Abstract
Of the many disciplines that rely on calculus, physics is among those with the strongest connections to this branch of mathematics. For instance, the derivative—one of the key notions of calculus—is used to describe velocity and acceleration, which play a central role in mechanics. In post-secondary education, in particular at the college level, it is not unusual for students to enroll in calculus and mechanics courses in the same year, and even the same term. In mathematics education, however, there is scant research focusing on students’ construction of the notion of derivative in a mechanics context, and existing studies offer contradictory views on the effectiveness of using mechanics to teach derivatives. To shed light on the use of derivatives in mechanics and calculus courses, our study focuses on practices involving the use of derivatives to study motion in both courses. We first conducted a praxeological analysis of five differential calculus textbooks and five mechanics textbooks to pinpoint their use of derivatives in the study of motion. This analysis was complemented by interviews with four mathematics teachers and three mechanics teachers, to compare their praxeologies with those of the textbooks. We then identified consistencies and inconsistencies between practices employed in both courses, which may have an impact on students’ learning, and formulated recommendations for teaching the notion of derivative in kinematics.
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Notes
The calculus sequence consists of differential calculus (usually Term 1), integral calculus (usually Term 2), and an optional multivariable calculus course (usually Term 4). Students in College A take differential calculus in their first term.
“Despite the name, free fall is not restricted to objects that are literally falling. Any object moving under the influence of gravity only, and no other forces, is in free fall. This includes objects falling straight down, objects that have been tossed or shot straight up, and projectile motion” (Knight, 2017, p. 50).
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Hitier, M., González-Martín, A.S. Derivatives and the Study of Motion at the Intersection of Calculus and Mechanics: a Praxeological Analysis of Practices at the College Level. Int. J. Res. Undergrad. Math. Ed. 8, 293–317 (2022). https://doi.org/10.1007/s40753-022-00182-z
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DOI: https://doi.org/10.1007/s40753-022-00182-z