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An Exploration of Critical Thinking Stages of Junior High School Students in Solving Contradictory Mathematical Problems

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Title: An Exploration of Critical Thinking Stages of Junior High School Students in Solving Contradictory Mathematical Problems
Language: English
Authors: Agusman, Purwanto, Rustanto Rahardi
Source: Journal of Research and Advances in Mathematics Education. 2025 10(3):200-217.
Availability: Universitas Muhammadiyah Surakarta Department of Education. Ahmad Yani Street, Pabelan Kartasura, Surakarta, Central Java, 57162 Indonesia. Tel: +62-271-717417 ext. 2554; e-mail: jramathedu@ums.ac.id; Web site: https://journals2.ums.ac.id/index.php/jramathedu
Peer Reviewed: Y
Page Count: 18
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Junior High Schools
Middle Schools
Secondary Education
Elementary Education
Grade 8
Descriptors: Critical Thinking, Junior High School Students, Mathematics Instruction, Problem Solving, Grade 8, Cognitive Processes, Foreign Countries, Word Problems (Mathematics), Thinking Skills
Geographic Terms: Indonesia
ISSN: 2503-3697
2541-2590
Abstract: Critical thinking is a fundamental competence in 21st-century education, particularly in mathematics, where students frequently encounter contradictory information that requires logical reasoning and reflective judgment. This study explores the stages of critical thinking among junior high school students when solving contradictory mathematical problems. A qualitative descriptive design was employed, involving two eighth-grade students from one of public junior high school in Malang regency, who were selected based on their skeptical responses to illogical mathematical tasks. Data were collected through open-ended tests and interviews, then analyzed to capture reasoning patterns and problem-solving strategies. The findings revealed three distinct stages of mathematical critical thinking: (1) Initial Stage (interpretation), where anomalies are sensed; (2) Tracing Stage (analysis), where contradictions are identified; and (3) Global View Stage (evaluation and inference), where holistic reasoning and alternative solutions are proposed. Subject 1 demonstrated conceptual awareness, cognitive flexibility, and evaluative rigor, while Subject 2 showed procedural accuracy but limited inferential precision. These findings suggest that contradictory problems can serve as effective instructional tools for balancing procedural and conceptual reasoning. Practical implications highlight the need for integrating contradictory problems into mathematics instruction to promote metacognitive reflection. Future research should expand participant diversity, employ longitudinal and experimental designs, and explore affective dispositions influencing students' critical engagement.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1487607
Database: ERIC
FullText Text:
  Availability: 0
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  Data: An Exploration of Critical Thinking Stages of Junior High School Students in Solving Contradictory Mathematical Problems
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  Data: <searchLink fieldCode="AR" term="%22Agusman%22">Agusman</searchLink><br /><searchLink fieldCode="AR" term="%22Purwanto%22">Purwanto</searchLink><br /><searchLink fieldCode="AR" term="%22Rustanto+Rahardi%22">Rustanto Rahardi</searchLink>
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  Data: <searchLink fieldCode="SO" term="%22Journal+of+Research+and+Advances+in+Mathematics+Education%22"><i>Journal of Research and Advances in Mathematics Education</i></searchLink>. 2025 10(3):200-217.
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  Label: Availability
  Group: Avail
  Data: Universitas Muhammadiyah Surakarta Department of Education. Ahmad Yani Street, Pabelan Kartasura, Surakarta, Central Java, 57162 Indonesia. Tel: +62-271-717417 ext. 2554; e-mail: jramathedu@ums.ac.id; Web site: https://journals2.ums.ac.id/index.php/jramathedu
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  Data: Y
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  Data: 18
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  Data: 2025
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  Data: Journal Articles<br />Reports - Research
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  Data: <searchLink fieldCode="EL" term="%22Junior+High+Schools%22">Junior High Schools</searchLink><br /><searchLink fieldCode="EL" term="%22Middle+Schools%22">Middle Schools</searchLink><br /><searchLink fieldCode="EL" term="%22Secondary+Education%22">Secondary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+8%22">Grade 8</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Critical+Thinking%22">Critical Thinking</searchLink><br /><searchLink fieldCode="DE" term="%22Junior+High+School+Students%22">Junior High School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Instruction%22">Mathematics Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Problem+Solving%22">Problem Solving</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+8%22">Grade 8</searchLink><br /><searchLink fieldCode="DE" term="%22Cognitive+Processes%22">Cognitive Processes</searchLink><br /><searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink><br /><searchLink fieldCode="DE" term="%22Word+Problems+%28Mathematics%29%22">Word Problems (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Thinking+Skills%22">Thinking Skills</searchLink>
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  Label: Geographic Terms
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  Data: <searchLink fieldCode="DE" term="%22Indonesia%22">Indonesia</searchLink>
– Name: ISSN
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  Data: 2503-3697<br />2541-2590
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Critical thinking is a fundamental competence in 21st-century education, particularly in mathematics, where students frequently encounter contradictory information that requires logical reasoning and reflective judgment. This study explores the stages of critical thinking among junior high school students when solving contradictory mathematical problems. A qualitative descriptive design was employed, involving two eighth-grade students from one of public junior high school in Malang regency, who were selected based on their skeptical responses to illogical mathematical tasks. Data were collected through open-ended tests and interviews, then analyzed to capture reasoning patterns and problem-solving strategies. The findings revealed three distinct stages of mathematical critical thinking: (1) Initial Stage (interpretation), where anomalies are sensed; (2) Tracing Stage (analysis), where contradictions are identified; and (3) Global View Stage (evaluation and inference), where holistic reasoning and alternative solutions are proposed. Subject 1 demonstrated conceptual awareness, cognitive flexibility, and evaluative rigor, while Subject 2 showed procedural accuracy but limited inferential precision. These findings suggest that contradictory problems can serve as effective instructional tools for balancing procedural and conceptual reasoning. Practical implications highlight the need for integrating contradictory problems into mathematics instruction to promote metacognitive reflection. Future research should expand participant diversity, employ longitudinal and experimental designs, and explore affective dispositions influencing students' critical engagement.
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  Data: 2025
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RecordInfo BibRecord:
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    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 18
        StartPage: 200
    Subjects:
      – SubjectFull: Critical Thinking
        Type: general
      – SubjectFull: Junior High School Students
        Type: general
      – SubjectFull: Mathematics Instruction
        Type: general
      – SubjectFull: Problem Solving
        Type: general
      – SubjectFull: Grade 8
        Type: general
      – SubjectFull: Cognitive Processes
        Type: general
      – SubjectFull: Foreign Countries
        Type: general
      – SubjectFull: Word Problems (Mathematics)
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      – SubjectFull: Thinking Skills
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      – SubjectFull: Indonesia
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    Titles:
      – TitleFull: An Exploration of Critical Thinking Stages of Junior High School Students in Solving Contradictory Mathematical Problems
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            NameFull: Rustanto Rahardi
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              Y: 2025
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