• The Mathematical Education
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• v.49 no.2
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• pp.223-246
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• 2010

Goos(2004) introduced educational researchers' demand for change on the way that mathematics is taught in schools and the series of curriculum documents produced by the National council of Teachers of Mathematics. The documents have placed emphasis on the processes of problem solving, reasoning, and communication. In Korea, the national curriculum documents have also placed increased emphasis on mathematical activities such as reasoning and communication(1997, 2007).The purpose of this study is to analyze the impact of inquiry-oriented instruction with guided reinvention on students' mathematical activities containing communication and reasoning for science high school students. In this paper, we introduce an inquiry-oriented instruction containing Polya's plausible reasoning, Freudenthal's guided reinvention, Forman's sociocultural approach of learning, and Vygotsky's zone of proximal development. We analyze the impact of mathematical findings from inquiry-oriented instruction on students' mathematical activities containing communication and reasoning.

• Korean Journal of Logic
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• v.12 no.2
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• pp.59-88
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• 2009

According to David Hume, a deductive demonstration for inductive inference is not possible, because inductive inference is not deductive; and an inductive demonstration for inductive inference is not possible either, because such a demonstration is circular. Thus, on his view, there is no way of justifying inductive inference. Ever since Hume raised this problem of induction, a fair number of philosophers have tried to solve it. Nevertheless there is still no solution which is plausible enough to receive wide endorsement. According to Wilfrid Sellars, we cannot justify inductive inference by any theoretical reasoning; we can vindicate it only by a certain sort of practical reasoning. In this paper, I defend this Sellarsian proposal by developing and explaining it.

• Korean Journal of Cognitive Science
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• v.10 no.4
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• pp.71-83
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• 1999

Conventional symbolic inference systems lack flexibility because they do not well reflect flexible semantic structure of knowledge and use symbolic logic for their basic inference mechanism. For solving this problem. we have recently proposed the 'Connectionist Semantic Network(CSN)' as a model for flexible knowledge representation and inference based on neural networks. The CSN is capable of carrying out both approximate reasoning and commonsense reasoning based on similarity and association. However. we have difficulties in representing general and structured high-level knowledge and variable binding using the connectionist framework of the CSN. In this paper. we propose a hybrid system called SymCSN(Symbolic CSN) that combines a symbolic module for representing general and structured high-level knowledge and a connectionist module for representing and learning low-level semantic structure Simulation results show that the SymCSN is a plausible model for human-like flexible knowledge representation and inference.

• Journal of Educational Research in Mathematics
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• v.13 no.3
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• pp.365-382
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• 2003

This study intends to develope and apply mathematical activities for gifted students. According to the Polya's research and Krutetskii's study, mathematical activities were developed and observed. The activities were aimed at discovery of Euler's theorem through exploration of soccer ball at first. After the repeated application and reflection, the aim and the main activities were changed to the exploration of soccer ball itself and about related mathematical facts. All the students actively participated in the activities, proposed questions need to be proved, disproved by counter examples during the fourth program. Also observation, conjectures, inductive arguments played a prominent role.

• Journal of The Korean Association For Science Education
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• v.31 no.5
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• pp.694-708
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• 2011

In this study, we developed tasks including cognitive scaffolding for students to explain scientific phenomena using valid evidences in science classroom and sought to investigate how tasks influence the development of small group scientific argumentation. Heterogeneous small groups in gender and achievement were organized in one classroom and the tasks were applied to the class. Students were asked to write down their own ideas, share individual ideas, and then choose the most plausible opinion in a group. One group was chosen for investigating the effect of tasks on the development of small group argumentation through the analysis of discourse transcripts of the group in 10 lessons, students' semi-structured interview, field note, and students' pre- and post argument tests. The discrepant argument examples were included in the tasks for students to refute an argument presenting evidences. Moreover, comparing opinion within the group and persuading others were included in the tasks to prompt small group argumentation. As a result, students' post-argument test grades were increased than pre-test grades, and they argued involving evidences and reasoning. The high level of arguments has appeared with high ratio of advanced utterances and lengthening of reasoning chain as lessons went on. Students had elaborate claims involving valid evidences and reasoning by reflective and critical thinking while discussing about the tasks. In addition, tasks which could have various warrants based on the data led to students' spontaneous participation. Therefore, this study has significance in understanding the context of developing small group argumentation, providing information about teaching and learning context prompting students to construct arguments in science inquiry lessons in middle school.

