Infinite series are known to be challenging for Calculus II students, perhaps because they lack intellectual need for the content. In their analysis of Calculus textbooks found few instances of potential intellectual needs for infinite series. This study combines a textbook analysis with interviews of four professors and observations of their…

Prior studies have identified the impact beliefs have on mathematics instructors' instructional practice, such as their choice to (or not to) lecture. However, the role of instructional context role in influencing beliefs and instruction has not been thoroughly researched. This paper explores how course context and beliefs could impact mathematics…

The lecture format, while being the subject of much criticism, is still one of the most common formats of university mathematics teaching. This paper investigates lecturing as a means of modelling mathematical discourse, sometimes highlighted in the literature as one of its most important functions. The data analysed in the paper are taken from…

This study compares the effects of student-centred teaching methods, teacher-centred methods, and teacher-student interactive methods on students' mathematics academic achievement. For this purpose, calculus, compound interest, annuities, and depreciation topics were taught to first-year college students in three different groups: traditional…

This study examined the extent to which college algebra instructors employ pedagogical practices previously found to assist students master difficult STEM content material and address their own previous math deficits. Faculty classroom behaviors were assessed with a modified version of the Generalized Observation and Reflection Platform (GORP).…

Active learning is becoming more widely accepted in mathematics as a superior teaching method for student learning and, as a result, faculty are increasingly convinced of the benefits. Our study was designed to close a research gap by determining how to support mathematics faculty in transforming their instruction to active learning. We…

The dominant image of mathematics as an abstract, universal, disinterested, and pure body of knowledge both misrepresents disciplinary practice and alienates many students. Undergraduate proof-based courses such as real analysis, which are supposed to introduce students to contemporary academic mathematics, often contribute to such idealized…

This paper investigates mathematics teaching to first year students of two mathematics departments in the context of large-group lectures. It goes beyond what may be seen as implicit in this context by focussing on the links between two lecturers' thinking about students' learning of advanced mathematics and their practice. Data includes lecture…

This paper reports findings from a case study of the impact that teaching using guided notes has on university mathematics students' note-taking behaviour. Whereas previous research indicates that students do not appreciate the importance of lecturers' non-written comments and record in their notes only what is written on the board when taught…

Background: In the US, there is significant interest from policy boards and funding agencies to change students' experiences in undergraduate mathematics classes. Even with these reform initiatives, researchers continue to document that lecture remains the dominant mode of instruction in US undergraduate mathematics courses. However, we have…

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…

As calculus instruction moves further from lecture-based instruction toward student-centered pedagogy, support services must align with the changing goals for the course. This paper describes the work of a department as they collectively design and redesign a co-requisite Calculus I course, in an effort to better promote students' academic and…

We report on a study of decision-making in mathematics lectures. The data comes from accounts of classroom incidents written over two academic years by three university mathematics lecturers who set out to reflect on, and improve, their practice by collectively engaging in a professional development project using Mason's Discipline of Noticing.…

We discuss a decade of initiatives to improve the teaching and learning of calculus at The Ohio State University. Calculus at OSU is taught in lecture/recitation format with large lectures and is tightly coordinated, so all innovations had to occur within that framework. We show how many smaller projects built upon one another to create a larger…

In this study, we examined a mathematician and one of his students' teaching journals and thought processes concurrently as the class was moving towards the proof of the Fundamental Theorem of Galois Theory. We employed Tall's framework of three worlds of mathematical thinking as well as Piaget's notion of accommodation to theoretically study the…