• Open Access

Problem-solving rubrics revisited: Attending to the blending of informal conceptual and formal mathematical reasoning

Michael M. Hull, Eric Kuo, Ayush Gupta, and Andrew Elby
Phys. Rev. ST Phys. Educ. Res. 9, 010105 – Published 11 February 2013

Abstract

Much research in engineering and physics education has focused on improving students’ problem-solving skills. This research has led to the development of step-by-step problem-solving strategies and grading rubrics to assess a student’s expertise in solving problems using these strategies. These rubrics value “communication” between the student’s qualitative description of the physical situation and the student’s formal mathematical descriptions (usually equations) at two points: when initially setting up the equations, and when evaluating the final mathematical answer for meaning and plausibility. We argue that (i) neither the rubrics nor the associated problem-solving strategies explicitly value this kind of communication during mathematical manipulations of the chosen equations, and (ii) such communication is an aspect of problem-solving expertise. To make this argument, we present a case study of two students, Alex and Pat, solving the same kinematics problem in clinical interviews. We argue that Pat’s solution, which connects manipulation of equations to their physical interpretation, is more expertlike than Alex’s solution, which uses equations more algorithmically. We then show that the types of problem-solving rubrics currently available do not discriminate between these two types of solutions. We conclude that problem-solving rubrics should be revised or repurposed to more accurately assess problem-solving expertise.

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  • Received 25 February 2012

DOI:https://doi.org/10.1103/PhysRevSTPER.9.010105

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Michael M. Hull1, Eric Kuo1, Ayush Gupta1, and Andrew Elby2

  • 1Department of Physics, University of Maryland, College Park, Maryland 20742, USA
  • 2Department of Teaching, Learning, Policy, and Leadership, University of Maryland, College Park, Maryland 20737, USA

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Vol. 9, Iss. 1 — January - June 2013

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