RUME 27
2025
Alexandria, Virginia
Partitioning Physical Attributes for Riemann Sum Approximations: Underexamined Competency
Page: 27
Researchers have investigated several interpretations of definite integrals and their notation, and they have recognized that one particular interpretation, Adding Up Pieces (e.g., Jones, 2013), is especially important for applying definite integrals to physics and other domains. This same research has paid less attention to how students partition physical attributes, and thus construct pieces, in ways consistent with constructing Riemann sum approximations and definite integrals. We analyzed how 8 students taking calculus-based physics courses constructed Riemann sum approximations and integrals for one task about water pressure on a tank wall. All of the students recognized that integration was relevant, but half did not partition the wall in ways compatible with constructing Riemann sum approximations or definite integrals that solved the task. We conjecture that seeing integrands as rates of change and structuring situations in terms of level curves for rates of change is a significant, but underexamined competency.