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

Abstract

Much research in engineering and physics education has focused on improving students' problemsolving 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 problemsolving 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.

Drawing physical insight from mathematics via extreme case reasoning

“…Although novices sometimes do the same [4], the phenomenon is little-studied in physics education research, and is rarely an instructional goal. When it is an instructional goal, it can be difficult to design systems that reward students for expert-like mathematical sense-making without making it just another checkbox on a rubric [17]. In the example of Bert, we see that guiding students through epistemic games such as examine extreme cases can cause significant shifts to students' epistemic frames and lead to new, creative sorts of blended mathematical and physical cognition.…”

Unexpected attitudinal growth in a course combining reformed curricula

“…The interview protocol also probed students' epistemological stances with prompts such as "How do you know when you really understand an equation?" [55,56]. The post-P151 interviews were similar to the interviews that took place during P151 but with questions specifically designed for the interviewee based upon the first interview and that student's survey responses.…”

“…To that end, interview prompts included questions about physics class experiences in both high school and P151. The protocols also contained physics problems that were collected primarily from PER literature [1,15,52,55,56] and organized based upon epistemological themes that emerged from interviews conducted with previous P151 students. If a fall 2013 interviewee touched on one of these themes, M. M. H. would consider asking him to solve some or all of the problems associated with that theme.…”

The Exploration of Using E-Scaffolding in Solving Physics Problem

“…Problem-solving is used to solve the unusual problems. Problem-solving is as an important role in everyday life, especially on scientists and technicians (Hull, Kuo, Gupta & Elby, 2013). In addition, problem-solving is also an important element in all areas of science (Ibrahim & Rebello, 2012) and (Adeoye, 2010).…”