EXPLORING THE ORIGINS, USES, AND INTERACTIONS OF STUDENT INTUITIONS -COMPARING THE LENGTHS OF PATHS

Sixteen middle school students ranked the lengths of various paths in two audiotaped problem-solving interviews. Every student invoked at le ast one of four intuitions that originated from their everyday experie nces: compression, detour, complexity, and straightness. After their i ntuitions proved inadequate in the pretest, they were taught an applic able algorithm. However, they used their intuitions again during the p osttest before applying the instructed algorithm. The reuse of the ina dequate intuitions demonstrates their robustness and their continued h igher cueing priority despite the presence of the successful algorithm . When students applied multiple intuitions that conflicted, they ofte n vacillated. Eventually, most students chose one. Nevertheless, they continued using the rejected intuition to compare other paths. As a re sult, their problem solving suggests that their intuitions are sparsel y connected fragments. On the other hand, when intuitions support a co mmon conclusion, students may integrate them to create a larger knowle dge structure.