For example, if a student listed both drawing diagrams and subproblems in their reflection then we would assign expansive=2 for that student. Likewise a student could mention a certain number of limiting strategies, e.g., if they mentioned the rolodex method and listing knowns then they would be assigned a value of limiting=2.
This allows us to define a scale for a student’s problem-solving preference
pscale=(expansive−limiting)/(expansive+limiting)
which has two limits, pscale=−1 corresponds to a student who solely describes limiting strategies, and pscale=+1 corresponds to a student who solely describes expansive strategies. The average coding between the two raters is used to calculate pscale.
The distribution of pscale for reflections written at the start of the semester is shown in Fig. 2 in the filled histograms. Only the 216 students who have written a reflection at both the beginning and end of the semester are included in this plot and the following averages. At the start of the semester many of students can be classified as using limited strategies (pscale=−1) and the class average is⟨pscale⟩pre=−0.35±0.05.