• Communications of Mathematical Education
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• v.16
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• pp.245-267
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• 2003

수학적 문제 해결은 수학 교육에서 중요한 이슈이고 문제 해결 전략으로서의 유추를 주제로 본 연구에서는 중학생들을 대상으로 단순히 유사한 문제를 제시하는 것만으로 문제 해결에 성공을 할 수 있는지, 문제 해결에 성공을 할 수 없다면 중학생들에게 어떤 과정을 제시해야만 문제 해결 과정에서 유추를 사용하여 문제를 해결 할 수 있는지를 알아보고자 한다. 이를 위하여 본 연구에서는 유추에 의한 문제 해결과정을 표상 형성, 인출, 사상, 적합성, 스키마 형성의 과정으로 보고, 이러한 과정 중 사상 단계에서 사상 과정의 명료화를 중심으로 학생들의 유추 추론에 의한 문제해결 과정을 탐구하였다. 연구 결과, 유추 추론 과정에서 근거 문제만을 제시하는 것은 목표 문제를 해결하는데 유추 추론의 성공을 보장한다고 할 수 없었으며, 근거 문제가 제시되었는데도 목표 문제를 해결하지 못하는 경우 사상 과정을 명료화하자 목표 문제를 성공적으로 해결하였다. 또한 학생들은 목표 문제의 성공 이후 유사한 새로운 목표문제를 푸는데 성공하였다.

• Journal of the Korean Geographical Society
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• v.46 no.4
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• pp.534-553
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• 2011

Analogical thinking is a problem-solving strategy to use a familiar problem (or base analog) to solve a novel problem of the same type (the target problem). The purpose of this study is to provide new insight into geography teaching and learning by connecting cognitive science research on analogical thinking with issues of geography education and suggest that teaching with analogies can be a productive instructional strategy for geography. In this study, using the various examples of analogical thinking used in geography we defined analogical thinking, addressed the theoretical models on analogical transfer, and discussed conditions that make an effective analogical transfer. The major research findings include the following: a) the spatial analogy, indicating skills to find places that may be far apart but have similar locations, and therefore have other similar conditions and/or connections, can provide a useful way to design contents for place learning; b) representational transfer, specifying a common representation for two problems, can play a key role in solving geographic problems requiring data visualization and spatialization processes; and c) either asking learners to compare/analyze similar examples sharing common structure or providing them examples bridging the gap between concrete, real-life phenomena and the ideas and models can contribute to learning in geographic concepts and skills. The spatial analogy requiring both geographic content knowledge and visual/spatial thinking has the potential to become a content-specific problem-solving strategy. We ended with recommendations for future research on analogy that is important in geography education.

• Journal of the Korean School Mathematics Society
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• v.15 no.3
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• pp.535-563
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• 2012

This study was conducted to confirm the necessity of analogical thinking and to empirically verify the effectiveness of analogical reasoning through the visual representation by analyzing the factors of problem solving depending on analogical conditions. Four conditions (a visual representation mapping condition, a conceptual mapping condition, a retrieval hint condition and no hint condition) were set up for the above purpose and 80 twelfth-grade students from C high-School in Cheong-Ju, Chung-Buk participated in the present study as subjects. They solved the same mathematical problem about sequence of complex numbers in their differed process requirements for analogical transfer. The problem solving rates for each condition were analyzed by Chi-square analysis using SPSS 12.0 program. The results of this study indicate that retrieval of base knowledge is restricted when participants do not use analogy intentionally in problem solving and the mapping of the base and target concepts through the visual representation would be closely related to successful analogical transfer. As the results of this study offer, analogical thinking is necessary while solving mathematical problems and it supports empirically the conclusion that recognition of the relational similarity between base and target concepts by the aid of visual representation is closely associated with successful problem solving.

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.51-67
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• 2017

Analogical reasoning is a mathematically useful way of thinking. By analogy reasoning, students can improve problem solving, inductive reasoning, heuristic methods and creativity. The purpose of this study is to analyze the analogical reasoning of preservice mathematics teachers while constructing quadratic curves defined by eccentricity. To do this, we produced tasks and 28 preservice mathematics teachers solved. The result findings are as follows. First, students could not solve a target problem because of the absence of the mathematical knowledge of the base problem. Second, although student could solve a base problem, students could not solve a target problem because of the absence of the mathematical knowledge of the target problem which corresponded the mathematical knowledge of the base problem. Third, the various solutions of the base problem helped the students solve the target problem. Fourth, students used an algebraic method to construct a quadratic curve. Fifth, the analysis method and potential similarity helped the students solve the target problem.

