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Causes of Proof Construction Failure in Proof by Contradiction

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Title: Causes of Proof Construction Failure in Proof by Contradiction
Language: English
Authors: Hamdani, Deni (ORCID 0000-0002-2876-979X), Purwanto (ORCID 0000-0003-0974-4068), Sukoriyanto (ORCID 0000-0003-1700-6735), Anwar, Lathiful (ORCID 0000-0001-6046-0146)
Source: Journal on Mathematics Education. 2023 14(3):415-448.
Availability: Indonesian Mathematical Society. Jl. Padang Selasa 524, Palembang, South Sumatra 30139, Indonesia. Tel: +618-127-106777; Fax: +627-113-20310; Web site: http://jme.ejournal.unsri.ac.id/index.php/jme
Peer Reviewed: Y
Page Count: 34
Publication Date: 2023
Document Type: Journal Articles
Reports - Research
Descriptors: Validity, Mathematical Logic, Mathematics Instruction, Guidelines, Failure, Problem Solving, Teacher Education Programs, Foreign Countries
Geographic Terms: Indonesia
ISSN: 2087-8885
2407-0610
Abstract: Failure to deduce false suppositions in proof by contradiction is still considered "more difficult" than proving the conditional ?? to ?? in proof by contraposition. This study aims to identify the types of proof construction failures based on the action steps of proof by contradiction, then offer a framework of construction failure hypothesis specifically used in proof by contradiction. The research data were collected and analyzed from the work of students who have agreed to be research participants, a total of 83 students. The results of the analysis of student work successfully identified four types of failures, namely formulating suppositions, constructing and manipulating suppositions, identifying contradictions, and disproving suppositions. These four types of failures then became the material for the development of the hypothesis framework of a failure to construct proof by contradiction, which consists of 17 hypothesis nodes divided into three main hypotheses, namely: operational (action), affective (emotional), and foundational (logical reasoning). The failure hypothesis framework justifies that the sources of the failure of proof construction in proof by contradiction are understanding of the act of producing a proof by contradiction, emotionality towards the coherence of the construction steps, disproving suppositions, beliefs, use of appropriate definitions-theorems and axioms, and cognitive tension in proof by contradiction; and formal logic of the act of producing a proof by contradiction, as well as differences in the underlying logic with other acts.
Abstractor: As Provided
Entry Date: 2023
Accession Number: EJ1400324
Database: ERIC
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  Data: Causes of Proof Construction Failure in Proof by Contradiction
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  Data: <searchLink fieldCode="AR" term="%22Hamdani%2C+Deni%22">Hamdani, Deni</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-2876-979X">0000-0002-2876-979X</externalLink>)<br /><searchLink fieldCode="AR" term="%22Purwanto%22">Purwanto</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0003-0974-4068">0000-0003-0974-4068</externalLink>)<br /><searchLink fieldCode="AR" term="%22Sukoriyanto%22">Sukoriyanto</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0003-1700-6735">0000-0003-1700-6735</externalLink>)<br /><searchLink fieldCode="AR" term="%22Anwar%2C+Lathiful%22">Anwar, Lathiful</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0001-6046-0146">0000-0001-6046-0146</externalLink>)
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  Data: <searchLink fieldCode="SO" term="%22Journal+on+Mathematics+Education%22"><i>Journal on Mathematics Education</i></searchLink>. 2023 14(3):415-448.
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  Data: Indonesian Mathematical Society. Jl. Padang Selasa 524, Palembang, South Sumatra 30139, Indonesia. Tel: +618-127-106777; Fax: +627-113-20310; Web site: http://jme.ejournal.unsri.ac.id/index.php/jme
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  Data: 34
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  Data: Failure to deduce false suppositions in proof by contradiction is still considered "more difficult" than proving the conditional ?? to ?? in proof by contraposition. This study aims to identify the types of proof construction failures based on the action steps of proof by contradiction, then offer a framework of construction failure hypothesis specifically used in proof by contradiction. The research data were collected and analyzed from the work of students who have agreed to be research participants, a total of 83 students. The results of the analysis of student work successfully identified four types of failures, namely formulating suppositions, constructing and manipulating suppositions, identifying contradictions, and disproving suppositions. These four types of failures then became the material for the development of the hypothesis framework of a failure to construct proof by contradiction, which consists of 17 hypothesis nodes divided into three main hypotheses, namely: operational (action), affective (emotional), and foundational (logical reasoning). The failure hypothesis framework justifies that the sources of the failure of proof construction in proof by contradiction are understanding of the act of producing a proof by contradiction, emotionality towards the coherence of the construction steps, disproving suppositions, beliefs, use of appropriate definitions-theorems and axioms, and cognitive tension in proof by contradiction; and formal logic of the act of producing a proof by contradiction, as well as differences in the underlying logic with other acts.
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      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 34
        StartPage: 415
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      – SubjectFull: Validity
        Type: general
      – SubjectFull: Mathematical Logic
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      – SubjectFull: Mathematics Instruction
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      – SubjectFull: Guidelines
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      – SubjectFull: Failure
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      – SubjectFull: Problem Solving
        Type: general
      – SubjectFull: Teacher Education Programs
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      – SubjectFull: Foreign Countries
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      – SubjectFull: Indonesia
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      – TitleFull: Causes of Proof Construction Failure in Proof by Contradiction
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