Prior research in physics education has documented persistent student difficulties with projectile motion, particularly the failure to conceptualize horizontal and vertical components as independent kinematic processes. This study examines the impact of an instructional intervention designed to support functional decomposition of two-dimensional motion among advanced high school students (N = 24) enrolled in an AP Physics 1 course. The students had no prior formal physics instruction; some (N = 8) were concurrently enrolled in Precalculus, while the remainder were enrolled in Calculus. Most participants were seniors (N = 18), with the remaining students being juniors (N = 6).
Over three 45-minute instructional units, students were explicitly scaffolded to represent horizontal, x(t), and vertical, y(t), motion as independent vector-valued functions. Instruction combined a PhET simulation-based laboratory with analytic problem-solving tasks that required students to analyze two-dimensional motion, examine projectile trajectories, and resolve position, velocity, and acceleration into horizontal and vertical components.
Student learning was assessed using mixed methods, including survey responses and descriptive analyses of performance on kinematics tasks. Results indicate that the intervention supported students’ recognition of the need for two-dimensional mathematical analysis. This shift was evident in increased consistency in separating gravitational and non-gravitational influences and in articulating the independence of motion components. Qualitative evidence further suggests a transition from equation-driven reasoning toward model-based reasoning grounded in functional representations. These findings support explicit functional modeling and simulation-supported inquiry as effective strategies for addressing persistent misconceptions in two-dimensional kinematics.

Authors:
Andrzej Sokolowski, The Woodlands Christian Academy, United States

About the Presenter(s)
Andrzej Sokolowski, Ph.D., is an Adjunct Professor of Mathematics and Physics at Lone Star College and a physics instructor at The Woodlands Christian Academy, USA. His research focuses on integrating mathematical reasoning into physics instruction.

Connect on Linkedin
https://www.linkedin.com/in/sokolowski-andrzej-708ab1a1/

Connect on ResearchGate
https://www.researchgate.net/profile/Andrzej-Sokolowski-6/research

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