“So it's the same equation.“: A blending analysis of student reasoning with functions in kinematics

Abstract

Student use of mathematics in physics is an area of current interest in both PER and the Research in Undergraduate Math Education (RUME) community. In particular, the function concept has been widely studied in RUME but has received less attention in PER. Using a grounded approach, this study probes the ability of introductory physics students to (1) interpret graphical representations of position vs. time functions and their corresponding derivatives and to (2) translate the graphical representation into a meaningful symbolic representation. Data were collected through think-aloud interviews and analyzed using a conceptual blending framework [1]. We created what we believe to be an “ideal expert blend“ of math and physics mental spaces against which the student responses were compared. We focus on case studies of two students whose approaches differed and examine how blending influenced responses to a novel graphical representation.