RUME 28
2026
Alexandria, Virginia
Approximation, Riemann Sums, and Coordination Class Theory
Page: 81
Researchers have recognized Adding Up Pieces (e.g., Jones, 2013) to be a critical interpretation when applying definite integrals to problems in physics and other domains. At the same time, researchers have not investigated as closely students’ moment-to-moment reasoning when constructing pieces of an approximation and how that reasoning might vary across situations. We interviewed 11 students enrolled in calculus-based physics courses using tasks that asked for approximations, not definite integrals. Individual students approached approximations in more than one way––depending on the problem situation and how it was presented––and they did not always make connections among their different approaches. Based on this observation, we conjecture that approximation in service of Riemann sums is a good candidate for a coordination class (e.g., diSessa, 2002; diSessa & Wagner, 2005). We summarize the theory, present the case of one student, and draw out implications for research and instruction.