Analysis of vector concept understanding and its correlation with basic mathematical abilities of prospective science teachers

Abstract

This study investigates the relationship between basic mathematical skills and the understanding of vector concepts among 54 prospective science teachers enrolled in basic physics and basic math courses. The research employed a descriptive and correlational quantitative approach, utilizing data from vector tests and basic mathematics assessments administered during the courses. Descriptive statistical analyses revealed that participants showed varying levels of proficiency in both vector understanding and basic mathematical abilities, with average scores indicating a moderate level of competence overall. Correlational analysis using Pearson correlation coefficients found a significant positive relationship (<i>r=0.477, ρ=0.001</i> ) between basic mathematical skills and the understanding of vector concepts, suggesting that higher proficiency in basic mathematical skills corresponds to better understanding of vector concepts. Further analysis segmented by dimensions of vector operations indicated stronger correlations in two-dimensional vector understanding (<i>r=0.503, ρ=0.000</i> ) compared to one-dimensional operations (<i>r=0.348, ρ=0.014</i> ). Basic geometry emerged as the most influential predictor of understanding of vector concepts, exhibiting the highest correlation with both overall understanding of vector concepts (<i>r=0.444, ρ=0.001</i> ) and 2D understanding of vector concepts (<i>r=0.430, ρ=0.0021</i> ). These findings underscore the critical role of mathematical competence, particularly in geometric reasoning, in facilitating conceptual understanding in physics education. In conclusion, strengthening basic mathematics skills among prospective science teachers is essential for enhancing their ability to teach and understand physics, particularly in topics like vectors. Future research should explore instructional strategies to address gaps in math-physics integration.