This paper aims to contribute to the growing field of research on teaching practices in higher education, with a focus on the prevalent yet unresearched practice of concept introduction in lectures. This small-scale case-study provides data which lend themselves to a comparative analysis, with a view to describing and accounting for the dispersion…

Flipped classrooms are increasingly popular due to improvements in online technology and expected benefits in student engagement and learning. Although research has increased dramatically in the last 10 years, few studies have assessed the effectiveness of flipping large enrollment, barrier mathematics courses. Creating a comprehensive flipped…

Flipped instruction is increasing in popularity, however research that moves beyond descriptions of its implementation in mathematics classes is lacking. We sought to better understand how students taking an introductory college algebra course used the resources provided within a flipped instructional model and how students viewed such resources…

This study aims to evaluate the consistency of teaching content with teaching approaches in calculus on the basis of lecturers' views. In this sense, the structures of the examples given in two commonly used calculus textbooks, both in traditional and reform classrooms, are compared. The content analysis findings show that the examples in both…

This paper reports on a study about how the mathematics textbook was perceived and used by the teacher in the context of a calculus part of a basic mathematics course for first-year engineering students. The focus was on the teacher's choices and the use of definitions, examples and exercises in a sequence of lectures introducing the derivative…

This paper describes a case study of two pure mathematicians who flipped their lecture to teach matrix determinants in two large mathematics service courses (one at Stage I and the other at Stage II). The purpose of the study was to transform the passive lecture into an active learning opportunity and to introduce valuable mathematical skills,…

This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused…

A group of mathematicians and mathematics educators are collaborating in the fine-grained examination of selected "slices" of video recordings of lectures, drawing on Schoenfeld's Resources, Orientations and Goals framework of teaching-in-context. In the larger project, we are exploring ways in which this model can be extended to examine…

Lectures have been widely criticized as a method of teaching, but remain a standard component of most university mathematics courses. Does this necessarily harm students' education? This critical review contends that many arguments against lecturing are misconceived, at least when applied to mathematics. The effectiveness of lectures in carrying…

This article describes a qualitative study which was undertaken to improve the delivery methods and feedback opportunity in honours mathematics lectures which are delivered through Access Grid Rooms. Access Grid Rooms are facilities that provide two-way video and audio interactivity across multiple sites, with the inclusion of smart boards. The…

In this article, I present some "axioms" that relate to undergraduate mathematics education. When I first heard the word axiom, it was defined as a "self-evident truth"; but an axiom is not a truth, it is a subjective assumption on which an argument or proof can be based. My purpose in presenting these axioms is to stimulate debate about…

This study documents students' views about the nature of mathematics, the mathematics learning process and factors within the classroom that are perceived to impact upon the learning of mathematics. The participants were senior secondary school students. Qualitative and quantitative methods were used to understand the students' views about their…

This paper describes some of the myths on training lecturers in mathematics, discusses briefly the nature of teaching and learning, and suggests some ways of analyzing the tasks in teaching and learning. (Author/MK)