Investigating Transfer of Knowledge of 2-D Kinematics to 2-D Dynamics Contexts in the Calculus-Based Mechanics Physics Course for Future Engineers

To analyze forces in contexts in which an object, modeled as a particle, moves on a two-dimensional trajectory, one often needs to coordinate between the components of the acceleration parallel and perpendicular to the trajectory with forces resolved in these two ever-changing directions. Education researchers have mapped the landscapes of student ideas of forces and of two-dimensional motion separately. At the same time, the literature on transfer illustrates how difficult transfer and coordination are in general. The present work contributes to the knowledge base by investigating ways in which students coordinate their knowledge of velocity and acceleration in two dimensions with the knowledge of forces that is required for applying Newton's Second Law in these kinds of problems. The context of the investigation is the first calculus-based course in the typical physics sequence for future scientists and engineers, including versions of the course taught in a studio format. Results from student interviews and student written work will be presented and implications for instruction will be discussed. This work is part of the multifaceted collaborative project "Mechanics of Inclusion and Inclusivity in Mechanics," which is funded by the California Governor's Office of Planning and Research Learning Lab. Our project involves physics and engineering faculty and students at Cal Poly San Luis Obispo and Allan Hancock College, with support from education faculty at UC Santa Barbara and researchers from Tufts University and Oregon State University.