International Journal of Research in Undergraduate Mathematics Education

https://link.springer.com/journal/40753

List of Papers (Total 109)

Exploring the Impact of the Corequisite Classroom Climate on Students’ Attitudes Toward Mathematics

Many postsecondary institutions across the United States have adopted the corequisite model of academic support to facilitate student learning and the successful completion of introductory mathematics courses within students’ first year of college enrollment. While research have highlighted the benefits of corequisites in terms of academic outcomes, there is little qualitative...

Impact of a Mathematics Bridging Course on the Motivation and Learning Skills of University Students

The transition from secondary to tertiary education is an exciting and yet challenging event in the educational biography of students. During this transition, students often meet with unexpected challenges, which may cause them to drop out from their degree program. Many universities offer bridging courses or longer-term interventions to support their incoming students in this...

Refutations and Reasoning in Undergraduate Mathematics

This paper concerns undergraduate mathematics students’ understandings of refutation and their related performance in abstract conditional inference. It reports on 173 responses to a refutation instrument that asked participants to: 1) state ‘true’ or ‘false’ for three statements, providing counterexamples or reasons if they thought these false (all three were false); 2) evaluate...

Measuring the Mathematical Maturity of Students in an Academic Development Programme

This study focuses on students who are registered for the University of Pretoria’s academic development programme, the Four-year Programme (FYP). The programme was introduced as a gateway for students who are under-prepared but have the potential to succeed. This programme helps them to then continue their studies in mainstream science programmes. Our research focuses on...

On-Campus vs Distance Tutorials in Preparatory Courses for Mathematics Student Teachers – Performance Gains and Influencing Factors

Due to COVID-19 pandemic restrictions, new instructional designs for mathematics courses have recently been developed. Unlike traditional e-learning courses, distance learning via videoconferencing contains more synchronous elements and is therefore more closely related to classroom instruction. Since theories of person-environment fit suggest that course modality may have an...

From Collaborative Construction, Through Whole-Class Presentation, to a Posteriori Reflection: Proof Progression in a Topology Classroom

Coming from a social perspective, we introduce a classroom organizational frame, where students’ proofs progress from collaborative construction in small groups, through whole-class presentation at the board by one of the constructors, to a posteriori reflection. This design is informed by a view on proofs as successive social processes in the mathematics community. To illustrate...

Enacting Culturally Relevant Pedagogy when “Mathematics Has No Color”: Epistemological Contradictions

Culturally relevant pedagogy (CRP) seeks to improve equity in instruction and leverage students’ experiences by promoting academic success, cultural competence, and sociopolitical consciousness. We examine instructors’ perceptions of student identity to understand the ways undergraduate mathematics instructors are enacting or experiencing barriers to enacting CRP. Interviews with...

First-Year Engineering Students’ Interpretations of Differentials and Definite Integrals

In this paper we focus on Norwegian first-year engineering students’ interpretations of differentials and definite integrals. Through interviews with 15 engineering students, we investigated how the students interpreted the different symbols involved in the Fundamental Theorem of Calculus (FTC), as displayed in the textbook used in their calculus course. Through the students...

“Find the area enclosed by...” Parceling an especially robust model of reasoning among first-year students

Mathematics education research has been aware that calculus students can draw on single definite integrals as a model to compute areas (SImA), without minding whether the function changes its sign in the assigned interval. In this study, I take conceptual and empirical steps to understand this phenomenon in more depth. Building on Fischbein’s theory, I conceptualize area as a...

Student Understanding of the Sign of Negative Definite Integrals in Mathematics and Physics

In a study of student understanding of negative definite integrals at two institutions, we administered a written survey and follow-up clinical interviews at one institution and found that “backward integrals”, where the integral was taken from right to left on the x-axis, were the most difficult for students to interpret. We then conducted additional interviews focused on...

Students’ Strategic Usage of Formative Quizzes in an Undergraduate Course in Abstract Algebra

Besides homework assignments, optional quizzes are a commonly used means for formative assessment in tertiary mathematics education. Instructors, for example, implement these to help students detect gaps in their understanding, or to foster a continuous and active engagement with the content. The extent to which these goals are reached, however, strongly depends on how students...

A Collaboratively-Derived Research Agenda for E-assessment in Undergraduate Mathematics

This paper describes the collaborative development of an agenda for research on e-assessment in undergraduate mathematics. We built on an established approach to develop the agenda from the contributions of 22 mathematics education researchers, university teachers and learning technologists interested in this topic. The resulting set of 55 research questions are grouped into 5...

Exploring the Perceived Relevance of University Mathematics Studies by First-Semester Teaching Students

As earlier research results suggest that many mathematics teaching students criticize a missing relevance in their studies, we explore explanations and interrelationships of their relevance assessments. We aim at finding out how one could support the students in attributing relevance to their study programs. A two-fold model for relevance assessments in mathematics teacher...

Undergraduate Students’ Perceptions of Features of Active Learning Models for Teaching and Learning to Teach Mathematics

The recent push toward active learning – engaging students in the learning process – is meant to benefit students. Yet there is still much to learn about students’ perceptions of this phenomenon. We share results from an interview study of students’ perceptions of features of two active learning models institutionalized at a large doctoral-granting university – a model for...

The Limit Notion at Three Educational Levels in Three Countries

This paper documents how the limit concept is treated in high school, at a university and in teacher education in England, France and Sweden. To this end we make use of vignettes, data-grounded accounts of the situation at the three levels in the three countries. These are analysed using the Anthropological Theory of the Didactic (ATD). While university praxeologies are...

‘Scaffolding’ or ‘Filtering’: A Review of Studies on the Diverse Roles of Calculus Courses for Students, Professionals and Teachers

Calculus courses have been attracting the attention of mathematics education researchers over the last decades. Recent publications and special issues dedicated to calculus highlight the diverse roles of calculus courses in the pathways for STEM studies within and across educational levels, as well as issues related to the academic preparation of future STEM professionals...

ConcepTests in Undergraduate Real Analysis: Comparing Peer Discussion and Instructional Explanation Settings

Peer Instruction, first introduced by Eric Mazur in the late '90 s, is a method aiming at active student participation in lectures. It includes conceptual questions (so-called ConcepTests) presented to the students, who vote on answer alternatives presented to them and then discuss their answers in small groups. As professors have been reported to implement several variants of...