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Journal : JRAMathEdu (Journal of Research and Advances in Mathematics Education)

An exploration of critical thinking stages of junior high school students in solving contradictory mathematical problems Agusman, Agusman; Purwanto, Purwanto; Rahardi, Rustanto
JRAMathEdu (Journal of Research and Advances in Mathematics Education) Volume 10 Issue 3 July 2025
Publisher : Lembaga Pengembangan Publikasi Ilmiah dan Buku Ajar, Universitas Muhammadiyah Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23917/jramathedu.v10i3.8911

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 SMP Negeri 01 Sumber Pucung, Malang, 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.
Co-Authors Abdu, Muhammad Abdul Jabar Idharudin Abdurahman Abdurrahman Ahmad Efendi Aldha, Sitti Febriyany Anastasia Sri Lestari Annisa, Sarah Dwi Aswad, Aswad August Halomoan Siregar Baharuddin, Rhamdhani Fitrah Basoka, Muhammad Darmawan Budi Handrianto Budijanto Widjaja Deby Handayani Dewi, Winona Kumara Erniwati Erniwati Eryck, Muhamad Fahmi Fateha, Fateha Fathiah Fathiah Ferry Hidayat Fransiska, Dina Hari Eko Irianto Hasriani Muis Idwan, Idwan Irianto, Dendi Ikhwan Irma Setiawan, Irma Iskandar Iskandar Joko Santoso Laksono Trisnantoro Maemuna Sa'diyah Maharani Fizwar, Putri Mario Andriaskiton Marlinda Ramdhani Martayadi, Uwi Martin, Nurhidayat Masuwd, Mowafg Mesakh, Januardi Mexano Hans Gery Michael Novranda Surbakti Muhammad Abduh Muhammad Adam Suni Muhammad Hamka Muhammad Ilyas Muhammad Rafiq Mujahid Mujahid, Mujahid Musaddat, Syaiful Nasti Putri, Anggun Nurmadhani Fitri Suyuthi Oktaviani, Asih Pajriati, Merry Patmaniar, Patmaniar PERMATA SARI, SHINTA Poetri, Tika Annisa Eka Purwanto Purwanto Rahendra Maya Rahendra Maya, Rahendra Ramdhani, Marlinda Rinaldi, Alhazar RISA WAHYUNI EDT Robin Robin, Robin Rustanto Rahardi Saharudin Saharudin Samsuddin Samsuddin Sapiin, Sapiin Sayfullah S, Muh. sayfullah, Muh Sayfullah, Muh. Singgih Wibowo, Singgih Slamet Haryadi Sofyan, Silvia Susanti, Pipit Aprilia SYAMSU ALAM Tamba, Iventura Fitra Uli Taslinawati, Taslinawati Uju Uju Umar, Mohamad Fahrul Himalaya Vatur, Kayla Maharani Victor Victor Wahyu Hidayat Wahyuni, Risa Wahyuni, Wika Wika Wahyuni Zaunit, Muthia Miranda