Researchers from many countries have pointed out the difficulty of transitioning from high school to university settings, especially within the context of mathematics courses. With its abstract content, deductive thinking structure, and unique language, university mathematics is quite different from high school mathematics for students…

Active learning is becoming more widely accepted in mathematics as a superior teaching method for student learning and, as a result, faculty are increasingly convinced of the benefits. Our study was designed to close a research gap by determining how to support mathematics faculty in transforming their instruction to active learning. We…

In this study, we investigated the literacy practices of undergraduate calculus students and non-mathematics STEM faculty members as they read excerpts from a calculus textbook. We found several differences in their practices that appeared to be tied to the didactical nature of the excerpts and the participants' identities and power relationships…

Most institutions of higher learning offer undergraduate mathematics tutoring, yet little is known regarding the work tutors do or the knowledge needed to enact that work. We explore the mathematical knowledge needed for the work of undergraduate peer drop-in mathematics tutoring. The data consists of transcripts from eight stimulated recall…

In this article, an analysis of six fisheries biology assignments involving mathematical models is conducted, focusing on the type of participation that they offer. The purpose of the analysis is to identify the characteristics of the mathematical discourse of the assignments and to expose their relationship with the biological context with the…

Despite the prevalence of undergraduate drop-in mathematics tutoring, little is known about the behaviors of this specific group of tutors. This study serves as a starting place for identifying their behaviors by addressing the research question: what observable behaviors do undergraduate drop-in mathematics tutors exhibit as they interact with…

While many aspects of the teaching and learning of specific advanced mathematics courses have been studied, limited work has examined mathematical themes like sameness or its instantiations across disciplines. In this paper, we explore algebraists' collective example space for mathematical sameness. We used qualitative methods to analyze survey…

Peer Instruction, first introduced by Eric Mazur in the late '90s, 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…

Undergraduate concepts are often first introduced in a single-dimensional setting and then extended to multiple dimensions. For instance, many undergraduate real analysis students will first learn of the metric topology on [set of real numbers] before being exposed to more general metric spaces. I conducted a paired teaching experiment (Steffe…

The success of the teaching - learning process in terms of learning outcomes is determined by several factors, primarily the lecturer's teaching approach used. Despite the importance of the teaching approach, little is known concerning the teaching approaches used by mathematics lecturers in Tanzanian higher education institutions. This study…

Proof by mathematical induction poses a persistent challenge for students enrolled in proofs-based mathematics courses. Prior research indicates a number of related factors that contribute to the challenge, and suggests fruitful instructional approaches to support students in meeting that challenge. In particular, researchers have suggested…

Fractals describe many natural phenomena; their strong visual-figurative nature found its mathematical conceptualization in the concept of self-similarity. In the current study, we investigate how students construct (fully or partially) the self-similarity concept while recursively constructing the Sierpinski triangle, working in small group and…

Recent research on integration has shown the importance of quantities-based meanings for integrals. However, this research body is still in need of detailed empirical accounts of "how" students develop such understandings across an entire unit on integration. This paper contributes by providing one such account, based on a…

"Representational transformation diagrams" are used to compare and contrast standard textbook presentations of vector line integrals in undergraduate courses in both mathematics and physics. These presentations are taken as the lower anchor in a learning trajectory. Two principal approaches in the lower division are identified, roughly…

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…