Background: Sound learning design should be based on the constructive alignment of intended learning outcomes (LOs), teaching and learning activities and formative and summative assessment. Assessment validity strongly relies on its alignment with LOs. Valid and reliable formative assessment can be analysed as a predictor of students' academic…

In this paper we develop a case for introducing a new teaching tool to undergraduate mathematics. Lean is an interactive theorem prover that instantly checks the correctness of every step and provides immediate feedback. Teaching with Lean might present a challenge, in that students must write their proofs in a formal way using a specific syntax.…

In this case study we explored how a mathematician's teaching of the Cauchy-Riemann (CR) equations actualized the virtual aspects of the equations. Using videotaped classroom data, we found that in a three-day period, this mathematician used embodiment to animate and bind formal aspects of the CR equations (including conformality), metaphors,…

Knowledge required to teach mathematics at the university level is a current and relevant research topic in Mathematics Education. Thus, the case study presented in this article pertains to one mathematics lecturer whose knowledge is examined focusing on his delivery of a Multivariable Calculus course. The data required were gathered via classroom…

Active learning practices, like groupwork, are becoming more widely used in post-secondary mathematics classrooms. These practices are often talk-intensive and require interpersonal interactions. As such, it remains an open question the extent to which practices like groupwork equitably support students with different social identities, including…

In this study, we explored the effect of delayed enrollment in college-level mathematics upon entry into a 4-year university for students who were not placed into remedial mathematics (i.e. college ready). For students who attempted a mathematics course, delayed enrollment in mathematics did not have an effect on GPA, graduating within 6-years or…

Action-Process-Object-Schema (APOS) theory and the triad of schema development are used as the framework in this study to investigate students' understanding of the concept of "circle." In this report, results are presented from the data analysis of responses to questions in semi-structured interviews of 15 students enrolled in a college…

A productive understanding of rate of change concept is essential for constructing a robust understanding of derivatives. There is substantial evidence in the research that students enter and leave their Calculus courses with naive understandings of rate of change. Implementing a short unit on "what is rate of change" can address these…

Creating sustained, transformative change within and across organizations is challenging, particularly when those undertaking change act as individuals. COMmunities of Practice (CoPs) are organically created collaborations among like-minded participants, working toward a common set of goals (Lave & Wenger, 1991; Wenger-Trayner &…

This paper reports on university students' responses to an inverse proportion question. The authors conclude that inverse proportion is a difficult concept that requires constant reinforcement, using approaches to teaching that facilitate deeper conceptual understanding.

Though teacher education programs must document candidates' teaching dispositions, there is a gap in the literature around what faculty may learn by observing students in contexts outside of the k-12 classroom. This case study explores what faculty may learn about teaching dispositions by observing tutors. For our study, three mathematics…

In this article, the authors discuss how a system change framework was developed to change the way a school system worked for students. Decades of reports documented inequitable placement into and completion of remedial mathematics in the University of Wisconsin System (UW System). Incoming "undecided" students often enrolled in college…

Since Personalized Instruction increases the motivation, interest, performance and attitude of the student, it is aimed to develop an instructional management system that can be adapted to the individual, taking into account the prior knowledge level of the person who provides the personalization of all instructional materials. The project is…

Lecture capture (LC), the process of recording face-to-face lectures for future viewing, has become a common technology in Western universities in the twenty-first century, yet research on its effectiveness has lagged behind its implementation. Despite the rapid, widespread implementation, research regarding the impact LC has on pedagogy and…

Promoting equitable classrooms is a goal of postsecondary mathematics education, but there is still limited research on how faculty learn to teach more equitably. Despite the variety of techniques developed in primary and secondary education, there has been less use in higher education. This manuscript focuses on the 'assigning competence'…