Experts’ understanding of partial derivatives using the partial derivative machine

[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 st...

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Autores principales:	David Roundy, Eric Weber, Tevian Dray, Rabindra R. Bajracharya, Allison Dorko, Emily M. Smith, Corinne A. Manogue
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2015
Materias:	Special aspects of education LC8-6691 Physics QC1-999
Acceso en línea:	https://doaj.org/article/b5954dd03af84d1499d17ff49e1d2879
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spelling	oai:doaj.org-article:b5954dd03af84d1499d17ff49e1d28792021-12-02T11:53:20ZExperts’ understanding of partial derivatives using the partial derivative machine10.1103/PhysRevSTPER.11.0201261554-9178https://doaj.org/article/b5954dd03af84d1499d17ff49e1d28792015-09-01T00:00:00Zhttp://doi.org/10.1103/PhysRevSTPER.11.020126http://doi.org/10.1103/PhysRevSTPER.11.020126https://doaj.org/toc/1554-9178[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.David RoundyEric WeberTevian DrayRabindra R. BajracharyaAllison DorkoEmily M. SmithCorinne A. ManogueAmerican Physical SocietyarticleSpecial aspects of educationLC8-6691PhysicsQC1-999ENPhysical Review Special Topics. Physics Education Research, Vol 11, Iss 2, p 020126 (2015)
institution	DOAJ
collection	DOAJ
language	EN
topic	Special aspects of education LC8-6691 Physics QC1-999
spellingShingle	Special aspects of education LC8-6691 Physics QC1-999 David Roundy Eric Weber Tevian Dray Rabindra R. Bajracharya Allison Dorko Emily M. Smith Corinne A. Manogue Experts’ understanding of partial derivatives using the partial derivative machine
description	[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.
format	article
author	David Roundy Eric Weber Tevian Dray Rabindra R. Bajracharya Allison Dorko Emily M. Smith Corinne A. Manogue
author_facet	David Roundy Eric Weber Tevian Dray Rabindra R. Bajracharya Allison Dorko Emily M. Smith Corinne A. Manogue
author_sort	David Roundy
title	Experts’ understanding of partial derivatives using the partial derivative machine
title_short	Experts’ understanding of partial derivatives using the partial derivative machine
title_full	Experts’ understanding of partial derivatives using the partial derivative machine
title_fullStr	Experts’ understanding of partial derivatives using the partial derivative machine
title_full_unstemmed	Experts’ understanding of partial derivatives using the partial derivative machine
title_sort	experts’ understanding of partial derivatives using the partial derivative machine
publisher	American Physical Society
publishDate	2015
url	https://doaj.org/article/b5954dd03af84d1499d17ff49e1d2879
work_keys_str_mv	AT davidroundy expertsunderstandingofpartialderivativesusingthepartialderivativemachine AT ericweber expertsunderstandingofpartialderivativesusingthepartialderivativemachine AT teviandray expertsunderstandingofpartialderivativesusingthepartialderivativemachine AT rabindrarbajracharya expertsunderstandingofpartialderivativesusingthepartialderivativemachine AT allisondorko expertsunderstandingofpartialderivativesusingthepartialderivativemachine AT emilymsmith expertsunderstandingofpartialderivativesusingthepartialderivativemachine AT corinneamanogue expertsunderstandingofpartialderivativesusingthepartialderivativemachine
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Experts’ understanding of partial derivatives using the partial derivative machine

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