Undergraduate students study the topic of binomial series expansion as part of their Calculus course. The purpose of this study was to explore the mental constructions of binomial series expansion of a class of 159 students. Data were collected through a written assessment task by each member of the class. A convenient sample of eleven students…

Multi-voxel pattern recognition techniques combined with Hidden Markov models can be used to discover the mental states that people go through in performing a task. The combined method identifies both the mental states and how their durations vary with experimental conditions. We apply this method to a task where participants solve novel…

This study examined the hypothesis that prior experience with augmented-quotient problems would positively influence performance on remainder-only problems and quotient-only problems. Analysis of sixth through eighth grade students' (n=545) responses to test forms that systematically varied the order of appearance of these three division problems,…