but also for students to make meaningful conjectures, by which mathematical knowledge is constructed. However, there has been lack of researches connecting the two reasoning skills. In particular, no research focused on the interplay between the two in didactic transposition. This study investigated the process of knowledge construction by metaphor and analogy and their roles in didactic transposition. In conclusion, three kinds of models using metaphor and analogy in didactic transposition were elaborated.

• Journal of the Korean School Mathematics Society
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• v.17 no.2
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• pp.291-319
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• 2014

The purpose of this study is to investigate students' thinking and understanding through working on Worked-out Examples on numbers and operations, specifically, radical and real numbers and operations in the middle grades. For this purpose, we developed a set of Worked-out Examples; middle school students independently worked on them. Then two students were interviewed. These data were analyzed by using the framework of mathematical proficiency. The data analysis suggested that the students seemed to go through the processes involving a combination of understanding and computation, computation and reasoning, and understanding, computation and reasoning. Also, it appeared that most of the students have difficult solving problems involving with radical and real numbers in related to strategic competence.

• School Mathematics
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• v.18 no.1
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• pp.43-59
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• 2016

The purpose of this qualitative case study is to investigate differences among two gifted middle school students emerging through the process of algebra word problem solving from the covariational perspective. We collected the data from four middle school students participating in the mentorship program for gifted students of mathematics and found out differences between Junghee and Donghee in solving problems involving varying rates of change. This study focuses on their actions to solve and to generalize the problems situations involving constant and varying rates of change. The results indicate that their covariational reasoning played a significant role in their algebra word problem solving.

• Journal of the Korean School Mathematics Society
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• v.10 no.1
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• pp.91-111
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• 2007

This study investigated how high school students predict the rule, the sum of sequence for the concept of sequence, for the given patterns based on inductive approach using computers that provide dynamic functions and materials that are visual. Students for themselves were able to induce the formula without using the given formula in the textbook. Furthermore, this study examined how these technology and materials affect students' understanding of the concept of actual infinity for those who have the concept of the potential infinity which is the misconception of infinity in a infinity series. This study shows that students made a progress from the concept of potential infinity to that of actual infinity with technology and materials used I this study. Students also became interested in the use of computer and the visualized materials, further there was a change in their attitude toward mathematics.

• Journal of Educational Research in Mathematics
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• v.24 no.1
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• pp.1-27
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• 2014

In the present study, we analyze the four participating 9th grade students' mathematical reasoning processes in their dragging activities while solving open-ended geometry problems in terms of abduction, induction and deduction. The results of the analysis are as follows. First, the students utilized 'abduction' to adopt their hypotheses, 'induction' to generalize them by examining various cases and 'deduction' to provide warrants for the hypotheses. Secondly, in the abduction process, 'wandering dragging' and 'guided dragging' seemed to help the students formulate their hypotheses, and in the induction process, 'dragging test' was mainly used to confirm the hypotheses. Despite of the emerging mathematical reasoning via their dragging activities, several difficulties were identified in their solving processes such as misunderstanding shapes as fixed figures, not easily recognizing the concept of dependency or path, not smoothly proceeding from probabilistic reasoning to deduction, and trapping into circular logic.

• Proceedings of the Korean Society of Computer Information Conference
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• 2016.01a
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• pp.71-72
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• 2016

베이지안 알고리즘은 추론 분야에서 오랜 기간 사용되어 왔다. 하지만 기본적인 베이지안 네트워크 이론만으로는 다양한 도메인에 적합한 추론 기능을 제공할 수 없기 때문에, 도메인의 특성에 맞는 알고리즘이 적용된 다양한 추론 기법들이 연구되어왔다. 본 논문에서는 실시간 지능화 서비스를 위하여 특정 도메인 영역에 대하여 자동으로 적합한 베이지안 네트워크 알고리즘을 선별하는 기법을 제안한며, 해당 기법의 적합도를 평가하기 위해서 수학적인 모델링과 추론 알고리즘 선택 기법에 대해 서술한다.

