The present paper explores the relationship between attitudes towards mathematics (ATM) and achievement in college calculus in active learning (AL) and lecture-based (LB) classrooms. Previous work on this relationship has mainly been limited to LB instruction, neglecting the impact of innovative approaches such as AL. Less attention has been paid…

The COVID-19 pandemic has posed one of the most challenging situations for the academicians as well as the students all around the world. Students being the biggest stake holders of the education process, their challenges during this pandemic become even more pivotal. These challenges vary in intensity and type depending on multiple items. In this…

Mathematical modelling has great potential to motivate students towards studying mathematics. This article discusses several different approaches to integrating research work with a second-year undergraduate, mathematical modelling subject. I found sourcing papers from the areas of epidemiology and ecology to be a fruitful source area,…

In this paper, we explain changes made in an introductory Real Analysis classroom that address common challenges and that may allow for all levels of students to meet a high standard of learning and written work. We aim for this goal by fusing elements of a hybrid course with scaffolded collaborative work to improve student learning. The hybrid…

Expert mathematicians use examples and visual representations as part of their informal mathematics reasoning when constructing proofs. In contrast, the ways undergraduates reason and work toward creating proofs is an open area of investigation, particularly in advanced mathematics. Furthermore, research on students' reasoning in topology is…

Even though K-12 mathematics educators have embraced the role of graphing calculators and computers, student use of technology in tertiary mathematics has been slow to implement in the USA context. Enter March 2020, a global health crisis, and the shift to online and remote learning. The immediate and dramatic cessation of in-person modes of…

The paper describes active learning strategies used in undergraduate college algebra and business calculus courses. There are a variety of active learning strategies described in the literature. We wanted to implement a few that together, satisfy the key characteristics of active learning strategies. The active learning strategies described in…

We describe the design and evaluation of an innovative course for beginning undergraduate mathematics students. The course is delivered almost entirely online, making extensive use of computer-aided assessment to provide students with practice problems. We outline various ideas from education research that informed the design of the course, and…

We investigate aspects of reform enacted in 66 class observations from 18 institutions collected as part of the National Study of University Calculus in the US. We examined four aspects related to how problems were solved in class: the extent of student involvement, the representations and technology used, and specific features of the problems…

This study used task-based interviews to examine students' reasoning about multivariable optimization problems in a volume maximization context. There are four major findings from this study. First, formulating the objective function (i.e. the function whose maximum or minimum value(s) is to be found) in each task came easily for 15 students who…

In this paper we explore the difficulties engineering undergraduates encounter with tertiary mathematics. Results from our survey (N = 71) show that students in our sample face issues mostly related to the challenging nature of university mathematics, the absence of worked examples during lectures and the discontinuity of school and university…

Greater flexibility with procedures is known to be associated with greater conceptual knowledge of mathematics and vice versa. In parallel, a student's emotional relationship to mathematics -- i.e. their 'affect' -- is known to influence how they learn and perform in mathematics. For example, a confident student may engage more fully with…

This study aims to explore the notion of the density of the set of rational numbers in the set of real numbers, as interpreted by undergraduate mathematics students. The data comprise 95 responses to a scripting task, in which participants were asked to extend a hypothetical dialog between two student characters, who argue about the existence of…

Despite the importance and many applications that parametric equations and curves have in mathematics and other sciences, there is a lack of research regarding this topic in mathematics education. The goal of this article is to explore university students' understanding of parametric equations and curves based on two lenses: Action, Process,…

In this paper, we consider the perceived effectiveness of using industry-based transdisciplinary, complex problems as a vehicle for final year undergraduate mathematics students to apply their knowledge and skills in realistic settings, preparing them for the world of work. The discussion centres on a recently designed, implemented and evaluated…