The effect of calculus and kinematics contexts on students’ understanding of graphs

Abstract

In this study, we compare students’ understanding of the derivative as slope and the antiderivative as the area under the curve using isomorphic graph-based problems in both calculus and kinematics contexts. Drawing from previous research, we designed two isomorphic tests, each with 12 items, and administered them to 543 university students. Our findings show that students performed significantly better on the kinematics test, with a higher rate of correct answers in some items. We also identified the most frequent errors and general trends in students’ selection of incorrect answers across both contexts. Based on these results, we provide specific recommendations for improving the instruction of these concepts. The analyses, recommendations, and tests included in the study can serve as valuable resources for mathematics and science education researchers and instructors teaching these topics. This study offers insights into how context influences students’ conceptual understanding, with implications for enhancing calculus and physics education.