<![CDATA[Background: Mathematical problem-solving ability is a fundamental competency in elementary mathematics education because it supports conceptual understanding, reasoning, and higher-order thinking. However, evidence regarding how gender and residential context contribute to variations in students’ problem-solving performance remains limited. Aims: This study examines variations in elementary students’ mathematical problem-solving ability across gender and residential contexts to provide empirical evidence for developing more equitable and responsive mathematics instruction. Methods: A quantitative ex post facto design was employed involving 116 fifth-grade students from three elementary schools in Cigedug Subdistrict, Indonesia. Students’ mathematical problem-solving ability was assessed using a Polya-based test encompassing four stages: understanding the problem, devising a plan, carrying out the plan, and looking back. Data were analyzed using descriptive statistics, Mann–Whitney U tests, Spearman’s rho correlation, and nonparametric effect size analysis. Results: Students demonstrated stronger performance in devising and carrying out solution plans than in understanding problems and reviewing solutions. Significant differences were identified only across residential contexts for problem understanding and looking back (p < 0.001), whereas no significant gender-based differences were observed (p > 0.05). Effect size analysis indicated that both factors had negligible practical influence on overall problem-solving ability. Conclusion: Variations in mathematical problem-solving ability are more evident across Polya’s problem-solving stages than across gender or residential contexts. Mathematics instruction should therefore prioritize strengthening conceptual understanding and reflective evaluation to improve students’ comprehensive problem-solving competence.]]>
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