Problem-Solving Rubrics Revisited: Attending to the Blending of Informal Conceptual and Formal Mathematical Reasoning

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....

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Published inPhysical review special topics. Physics education research Vol. 9; no. 1; pp. 010105 - 10120
Main Authors Hull, Michael M, Kuo, Eric, Gupta, Ayush, Elby, Andrew
Format Journal Article
LanguageEnglish
Published College Park American Physical Society 11.02.2013
Subjects
Case Studies
College Science
Communication
Communication (Thought Transfer)
Comparative Analysis
Engineering Education
Engineering research
Equations (Mathematics)
Expertise
Interviews
Kinematics
Logical Thinking
Maryland
Mathematical analysis
Mathematical Logic
Physics
Problem Solving
Science Education
Scoring Rubrics
Students
Maryland
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Summary: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 expert-like 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. (Contains 2 tables, 1 figure and 4 footnotes.)
ISSN:1554-9178
1554-9178
2469-9896
DOI:10.1103/PhysRevSTPER.9.010105