THE EFFECTS OF MATHEMATICAL UNDERSTANDING AND SELF-CONFIDENCE ON PROBLEM SOLVING AMONG GRADE 7 STUDENTS
Keywords:
mathematical problem-solving, mathematical understanding, self-confidenceAbstract
The objectives of this research were: (1) to compare mathematical problem-solving abilities among students with different levels of mathematical understanding, (2) to compare mathematical problem-solving abilities among students with varying levels of self-efficacy, and (3) to examine the influence of mathematical understanding and self-efficacy on mathematical problem-solving. The sample consisted of 120 Mathayom Suksa 1 (Grade 7) students from Sarakham Pittayakhom School, Maha Sarakham Province, selected using cluster random sampling. The research instruments included a mathematical understanding test, a self-efficacy questionnaire, a mathematical problem-solving test, and a semi-structured interview. Quantitative data were analyzed using frequency, percentage, mean, standard deviation, and one-way ANOVA. Qualitative data were analyzed using case study and descriptive analysis.
The results revealed that: 1) students with different levels of mathematical understanding had significantly different problem-solving abilities at the .05 level; 2) students with different levels of self-efficacy also had significantly different problem-solving abilities at the .05 level; and 3) students with high levels of both mathematical understanding and self-efficacy demonstrated complete and systematic problem-solving processes, effectively connecting prior knowledge with new problems and providing well-reasoned explanations. In contrast, students with moderate levels could solve routine problems but lacked confidence and clarity when asked to elaborate on their reasoning, while students with low levels struggled to interpret problems, plan solutions, and explain their ideas and reasoning.
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