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Unveiling students’ cognitive patterns in word problem solving: The case of single-variable linear equations Zaenal Arifin; Al Jupri
Jurnal Elemen Vol 11 No 4 (2025): October
Publisher : Universitas Hamzanwadi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29408/jel.v11i4.30786

Abstract

Students often struggle to transfer their procedural knowledge of linear equations into meaningful solutions when faced with word problems, revealing a persistent gap in integrating conceptual understanding, strategic reasoning, and metacognitive evaluation. This study investigates students’ cognitive profiles in solving mathematical word problems involving single-variable linear equations. Grounded in a synthesized framework from Polya’s heuristic model and the NCTM problem-solving process, the research focuses on five cognitive stages: understanding, analyzing, strategizing, executing, and evaluating. Using a qualitative descriptive method, data were collected from 30 eighth-grade students through written tasks and semi-structured interviews. The findings indicate strong performance in problem comprehension; however, there was a notable decline in evaluation and reflection stages. Interview data revealed that low-performing students often lacked conceptual understanding and demonstrated limited metacognitive awareness, whereas high performers integrated conceptual, procedural, and reflective thinking. This study highlights the gap between procedural fluency and strategic reasoning across performance levels, emphasizing the need for instructional approaches that integrate metacognitive scaffolding to enhance problem-solving competence. A diagnostic framework is proposed to support teachers in identifying and addressing students' cognitive needs.
Mapping Students' Errors in Mathematical Problem Solving Through the SOLO Taxonomy: A Qualitative Research Design Nia Kania; Mira Sagita; Muhammad Azam; Yasir Yasir; Yeni Dwi Kurino; Suci Trian Meliana; Rismayani Rismayani; Zaenal Arifin
International Journal of Mathematics and Mathematics Education Vol. 4 No. 2 (2026)
Publisher : EDUPEDIA Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.56855/ijmme.v4i2.2170

Abstract

Purpose – Mathematical problem solving in Basic Mathematics requires first-year university students to interpret information, select relevant concepts, apply algebraic procedures, and justify conclusions coherently. However, students’ incorrect or incomplete responses cannot be adequately interpreted through right-or-wrong scoring alone. This study aims to analyse first-year students’ errors in transforming equations into the standard form of quadratic equations using the Structure of Observed Learning Outcomes (SOLO) Taxonomy. Methodology – This study employed a descriptive qualitative approach. The data were obtained from a representative written response produced by a first-year university student enrolled in a Basic Mathematics course. The student’s solution was analysed by identifying the location of errors, classifying the types of errors, and mapping the structural quality of the response into SOLO levels: prestructural, unistructural, multistructural, relational, and extended abstract. Findings – The findings show that the student demonstrated meaningful but inconsistent algebraic understanding. The student correctly transformed some equations into standard quadratic form and identified the coefficients (a), (b), and (c). However, errors occurred in expansion, sign manipulation, simplification, and algebraic justification. The overall response was classified as multistructural with emerging relational characteristics, indicating that the student used several relevant procedures but did not consistently integrate them into a coherent and accurate solution. Novelty – This study contributes an integrated analytical framework that combines error analysis and the SOLO Taxonomy to interpret both the types of mathematical errors and the structural quality of students’ responses. Significance – The findings may assist Basic Mathematics lecturers in designing diagnostic feedback, assessment rubrics, and instructional interventions that support students’ transition from procedural performance to relational understanding.
Desain Pembelajaran Matematika Kontemporer Berorientasi TKA Zaenal Arifin; Nurul Farida; Ratna Sariningsih; Hadi Hadi; Nora Susilowaty; Subhan Ajiz Awalludin; Supriadi Supriadi; Jarnawi Afgani Dahlan; Sufyani Prabawanto
Journal of Community Service (JCOS) Vol. 4 No. 3 (2026)
Publisher : EDUPEDIA Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.56855/jcos.v4i3.2440

Abstract

Kegiatan pengabdian kepada masyarakat ini dilatarbelakangi oleh keterbatasan kapasitas guru dalam merancang pembelajaran matematika yang berorientasi pada Tes Kemampuan Akademik (TKA), khususnya di lingkungan MGMP Matematika MTs Kabupaten Majalengka. Pembelajaran masih didominasi pendekatan prosedural dan Lower Order Thinking Skills (LOTS), sementara kemampuan guru dalam mengembangkan instrumen asesmen berbasis penalaran dan literasi numerasi juga masih terbatas. Program ini bertujuan meningkatkan kompetensi pedagogis dan profesional guru dalam merancang pembelajaran matematika berbasis TKA serta mengembangkan instrumen asesmen berorientasi Higher Order Thinking Skills (HOTS). Pelaksanaan kegiatan menggunakan pendekatan participatory action research yang dipadukan dengan model capacity building melalui tahapan sosialisasi, pelatihan intensif, pendampingan implementatif, dan evaluasi. Kegiatan difokuskan pada pengembangan modul ajar berbasis konteks lokal dan penyusunan soal numerasi berbasis TKA. Hasil yang ditargetkan mencakup peningkatan kompetensi guru dalam merancang pembelajaran inovatif, tersusunnya modul ajar dan bank soal numerasi kontekstual, serta meningkatnya kualitas asesmen untuk mengukur kemampuan penalaran dan analisis siswa. Program ini diharapkan memperkuat ekosistem pembelajaran matematika yang adaptif dan kontekstual serta mendukung peningkatan kemampuan penalaran dan literasi numerasi siswa secara berkelanjutan.