DOI: 10.12688/f1000research.187341.1 ISSN: 2046-1402

Exploring the Gap Between Mathematical Beliefs and Problem Solving in Elementary School: A Mixed Methods Study

Aras Irianto, Ayu Fitri, Retno Andriani, Nurdin -, Fahrudin -, Indra Suhendra, Dwi Nanda Akhmad Romadhon
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Background The relationship between what students believe about mathematics and how well they actually solve problems has long been a focus of educational research, yet the gap between high beliefs and low performance remains underexplored among elementary school students. Methods This study used an explanatory sequential mixed-methods design (Creswell & Plano Clark, 2018). The quantitative phase involved 50 fifth-grade students from three elementary schools, who completed a mathematical beliefs questionnaire (44 items; α = 0.886; 37 valid items) and a problem-solving test (4 items; KR-20 = 0.78) covering integers, greatest common factor, least common multiple, and decimals. Belief-performance gap categories were identified using a median split. The qualitative phase involved semi-structured interviews with 8 purposively selected students (4 High-Belief-Low-Performance [HBLP], 4 Low-Belief-High-Performance [LBHP]), analyzed thematically following Braun and Clarke (2006). Results Pearson correlation indicated a significant, moderate positive relationship between mathematical beliefs and problem-solving ability (r = 0.52; p < 0.01; 95% CI [0.28, 0.70]; r 2  = 0.27). Gap identification yielded HBHP = 40%, LBLP = 26%, HBLP = 16%, and LBHP = 12%. Thematic analysis identified three drivers of HBLP (ineffective metacognitive control, hasty working habits, situational anxiety) and three drivers of LBHP (strong external support, compensatory persistence, and attribution of success to external factors consistent with the impostor phenomenon). Conclusions Mathematical beliefs are a significant but partial predictor of problem-solving success (accounting for 27% of variance); the belief-performance gap is better explained by group-specific mechanisms than by beliefs alone. Interventions should be differentiated: metacognitive-control training for HBLP students and attributional retraining for LBHP students.

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