• Journal of Educational Research in Mathematics
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• v.23 no.3
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• pp.335-351
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• 2013

This research assumes that abduction is so important as much as all the creative plausible reasoning to be based upon. We expect it to be deeply appreciated and be taught positively in school mathematics. We are noticing that every problem solving process must contain some steps of abduction and thus, we believe that those who are afraid of abduction cannot solve any newly faced problem. Upon these thoughts, we are looking into the middle school mathematics textbooks to see that how strongly various abductions are emphasized to solve problems in it. We modified types of abduction those were suggested by Eco(1983) or by Bettina Pedemonte, David Reid (2011) and investigated those books to see if, we may regard, various types of abduction be intended to be used to solve their problems. As a result of it, we found that more than 92% of the problems were not supposed to use creative abduction necessarily to solve it. And we interpret this as most authors of the textbooks have emphasis more on the capturing and understanding of basic knowledge of school mathematics rather than the creative reasoning through them. And we believe this need innovation, otherwise strong debates are necessary among the professionals of it.

• Journal of Educational Research in Mathematics
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• v.22 no.1
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• pp.101-115
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• 2012

Analogy, a plausible reasoning on the basis of similarity, is one of the thinking strategy for concept formation, problem solving, and new discovery in many disciplines. Statistics educators argue that analogy can be used as an useful thinking strategy in statistics as well. This study investigated the characteristics of students' analogical thinking in statistics. The mathematically gifted were asked to construct similar problems to a base problem which is a statistical problem having a statistical context. From the analysis of the problems, students' new problems were classified into five types on the basis of the preservation of the statistical context and that of the basic structure of the base problem. From the result, researchers provide some implications. In statistics, the problems, which failed to preserve the statistical context of base problem, have no meaning in statistics. However, the problems which preserved the statistical context can give possibilities for reconceptualization of the statistical concept even though the basic structure of the problem were changed.

• The Research Journal of the Costume Culture
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• v.19 no.4
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• pp.723-739
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• 2011

This research seeks to analyze western men's costume in the Baroque era in relation to men's physical beauty from its most detailed and interesting perspective to fomulate a plausible reasoning related to the aesthetic sense of body as expressed in men's costume. This research used national and international books, theses and internet data upon which to base a literature review for a correct understanding of Baroque style and at the same time empirical research to analyze the body image expressed in men's costume. The Baroque style expressed in the 17th century costume offered a dynamic feeling through wavy curves, and its brilliant and colorful decorations created a passionate and charming mood resembling a flame. Accordingly, this research studied the body image as it appeared in the form of 17th century western men's costume by dividing it into the contact beauty of the human body and the manner of hiding the architectural beauty of the human body. First, the exposed silhouette by clothing coming into contact with the human body could be found mainly in upper-class men's costume in the first half of the 17th century. The shorter and tighter doublets and knee breeches could be analyzed in terms of erotic imagery that emphasized masculinity, aristocratic imagery that stressed a distinctive status, and geometric imagery that expressed a triangular pattern. Second, the constructive expression by hiding the human body could be found in upper-class men's costume starting in the mid-17 century. The wearing of the justaucorps could be studied in terms of how it came into contact with the beauty of the human body but also how this clothing style the hid the architectural beauty of human body.

• Journal of Educational Research in Mathematics
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• v.19 no.4
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• pp.493-511
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• 2009

The purpose of this thesis is to discuss the characteristic methods of Mathematics Education. However, it is not simple to find the proper research method of Mathematics Education since Mathematics Education deals with the practice of teaching and learning mathematics, as well as the topics of scholarly research on the practice. Issues on Mathematics Education might vary with the epidemical aspects, which are basic attitudes toward the knowledge and understanding about Mathematics. Thus, this thesis will discuss two questions: First, What are the distinguishing characteristics of Mathematics Education as a field of study, when compared with ones of mathematics? Second, What are the characteristic methods of Mathematics Education, when compared with ones of other academic fields? For solving those questions, this thesis starts from meanings of science and education. And it also classifies Mathematics as formal science whereas Mathematics Education as social science by showing differences between Mathematics and Mathematics Education: research subject of Mathematics targets on mathematics itself and it uses the deductive method. On the other hand, Mathematics Education research handles the practice of mathematics of students and uses plausible reasoning. Also, it will also show why Mathematics Education shares lots of aspects with social science, not with natural science, which has many different characteristics from those of social science. Many researchers have agreed that Education should be categorized into the social science but misplaced Mathematics Education and Science Education into the natural science. It is true that physics and chemistry are natural science. And also it should be said that pure science is formal science. But it should be considered that just like Education, Mathematics Education and Science Education are in the category of social science.