• Education of Primary School Mathematics
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• v.15 no.2
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• pp.59-75
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• 2012

This study aims to find whether the solutions for well-structured problems learned in school can be transferred to the moderately-structured problem and ill-structured problem. For these purpose, research questions were set up as follows: First, what are the patterns of changes in strategies used in solving the mathematics problems with different level of structuredness? Second, From the group using and not using proportion algorithm strategy in solving moderately-structured problem and ill-structured problem, what features were observed when they were solving that problems? Followings are the findings from this study. First, for the lower level of structuredness, the frequency of using multiplicative strategy was increased and frequency of proportion algorithm strategy use was decreased. Second, the students who used multiplicative strategies and proportion algorithm strategies to solve structured and ill-structured problems exhibited qualitative differences in the degree of understanding concept of ratio and proportion. This study has an important meaning in that it provided new direction for transfer and analogical problem solving study in mathematics education.

• Education of Primary School Mathematics
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• v.17 no.1
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• pp.1-16
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• 2014

The purpose of this study is to analyze whether analogy distance and mathematical knowledge affect on transfer problems solving with different analogy distance. To conduct the study, transfer problems were classified into multiple categories: mathematical word problem based on rates, science word problem based on rates, and real-life problem based on rates with different analogy distance. Then analysed there are differences in participants' transfer ability and which mathematical knowledge contributes to the solution on over the three transfer problem. The study demonstrated a statistical significant difference(.05) in participants' three transfer problem solving and a gradual decrease of the participants' success rates of on transfer problems solving. Moreover, conceptual knowledge influenced transfer problem solving more than factual knowledge about rates. The study has an important implications in that it provided new direction for study about transfer of learning, and also show a good mathematics instruction on where teachers will put the focus in mathematical lesson to foster elementary students' transfer ability.

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.103-124
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• 2014

The process of analogical reasoning can be conventionally summarized in five steps : Representation, Access, Mapping, Adaptation, Learning. The purpose of this study is to develop more detailed model for reason of analogies considering the distinct characteristics of the mathematical education based on the process of analogical reasoning which is already established. Ultimately, This model is designed to facilitate students to use analogical reasoning more productively. The process of developing model is divided into three steps. The frist step is to draft a hypothetical model by looking into historical example of Leonhard Euler(1707-1783), who was the great mathematician of any age and discovered mathematical knowledge through analogical reasoning. The second step is to modify and complement the model to reflect the characteristics of students' thinking response that proves and links analogically between the law of cosines and the Pythagorean theorem. The third and final step is to draw pedagogical implications from the analysis of the result of an experiment.

• The Journal of Korean Association of Computer Education
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• v.16 no.2
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• pp.9-18
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• 2013

In secondary education, learning a computer science subject has the purpose to improve creative problem solving ability of students by learning computational thinking and principles. In particular, learning algorithm has been emphasized for this purpose. There are studies that learning algorithm has the effect of creative problem solving based on the leading studies that learning algorithm has the effect of problem solving. However, relatively the importance of the learning algorithm can weaken, because these studies depend on creative problem solving model or special contents for creativity. So this study proves that learning algorithm has the effect of creative problem solving in the view that common problem solving and creative problem solving have the same process. For this, analogical reasoning was selected among common thinking skills and divide-and-conquer algorithm was selected among abstractive principles for analogical reasoning in sorting algorithm. The frequency which solves the search problem by using the binary search algorithm was higher than the control group learning only sequence of sorting algorithm about the experimental group learning divide-and-conquer algorithm. This result means that learning algorithm including abstractive principle like divide-and-conquer has the effect of creative problem solving by analogical reasoning.

• Korean Journal of Child Studies
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• v.23 no.5
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• pp.1-17
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• 2002

The influence on children's analogical problem solving of structural highlighting during encoding and retrieval of sources was studied with 379 9-year-old participants. Performance on the first 2 of 4 tests determined the analogical level of each child. For the remaining 2 tests, the child was assigned to 1 of 12 different structural highlighting conditions, including 4 encoding conditions (reading, line, self-line, and self-explain) and 3 retrieval conditions (reminding, cued, and thematic comparison). Results showed that retrieval conditions, not encoding conditions, improved the analogical ability of the child. Children initially low in analogical ability improved in cued retrieval conditions; children initially high in analogical ability improved both in thematically compared and in cued retrieval conditions. Practical implications of the results were discussed.

• Proceedings of the Korean Information Science Society Conference
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• 2003.10a
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• pp.70-72
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• 2003

주어진 현재의 문제를 해결하기 위해서 과거에 유사하게 수행된 사례를 유추하여 유추된 사례의 해를 이용하는 사례 기반 추론(case-base reasoning)은 털러 분야에 응용되고 있지만, 사례기반 추론 시 새로운 사례를 해결하기 위하여 사례베이스 내의 모든 사례를 검색해야 하기 때문에 수행시간이 증가되는 단정을 지니고 있다. 본 연구에서는 하드 클러스터링 방법으로 완전하게 분류하는 것이 불가능할 수도 있다는 문제점을 개선시키기 위하여 퍼지 클러스터링을 방법을 이용하여 사례베이스를 분류함에 의하여 시스템의 수행시간을 감소시키면서 정확성을 높이게 되었다.