Proving that a given set is indeed a subgroup, one needs to show that it is non-empty, and closed under operation and inverses. This study focuses on the first condition, analysing students' responses to this task. Results suggest that there are three distinct problematic responses: the total absence of proving this condition, the problematic…

In this report we examine students' perceptions of the implementation of carefully designed curriculum materials (called modules) in linear algebra courses at three different universities. The curricular materials were produced collaboratively by STEM and mathematics education faculty as members of a professional learning community (PLC) over…

There is evidence that spontaneous learning leads to relational understanding and high positive affect. To study spontaneous abstracting, a model was constructed by combining the RBC model of abstraction with Krutetskii's mental activities. Using video-stimulated interviews, the model was then used to analyze the behavior of two Year 8 students…

In an attempt to capture the diverse experience of undergraduates at the University of Washington (UW), the authors designed and conducted the University of Washington's Study of Undergraduate Learning (UW SOUL), a longitudinal study that tracked 304 students (about five percent of the entering freshman and transfer class) through their…

This present study investigated engineering students' conceptions and misconceptions related to derivative, particularly interpreting the graph of a function and constructing its derivative graph. Participants were 147 first year engineering students from four universities enrolled in first year undergraduate calculus courses with or without the…

In an extension of research examining student-centered pedagogy, the present case study examined how at-risk students used Alien Rescue, a problem-based learning (PBL) software program for middle school science. Twenty-nine participants were observed and interviewed over the twelve class days in which they were engaged in Alien Rescue. Students'…

This article presents two statistical tasks, one on comparing data sets, another on repeated sampling, both of which have powerful connections to proportional reasoning. Students' work and reasoning on these tasks are included, as well as suggestions for ways to use these tasks with middle school students to connect statistical thinking to…