• 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.

• Korean Institute of Interior Design Journal
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• no.41
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• pp.266-274
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• 2003

Synectics is one of several techniques used to enhance brainstorming by taking a more active role and introducing metaphor and structure into the process. It is unclear at what level of specificity this should be formulated as a pattern. This thesis reviews recent computational as well as experimental work on analogical reasoning based on synectics. New results regarding information processing of analogical reasoning stages, major computational models and recent attempts to compare these models are reviewed. Computational models are also discussed in the computational as well as cognitive psychology perspectives. Future directions in analogical reasoning research are proposed. The following import is the need to accommodate the typology and normal assessment in the concrete circumstances where actual reasoning and problem solving take place. In order to get to this end, we used computational models by Thagard who take the stand of ‘Computational Philosophy of Science’, which assumes ‘Weak AI’ to explicate what constitute the very pecularity of Analogical Reasoning.

• Journal of Korean Elementary Science Education
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• v.34 no.4
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• pp.419-433
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• 2015

Analogical reasoning is a central component of human cognition and contributes to scientific discovery and to develop science education. In this study, we investigated the process features of lower elementary school students' analogical reasoning to explain mixture concept. The subjects are 24 lower elementary students. And the research design includes three phases instruction to investigate the features of students' self generated analogy. Phase 1 is the introduction of analogy in which student learn to use analogy. Phase 2 is a POE class about mixture conception. Piaget and Inhelder studied the conception of mixing among children in relation to cognitive development. In phase 2, we taught the student with Piaget and Inhelder's the experiment and observed the features of learning process about mixture conception. Phase 3 is students' generation of analogy (self generated analogy) for the experienced phenomena in phase 2. We analyzed the students' responses through the three phases in the view of Gentner's Structure Mapping Theory. The results showed that many lower elementary school students even before formal operation stage understood the mixture conception and made well their self generated analogy to explain the mixture conception in spite of the difficulty of making self generated analogy.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.45-61
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• 2009

The powerful role of analogical reasoning in discovering mathematics is well substantiated in the history of mathematics. Mathematically gifted students, thus, are encouraged to learn via in-depth exploration on their own based on analogical reasoning. In this study, 57 gifted students (31in the 7th and 26 8th grade) were asked to formulate or clarify analogy. Students produced fruitful constructs led by analogical reasoning. Participants in this study appeared to experience the deep thinking that is necessary to solve problems made with analogies, a process equivalent to the one that mathematicians undertake. The subjects had to reflect on prior knowledge and develop new concepts such as an orthogonal projection and a point of intersection of perpendicular lines based on analogical reasoning. All subjects were found adept at making meaningful analogues of a triangle since they all made use of meta-cognition when searching relations for analogies. In the future, methodologies including the development of tasks and teaching settings, measures to evaluate the depth of mathematic exploration through analogy, and research on how to promote education related to analogy for gifted students will enhance gifted student mathematics education.

• Journal of Gifted/Talented Education
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• v.23 no.5
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• pp.817-833
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• 2013

The study aims to analyze Thomas Young's problem solving processes of analogical reasoning during the formation of the interference theory of light, and to draw its implications for secondary science education, particularly for enhancing creativity in science. The research method employed in the study was literature review of the papers which Young himself had written about sound wave and property of light. His thinking processes and specific features in his thought that were obtained through analysis of his papers about light are as follows: Young reconsidered Newton's experiments and observations, and reinterpreted Newton's results in the new viewpoints. Through this analysis, Young discovered that Newton's interpretation about his own experiments and observations was faulty in a certain point of view and new interpretation is necessary. Based on the data, it is hypothesized that colors observed on thin plates and colors appeared repeatedly on Newton's ring are appeared because of the effect of light interference. Young used analogical reasoning during the process of inference of similarity between sound and light. And he formulated an hypothesis on the interference of light through using abductive reasoning from interference of water wave, and proved the hypothesis by constructing an creative experimental device, which is called a critical experiment. It is implicated that the analogical reasoning and experimental devices for explaining the light interference which Young created and used can be utilized for school science education enhancing creativity in science.

• 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.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.927-941
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• 2013

In this paper, we investigate and analysis high school students' generalization of cosine rule using analogy, and we study teaching and learning methods improving students' analogical thinking ability to improve mathematical thinking process. When students can reproduce what they have learned through inductive reasoning process or analogical thinking process and when they can justify their own mathematical knowledge through logical inference or deductive reasoning process, they can truly internalize what they learn and have an ability to use it in various situations.

• Journal of The Korean Association For Science Education
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• v.17 no.3
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• pp.323-332
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• 1997

In order to use analog more systematically in science class, an instructional model was designed on the basis of analogical reasoning processes (encoding, inference, mapping, application, and response) in the Sternberg's component process theory. The model has five phases (introducing target context, cue retrieval of analog context, mapping similarity and drawing target concept, application, and elaboration), and the instructional effects of using the model upon students' comprehension of science concepts and motivation level of learning were investigated. The treatment and control groups (1 class each) were selected from 8th-grade classes and taught about chemical change and chemical reaction for the period of 10 class hours. The treatment group was taught with the materials based on the model, while the control group was taught in traditional instruction without using analog. Before the instructions, modified versions of the Patterns of Adaptive Learning Survey and the Group Assessment of Logical Thinking were administered, and their scores were used as covariates for students' conceptions and motivational level of learning, respectively. Analogical reasoning ability test was also administered, and its score was used as a blocking variable. After the instructions, students' conceptions were measured by a researcher-made science conception test, and their motivational level of learning was measured by a modified version of the Instructional Materials Motivation Scale. The results indicated that the adjusted mean score of the conception test for the treatment group was significantly higher than that of the control group at .01 level of significance. No significant interaction between the instruction and the analogical reasoning ability was found. Although the motivational level of learning for the treatment group was higher than that for the control group, the difference was found to be statistically insignificant. Educational implications are discussed.

• 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.

• Korean Journal of Cognitive Science
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• v.17 no.1
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• pp.53-74
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• 2006

Similarity has been considered as one of basic concepts of cognitive psychology which is useful for explaining cognitive structure and process. MDS models(Shepard, 1964; Nosofsky, 1991) and Contrast model(Tversky, 1977) were proposed as early models of similarity comparison process. But, there have been a lot of theoretical doubts about the conceptual validity of similarity as a result of empirical findings which could not be explained by early models. Goldstone(1994) assumed that similarity could be defined by alignment processes, and suggested structural alignment as a prospective alternative for solving conceptual controversies so far. In this study, basic assumption and algorithms of MDS models(Shepard, 1944; Nosofsky, 1991) and Contrast model(Tversky, 1977) were described shortly and some theoretical limitations such as arbitrariness of selective attention and correlated structures were discussed as well. The conceptual characteristics and algorithms of SIAM(Goldstone, 1994) were described and how it has been applied to cognitive psychology areas such as categorization, conceptual combination, and analogical reasoning were reviewed. Finally, some theoretical limitations related with data-driven processing and alternative processing and possible directions for structural alignment were discussed.