Students’ thinking about problem solving tasks: the case of initial value problems

Abstract

Contributing to research on undergraduate students’ thinking about problem solving tasks, the present study reports on students’ reasoning about two initial-value problems i.e. first-order linear ordinary differential equations with initial conditions. A qualitative analysis of task-based interviews and work written by 34 students revealed that although the students knew the algebraic steps they had to use to solve the two problems, 16 students reported that steps involving integral calculus were particularly challenging. In fact, a majority of these students exhibited lack of facility with the u -substution integration technique, something that severed as a stumbling block for them when calculating the integrating factor in their attempt to solve the two problems. Only seven students were successful in mathematizing one of the problems. Five students created and used diagrams to support their thinking when solving one of the problems. These students reported that the creation of the diagrams helped them to solve one of the two problems. Overall, findings of this study suggest that helping students develop greater facility with integration techniques, and more broadly integral calculus, could increase students’ success when solving initial-value problems. Implications for instruction and directions for future research are discussed.