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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 Abdur Rahman As’ari Abdur Rohim, Abdur Agusman, Agusman Akhidayati, Ria Risyandani Alip Rahmawati Zahrotun Nisak Anik Rizka Rahmawati Anita Dewi Utami Ardan S, Muhammad Rey Ardan Saputra, Muhammad Rey Arnaningtyas Rofi'i Arwan Mhd. Said Astuti, Ririn Novia Cahyani, Nia Cahyaningtyas, Octavita Cholis Sa’dijah Christiyanto, Dana Yuli Dahliatul Hasanah Dana Yuli Christiyanto Destri Mega Arumanita Elis Dwi Wulandari Emanuel, Endrayana Putut Laksminto Erry Hidayanto Ewan Gunawan Faradila Nur Sabrina Fauziyyah Alimuddin HAFIIZH, MOCHAMMAD Herdiansyah, Adi Hery Susanto Hery Susanto Hijriani, Lailin Huda, Ristianur I Made Sulandra I Nengah Parta Indriati Nurul Hidayah Irianto, Savitri Oktavia Izzah Khairu Rahmah Janah, Miftakul Khalisa Naura Imanda Kusumaningtyas, Nopem Lailin Hijriani Lestary, Ratnah Lucky Tri Oktaviana Lutfika Zayyenu Zuhairini M Zainul Arifin Makbul Muksar Maulana Al - Ghofiqi Millenia Nugraha, Hermawan Septa Muhammad Rizaldi Nia Cahyani Novi Nurhayati Nugraha, Hermawan Septa Millenia Nursani Indah Pratiwi Octavita Cahyaningtyas Okviarini, Dewi Permadi, Hendro Prasetyo, Yudha Eka Purwanto Purwanto Purwanto Purwanto Putra, Zuhadur Ra'is Ariyono Qomarudin, Moch Hamzah Rachmat Wasqita Rahma Wahyu Rahmadani, Desi RIA ANGGRAINI Risna Zulfa Musriroh Rony, Zahara Tussoleha Saidah Ajilatun Nahdawiyah Sisworo Siti Na’imah Slamet . Subanji Subanji Sudirman Sudirman Sukoriyanto Susiswo Suwanto Suwanto Swasono Rahardjo Syaiful Hamzah Nasution Tjang Daniel Chandra Toto Nusantara Trianingsih Eni Lestari Widuri, Nabila Ekaputri Ziadatul Muslimah, Khilma Zuhadur Ra'is Ariyono Putra