In a study of student understanding of the power dissipated through simple networks of resistors, two consistent, contradictory response patterns were identified: a greater equivalent resistance always dissipates more power, and a lesser equivalent resistance always dissipates more power. After completing one of two sequences of practice-questions, the performance of students who had initially thought that less resistance meant more power improved, while the performance of the opposing group did not--despite one of the practice sequences specifically addressing the idea that more resistance means more power. Because one prior conception appears to be susceptible to practice while the other does not, specific attention must be given to interactions between differing ideas and the physical concept being taught. If an instructor only examines the performance of the entire class, an overall increase in performance might mask a misalignment between instruction and the understanding of a significant, pre-defined number of students.