Mathematical Problem-Solving Processes across Self-Efficacy Levels in Fifth-Grade Students

Source abstract

Solving least common multiple (LCM) and greatest common factor (GCF) word problems requires conceptual reasoning and systematic verification, yet how fifth-grade students’ problem-solving processes vary across mathematics self-efficacy levels remains insufficiently described. This study aims to examine these processes through Polya’s four problem-solving stages. The study employed a qualitative descriptive design involving 39 fifth-grade students at Dabasah 3 Public Elementary School, Bondowoso, Indonesia, who completed a 16-item self-efficacy questionnaire and an eight-item constructed-response LCM/GCF assessment. Five students with contrasting self-efficacy and performance profiles were purposively selected for interviews and analysis of written solutions, supported by a teacher interview and documentation. Descriptive results indicated moderate self-efficacy among 21 students (53.8%) and moderate problem-solving performance among 32 (82.1%). Cross-case findings showed that the high-self-efficacy student selected a suitable strategy but failed to detect errors when checking. Students with moderate self-efficacy demonstrated divergent performance, including one high-performing case, whereas the low-self-efficacy student hesitated and incompletely monitored solutions. Across cases, recording given information and verifying answers posed recurring difficulties. This study contributes case-based evidence that self-efficacy and demonstrated performance did not consistently align, with implications for combining confidence-building support with conceptual explanation, procedural accuracy, and explicit checking routines.