Characterizing the mathematical problem-solving strategies of transitioning novice physics students

Much work has been done to characterize the reasoning of students as they solve mathematics-intensive problems and characterizing differences in expert and novice problem solving. In this work, we characterize the problem-solving strategies in a classroom setting of “transitioning novices,” students who have completed an introductory physics course and have learned some problem-solving strategies, but are far from expertlike in their reasoning. We find that students mostly use intermediate strategies that reflect an understanding of specific relationships between quantities, such as analyzing the units of an expression, to reason about mathematical expressions. Few students use more sophisticated strategies like checking limits, which require students to run mental simulations to predict how a system will behave as different physical variables are changed. The teaching of more advanced strategies like limit checking will require careful scaffolding of the cognitive complexity, as students generally do not succeed when simply told to check limits. This is supported by the findings of Lin and Singh [Phys. Rev. Phys. Educ. Res. 7, 020104 (2011)] that careful scaffolding is needed to help students solve more complex problems. In this particular group, students were able to successfully analyze the dimensions of an expression and compute component forces and torques to check if their answer made sense. Our results show that there is a need to recognize and teach these intermediary strategies to enable more novice students to check their answers and encourage students to become more expertlike.

Figure 1

Version 3 of the experimental assessment.

Figure 2

Fraction of students who used a particular strategy that arrived at the correct answers; $y$ axis measures percentages. This is equivalent to dividing the (correct) column by the total column in Table 2. No students used EL in the contrasting cases (shelf) problem, and no student successfully used IFR in the verify (ladder) problem. Strategies are grouped by the level of sophistication. The least sophisticated strategies are identifying factors, next is identifying relationships, and most sophisticated is making predictions.