• Title/Summary/Keyword: 가추 유형

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Analysis of abduction and thinking strategies by type of mathematical problem posing (수학 문제 만들기 유형에 따른 가추 유형과 가추에 동원된 사고 전략 분석)

  • Lee, Myoung Hwa;Kim, Sun Hee
    • 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.

An Analysis on Abduction Type in the Activities Exploring 'Law of Large Numbers' ('큰 수의 법칙' 탐구 활동에서 나타난 가추법의 유형 분석)

  • Lee, Yoon-Kyung;Cho, Cheong-Soo
    • 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.

An Analysis of Problems of Mathematics Textbooks in regards of the Types of Abductions to be used to solve (교과서 문제해결에 포함된 가추의 유형 - 중학교 2학년과 3학년 수학 교과서를 중심으로-)

  • Lee, Youngha;Jung, Kahng Min
    • 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.

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Analysis on Types and Roles of Reasoning used in the Mathematical Modeling Process (수학적 모델링 과정에 포함된 추론의 유형 및 역할 분석)

  • 김선희;김기연
    • 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.

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A Comparison of Students' Reasoning Shown in Solving Open-Ended and Multiple-Choice Problems (개방형 문제와 선택형 문제 해결에 나타난 학생의 추론 비교)

  • Lee, Myoung Hwa;Kim, Sun Hee
    • 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.