Students' perceptions of cost are important predictors of academic and motivational outcomes. Though cost has been described as the anticipated effort one must put forth on an activity and what an individual sacrifices to complete a task, no known work has examined the extent to which anticipated cost beliefs predict experienced cost or whether…

This paper presents 'expert opinions' on what should be taught in a first-year linear algebra course at university; the aim is to gain a generic picture and general guiding principles for such a course. Drawing on a Delphi method, 14 university professors--called 'experts' in this study--addressed the following questions: What should be on a…

In 2010 the Irish second level mathematics curriculum underwent a period of significant change when a new mathematics curriculum was introduced. Some preliminary research has been carried out into the impact, if any, that this mathematics curriculum is having on students mathematics performance which have suggested that students' procedural skills…

For many mature-aged students, there can be a considerable gap between finishing formal study and beginning university. They are often required to draw on qualifications and skills, including mathematics, which are dated, but necessary for success. Most universities offer several pathways that prospective students can take to enter university:…

This paper reports on gender and participation in one inquiry-oriented undergraduate mathematics course. While there is evidence that inquiry can better support all learners, especially women, less is known about the distribution of participation in inquiry classrooms. Here, we focus on how men and women participated in both public spaces (in…

Self-assessment has been portrayed as a way to promote lifelong learning in higher education. While most of the previous literature builds on the idea of self-assessment as a formative tool for learning, some scholars have suggested using it in a summative way. In the present study, we have empirically compared formative and summative models for…

Many randomized controlled experiments in the classroom have found that mathematics learning is improved dramatically when practice problems of one kind are distributed across multiple assignments (spaced) and mixed with other kinds of problems (interleaved). In two studies, we investigated students' knowledge of spacing and interleaving. In Study…

Modeling projects in differential equations and engineering courses create an authentic activity and an opportunity to attain the holy grail of "deeper" learning. However, what do we mean by "deeper" learning and how do we create an environment that encourages that? This article describes a proposal and case study in using…

The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to…

In this work, students' thinking modes and representation types in linear algebra are investigated through statistical implicative analysis techniques. Specifically, our research question considers the implicative relationships between students' thinking modes and representation types of linear algebra. The participants were 74 undergraduate…

This study focuses on the undergraduate mathematics students' perceptions and applied techniques for the preparation for their final examination in Abstract Algebra. The results of this study suggest that the revision for the final examination involves, firstly, the review of the lecture notes, followed by the solution of the coursework together…

In this paper I explore eleven undergraduate students' comprehension of a proof taken from an undergraduate abstract algebra course. My interpretation of what it means to understand a proof is based on a proof comprehension model developed by Mejia-Ramos, et al. (2012). This study in particular examines the extent to which undergraduate students…

This article presents a project that is meant to deepen student understanding of what it would mean for one preference voting method to be "better" than another. In the project we show the students how to rigorously compare the methods of plurality and plurality with elimination, and we then allow them to compare two other voting methods…

The use of fully online instruction has been proliferating in higher education. In undergraduate mathematics, arguments about the effectiveness of fully online instruction have been met with contrasting claims about its potential. Some assert that fully online instruction can promote a deeper and richer conceptual understanding of mathematical…

In this paper we present two simulations designed with GeoGebra that illustrate dynamically a key concept in Vector Calculus: line integrals of vector fields, along with other associated mathematical properties and applications. Students are not required to know the GeoGebra environment: a user-friendly interface with buttons, functionalities and…