Research into mathematics education at university level includes a wide range of theoretical approaches. This poses considerable challenges to researchers in terms of understanding and harmonizing the compatibility and commensurability of those approaches. The research community has already problematised and studied these challenges using…

Professors in proof-based mathematics courses often intend that the feedback they provide on students' flawed proofs will promote proof comprehension. In this theoretical article, we investigate how such feedback can be formulated. Drawing on Lakatos's process of proof and refutation, we propose the notion of "heuristic refutation…

The increased relevancy and importance of quantitative literacy (QL) have called for educational reform in undergraduate mathematics course offerings. However, lack of clear guidelines has led to wide variability in the content and outcomes of math courses meant to address QL. Therefore, having an expert consensus regarding content and outcomes…

In 1908, Felix Klein suggested that to mend the discontinuity that prospective secondary teachers face, university instruction must account for teachers' needs. More than a century later, problems of discontinuity remain. Our project addresses the dilemma of discontinuity in university mathematics courses through simulating core teaching practices…

The development of the mathematical concept of the infinite, through the reflections that arise from personal notions and perceptions and the analysis of some ideas of Galileo and Cantor, invites us to investigate the relationship between intuition and formalization for the understanding of the said concept. This paper aims to observe and describe…

This paper examines how different approaches in mathematics education conceptualise the relationship between school mathematics and university mathematics. The approaches considered here include: (a) Klein's elementary mathematics from a higher standpoint; (b) Shulman's transformation of disciplinary subject matter into subject matter for…

One way that university mathematics departments across the United States are making efforts to improve their introductory mathematics courses is by implementing or increasing the level of course coordination. This can entail creating uniform course elements for multi-section courses and efforts to build a community of practice among the…

That the manifestation of cheating varies between disciplines is rarely discussed, an unspoken assumption being that assessment takes the form of written prose supported by a bibliography. Students and academics from disciplines, such as mathematics, not fitting this model can feel that their work is regarded as an aberration. 'Plagiarism' is not…

Several major themes related to rethinking assessment emerged from a search of the papers published in "PRIMUS." Authors explored ways to change the stakes of assessments, often with outcomes-based grading and testing structures. They explored changing the "structure" of assessments by considering media beyond written exams and…

Many mathematics departments have transition to proof (TTP) courses, which prepare undergraduate students for proof-oriented mathematics. Here we discuss how common TTP textbooks connect three topics ubiquitous to such courses: logic, proof techniques, and sets. In particular, we were motivated by recent research showing that focusing on sets is…

This theoretical paper sets forth two "aspects of predication," which describe how students perceive the relationship between a property and an object. We argue these are consequential for how students make sense of discrete mathematics proofs related to the properties and how they construct a logical structure. These aspects of…

R is becoming the standard for teaching statistics due to its flexibility, and open-source nature, replacing software programs like Minitab and SPSS. The main driver for reform within Scottish statistical undergraduate programs is the creation of the Scottish Qualification Authority's Higher Applications of Mathematics course which has statistics…

This article develops an analytical framework for analysing college (tertiary) statistics textbooks in terms of text accessibility by integrating the text, the reader, and the content into the framework. Five accessibility attributes of science texts were adapted to conceptualize the accessibility of statistics texts. For each accessibility…

In the multivariable calculus course, a standard application of triple integration is to find volumes of bounded regions in R[superscript 3]. In this article, we consider the problem of computing volumes, by way of examples, of regions bounded by planes and quadric surfaces. For illustration, we present the solution to two basic but non-standard…

In this position paper, we propose commognition for the study of proof teaching at university lectures through an integrative literature review. We critically examine studies that focused on proof teaching but did not use the commognitive framework. Through this examination, we gain an understanding of the pedagogical aspects of proof teaching and…