• Communications of Mathematical Education
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• v.17
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• pp.97-114
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• 2003

일선 교육 현장에서 영재를 지도함에 있어서 해결해야 할 당면 과제는 판별 도구와 학습 프로그램의 개발이다. 영재를 위한 수학 프로그램을 문제 해결형, 수학 탐구형, 과제 해결형의 3가지로 분류할 경우, 퍼즐은 문제 해결형과 수학 탐구형 프로그램의 특성을 공통적으로 갖고 있는 유형으로 수학적 지식의 통합과 연결성. 그리고 창의적 문제 해결력 신장 및 수학적 원리 ${\cdot}$ 법칙을 체험적으로 만들 수 있는 기회를 제공한다는 점에서 매우 가치있는 프로그램이다. 특히 조작퍼즐은 기존의 대수적 표현 체계로 학습하기가 힘든 관찰력이나 공간에 대한 인식과 표현력 친 공간 추론력을 기르는 데 유용하며, 게임적인 요소가 포함된 퍼즐은 지필에 의존해 왔던 수학학습에 대한 부정적인 인식을 해소하는 데 크게 기여할 것이다. 본 고에서는 수학 퍼즐의 종류 및 특성과 교육적 가치에 대해서 개괄적으로 살펴보고, 실제 프로그램 작성을 위한 정보를 제공과 영재들의 공감 감각을 기르기 위한 프로그램의 원을 이용한 수학 퍼즐의 개요를 제시한다.

• School Mathematics
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• v.12 no.4
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• pp.563-584
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• 2010

This study is aimed at analysing the mathematical thinking processes based on image by the mathematically gifted. For this, the 'Splitting a Tetrahedron' Task was used and mathematical thinking of the two middle school students were investigated. One of them deduced how many tetrahedral and octahedral were there when a tetrahedra was splitted by the surfaces which were parallel to each face of the tetrahedra without using any physical material. The other one solved the task using physical material and invented new images. A concrete image, indexical image and symbolic image were founded and the various roles of images could be confirmed.

• Journal of the Korean School Mathematics Society
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• v.15 no.3
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• pp.565-584
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• 2012

This study investigates how the GSP helps gifted and talented students understand geometric principles and concepts during the inquiry process in the generalization of the internal triangle, and how the students logically proceeded to visualize the content during the process of generalization. Four mathematically gifted students were chosen for the study. They investigated the pattern between the area of the original triangle and the area of the internal triangle with the ratio of each sides on m:n respectively. Digital audio, video and written data were collected and analyzed. From the analysis the researcher found four results. First, the visualization used the GSP helps the students to understand the geometric principles and concepts intuitively. Second, the GSP helps the students to develop their inductive reasoning skills by proving the various cases. Third, the lessons used GSP increases interest in apathetic students and improves their mathematical communication and self-efficiency.

• Journal of the Korean School Mathematics Society
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• v.11 no.3
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• pp.513-541
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• 2008

The purposes of the study were to investigate whether the use of the Geometer's Sketchpad(GSP) is more effective than the use of traditional tools such as ruler and protractor to enhance eighth- grade students' understanding of quadrilaterals and geometric reasoning ability and to examine how the use of the software affects on the development of students' understanding and reasoning ability. According to the results of the posttest, there was a significant difference in student achievement between students using GSP and students using ruler and protractor. Students using GSP significantly outperformed students using ruler and protractor on the posttest. Student interview data showed that the use of the GSP was more effective in developing students' geometric reasoning ability. Students using GSP achieved higher degrees of acquisition for van Hiele level 2 and 3 than students using ruler and protractor. Dynamic visual representations and hands-on experiences provided in GSP learning environment helped students approach quadrilateral concepts more conceptually and realize their pre-existing conceptual errors and re-conceptualize their mathematical ideas.