The metaphors that students form and encounter have been shown to exert a powerful influence on how they think about mathematics. In this paper, we explore the linguistic metaphors about learning and doing mathematics that were prevalent in 11 advanced mathematics lectures. We present four metaphor clusters that were common in the corpus that we…

We were interested in exploring the extent to which advanced mathematics lecturers provide students with opportunities to play a role in considering or generating course content. To do this, we examined the questioning practices of 11 lecturers who taught advanced mathematics courses at the university level. Because we are unaware of other studies…

We describe a case study in which we investigate the effectiveness of a lecture in advanced mathematics. We first videorecorded a lecture delivered by an experienced professor who had a reputation for being an outstanding instructor. Using video recall, we then interviewed the professor to determine the ideas that he intended to convey and how he…

This case study investigates the effectiveness of a lecture in advanced mathematics. We video recorded a lecture delivered by an experienced professor. Using video recall, we then interviewed the professor to determine the content he intended to convey and we analyzed his lecture to see if and how this content was conveyed. We also interviewed six…

In this article students' understanding of trigonometric functions in the context of two college trigonometry courses is investigated. The first course was taught by a professor unaffiliated with the study in a lecture-based course, while the second was taught using an experimental instruction paradigm based on Gray and Tall's (1994) notion of…