• The Mathematical Education
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• v.59 no.1
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• pp.81-99
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• 2020

This study examined the types of abduction and the thinking strategies by the mathematics problems posed by students. Four students who were 2nd graders in middle school participated in problem posing on four tasks that were given, and the problems that they posed were classified into equivalence problem, isomorphic problem, and similar problem. The type of abduction appeared were different depending on the type of problems that students posed. In case of equivalence problem, the given condition of the problems was recognized as object for posing problems and it was the manipulative abduction. In isomorphic problem and similar problem, manipulative abduction, theoretical abduction, and creative abduction were all manifested, and creative abduction was manifested more in similar problem than in isomorphic problem. Thinking strategies employed at abduction were examined in order to find out what rules were presumed by students across problem posing activity. Seven types of thinking strategies were identified as having been used on rule inference by manipulative selective abduction. Three types of knowledge were used on rule inference by theoretical selective abduction. Three types of thinking strategies were used on rule inference by creative abduction.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.323-345
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• 2015

This study examined the types of abduction appeared in the exploration activities of 'law of large numbers' in order to figure out relation between statistical reasoning and abduction. When the classroom discourse of students was analyzed by Peirce's abduction, Eco's abduction type and Toulmin's argument pattern, students used overcoded abduction the most in the discourse of abduction. However, there composed a low percent of undercoded abduction leading to various thinking, and creative abduction used to make new principles or theories. By the CAS calculators used in the process of reasoning, students were provided with empirical context to understand the concept of abstract probability, through which they actively participated in the argumentation centered on the reasoning. As a result, it was found that not only to understand the abduction, but to build statistical context with tools in the learning of statistical reasoning is important.

• Korean journal of communication and information
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• v.54
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• pp.76-97
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• 2011

What are the meanings of abduction as a methodology of Cultural Studies? By contextualizing Charles Sanders Peirce's logic of abduction in the discipline of Cultural Studies, I explore the epistemological discussion on the modern scientific research methodology of social sciences. Abduction is a kind of logical inference, which is often associated with guessing or intuition. Peirce's method of abduction and Cultural Studies' contextual formation in effect address an alternative methodology to positivism. Criticizing the modern Eurocentric structure of knowledge construction, I suggest that the virtue of abduction, as a logic of discovery, should be re-discovered in the context of Cultural Studies. Abduction holds important lessons for Cultural Studies as well as social sciences in general because of its focus on intuition, empathy, and intellectual collaboration. Through its elaboration of the logic of abduction, Cultural Studies is able to maintain not only its epistemological ground but also its methodological communicability.

• 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.

• School Mathematics
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• v.6 no.3
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• pp.283-299
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• 2004

It is a very important objective of mathematical education to lead students to apply mathematics to the problem situations and to solve the problems. Assuming that mathematical modeling is appropriate for such mathematical education objectives, we must emphasize mathematical modeling learning. In this research, we focused what mathematical concepts are learned and what reasoning are applied and used through mathematical modeling. In the process of mathematical modeling, the students used several types of reasoning; deduction, induction and abduction. Although we cannot generalize a fact by a single case study, deduction has been used to confirm whether their model is correct to the real situation and to find solutions by leading mathematical conclusion and induction to experimentally verify whether their model is correct. And abduction has been used to abstract a mathematical model from a real model, to provide interpretation to existing a practical ground for mathematical results, and elicit new mathematical model by modifying a present model.

• 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.

• Journal of Educational Research in Mathematics
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• v.26 no.1
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• pp.1-22
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• 2016

This study aims to design an exemplification task to facilitate the students' creative thinking, and to investigate mathematical creativity which emerges from exemplification. In particular, we aim to identify the ways to design exemplification tasks which encourage creative thinking, and characterize mathematical creativity fostered by exemplification. The findings showed that the students' creative thinking related to fluency, flexibility, elaboration, and originality emerged through exemplification.

• 기호학연구
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• no.54
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• pp.7-36
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• 2018

Michael Polanyi's idea of tacit knowledge came from the realization that scientific objectivity and critical philosophy had become too restrictive for philosophy, especially in the realm of meaning, which is beyond positivistic proof and contains more non-critical elements than critical ones. In social life, people still share certain kinds of knowledge and beliefs which they obtain without making or learning those explicitly. Contemplating the role and significance of tacit knowledge, he called for a post-critical philosophy that integrates the realm of meaning and thereby appreciates the intertwined nature of tacit and explicit knowledge. Polanyi's position towards skepticism and doubt shows similarities with Charles S. Peirce's thinking about the relationship between belief and doubt. Although Peirce's semeiotics stands firmly in the tradition of critical philosophy, he affirms that doubt cannot be a constant state of mind and only belief can form a basis for a specific way of life. Polanyi's approach differs from Peirce's by focusing on the impossibility of scientific knowledge based solely on principles and precision, and his emphasis on the crucial role of the community of scientists. Nevertheless, the deeper implications of Peirce's contemplations on belief and doubt have myriad ramifications on the philosophy of science as well as the sociology of science.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.461-481
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• 2009

The semiotic approach to the mathematics education has been studied in last 20 years by PME, ICME conferences. New cultural developments in multi-media, digital documents and digital arts and cultures may influence mathematical education and teaching and learning activities. Hence semiotical interest in the mathematics education research and practice will be increasing. In this paper the basic ideas of semiotics, such as Peirce triad and Saussure's dyad, are introduced with some mathematical applications. There is some similarities between traditional research topics for concept, representation and social construction in mathematics education research and semiotic approach topics for the same subjects. some semiotic applications for an arithmetic problem for work, induction, deduction and abduction syllogisms with respect to Peirce's triad, its meaning in scientific discoveries and learning in geometry and symmetry.

• School Mathematics
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• v.19 no.1
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• pp.153-170
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• 2017

This study conducted an analysis of types of reasoning shown in students' solving a problem and processes of students' reasoning according to type of problem by posing an open-ended problem where students' reasoning activity is expected to be vigorous and a multiple-choice problem with which students are familiar. And it examined teacher's role of promoting the reasoning in solving an open-ended problem. Students showed more various types of reasoning in solving an open-ended problem compared with multiple-choice problem, and showed a process of extending the reasoning as chains of reasoning are performed. Abduction, a type of students' probable reasoning, was active in the open-ended problem, accordingly teacher played a role of encouragement, prompt and guidance. Teachers posed a problem after varying it from previous problem type to open-ended problem in teaching and evaluation, and played a role of helping students' reasoning become more vigorous by proper questioning when students had difficulty reasoning.