Solution evaluation strategies used by first-year physics students

One expected outcome of physics instruction is that students develop quantitative reasoning skills, including strategies for evaluating solutions to problems. Examples of well-known “canonical” evaluation strategies include special case analysis, unit analysis, and checking for reasonable numbers. We report on responses from three tasks in different physics contexts prompting students in an introductory calculus-based physics sequence to evaluate expressions for various quantities: the velocity of a block at the bottom of an incline with friction, the final velocities of two masses involved in an elastic collision, and the electric field due to three point charges. Responses from written (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi mathvariant="italic">N</a:mi><a:mo>=</a:mo><a:mn>5</a:mn><a:mn>8</a:mn><a:mn>0</a:mn></a:mrow></a:math>) and interview (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mrow><d:mi mathvariant="italic">N</d:mi><d:mo>=</d:mo><d:mn>1</d:mn><d:mn>8</d:mn></d:mrow></d:math>) data were analyzed using modified grounded theory and phenomenology. We also employed the analytical framework of epistemic frames. Students’ evaluation strategies were classified into three broad categories: consulting external sources, checking through computation, and comparing to the physical world. Some of the evaluation strategies observed in our data, including canonical as well as noncanonical strategies, have been reported in prior research on evaluation, albeit sometimes with different names and with varying levels of generalizability. We note four major, general observations prompted by our results. First, most students did not evaluate solutions to physics problems using an approach that an expert would consider an evaluation strategy. Second, many students used evaluation strategies that emphasized computation. Third, many students used evaluation strategies that are not canonical but are nonetheless useful. Fourth, the relative prevalence of different strategies was highly dependent on the task context. We conclude with remarks including implications for classroom instruction.