The Relationship between Mathematical Reasoning, Mathematical Communication, and Students' Mathematical Problem-Solving Abilities
DOI:
https://doi.org/10.58421/gehu.v5i4.1684Keywords:
Mathematical communication, Mathematical problem-solving, Mathematical reasoning, Mathematics learningAbstract
Mathematical problem-solving ability is a fundamental competency in mathematics education that is influenced by various cognitive factors, including mathematical reasoning and communication. However, the individual and simultaneous contributions of these abilities to students' mathematical problem-solving performance remain insufficiently understood. This study aimed to examine the influence of mathematical reasoning and communication abilities on students' problem-solving. A quantitative study employing an ex post facto design was conducted with 23 eighth-grade students from a junior high school in Cirebon, Indonesia. Data were collected using validated essay-based instruments measuring mathematical reasoning, mathematical communication, and mathematical problem-solving abilities. The data were analysed using descriptive statistics, classical assumption tests, and multiple linear regression. The findings revealed that the regression model satisfied the assumptions of normality, multicollinearity, and heteroscedasticity. The regression analysis indicated that both mathematical reasoning and mathematical communication abilities significantly affected students' problem-solving performance (p < 0.001), explaining 85.6% of the variance in problem-solving performance. Partial regression analysis showed that mathematical reasoning ability did not have a statistically significant effect (β = 0.147, p = 0.352), whereas mathematical communication ability had a significant positive effect (β = 1.378, p < 0.001). These findings indicate that mathematical communication ability is a stronger predictor of students' problem-solving than mathematical reasoning. Therefore, mathematics instruction should emphasise learning activities that foster students' mathematical communication and reasoning, thereby enhancing their problem-solving performance.
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