TY - JOUR

T1 - Experts' understanding of partial derivatives using the partial derivative machine

AU - Roundy, David

AU - Weber, Eric

AU - Dray, Tevian

AU - Bajracharya, Rabindra R.

AU - Dorko, Allison

AU - Smith, Emily M.

AU - Manogue, Corinne A.

N1 - Publisher Copyright:
© 2015 authors. Published by the American Physical Society.

PY - 2015/9/23

Y1 - 2015/9/23

N2 - [This paper is part of the Focused Collection on Upper Division Physics Courses.] Partial derivatives are used in a variety of different ways within physics. Thermodynamics, in particular, uses partial derivatives in ways that students often find especially confusing. We are at the beginning of a study of the teaching of partial derivatives, with a goal of better aligning the teaching of multivariable calculus with the needs of students in STEM disciplines. In this paper, we report on an initial study of expert understanding of partial derivatives across three disciplines: physics, engineering, and mathematics. We report on the central research question of how disciplinary experts understand partial derivatives, and how their concept images of partial derivatives differ, with a focus on experimentally measured quantities. Using the partial derivative machine (PDM), we probed expert understanding of partial derivatives in an experimental context without a known functional form. In particular, we investigated which representations were cued by the experts' interactions with the PDM. Whereas the physicists and engineers were quick to use measurements to find a numeric approximation for a derivative, the mathematicians repeatedly returned to speculation as to the functional form; although they were comfortable drawing qualitative conclusions about the system from measurements, they were reluctant to approximate the derivative through measurement. On a theoretical front, we found ways in which existing frameworks for the concept of derivative could be expanded to include numerical approximation.

AB - [This paper is part of the Focused Collection on Upper Division Physics Courses.] Partial derivatives are used in a variety of different ways within physics. Thermodynamics, in particular, uses partial derivatives in ways that students often find especially confusing. We are at the beginning of a study of the teaching of partial derivatives, with a goal of better aligning the teaching of multivariable calculus with the needs of students in STEM disciplines. In this paper, we report on an initial study of expert understanding of partial derivatives across three disciplines: physics, engineering, and mathematics. We report on the central research question of how disciplinary experts understand partial derivatives, and how their concept images of partial derivatives differ, with a focus on experimentally measured quantities. Using the partial derivative machine (PDM), we probed expert understanding of partial derivatives in an experimental context without a known functional form. In particular, we investigated which representations were cued by the experts' interactions with the PDM. Whereas the physicists and engineers were quick to use measurements to find a numeric approximation for a derivative, the mathematicians repeatedly returned to speculation as to the functional form; although they were comfortable drawing qualitative conclusions about the system from measurements, they were reluctant to approximate the derivative through measurement. On a theoretical front, we found ways in which existing frameworks for the concept of derivative could be expanded to include numerical approximation.

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U2 - 10.1103/PhysRevSTPER.11.020126

DO - 10.1103/PhysRevSTPER.11.020126

M3 - Article

AN - SCOPUS:84951120542

VL - 11

JO - Physical Review Special Topics - Physics Education Research

JF - Physical Review Special Topics - Physics Education Research

SN - 1554-9178

IS - 2

M1 - 020126

ER -