As it is already observed by mathematicians and educators, there is a discrepancy between the formal techniques of mathematical logic and the informal techniques of mathematics in regards to proof. We examine some of the reasons behind this discrepancy and to what degree it affects doing, teaching and learning mathematics in college. We also…

Background: Calculus instruction is underexamined as a source of racialized and gendered inequity in higher education, despite research that documents minoritized students' marginalizing experiences in undergraduate mathematics classes. This study fills this research gap by investigating mathematics faculty's perceptions of the significance of…

The Mathematical Association of America's "Precalculus to Calculus: Insights and Innovations Conference" brought together representatives of mathematics departments from across the country with members of two national research projects to share and discuss both research findings and on-the-ground concerns of faculty. In this article, we…

This study describes how nine university professors managed their teaching when a shift from lecturing to inquiry-based learning was mandated in a large enrollment course, linear algebra for math majors. We describe the tensions that emerged and how they were resolved, in part via the production of worksheets that were used in teaching. We…

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 study investigated the ways in which college algebra students watch mathematics instructional videos about completing the square with the goal of identifying student responsibilities within a particular video and across different videos. Guided by the theory of didactic situations that has defined implicit teacher and student responsibilities…

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…

In the calculus classroom, integrating applications with the theoretical and procedural conveys the relevance of the material. Since Newton and Leibniz developed calculus in the context of physics and astronomy, applications in these fields tend to predominate. To engage and excite our students, pedagogical considerations must include broader…

Recreating the social aspects of face-to-face teaching in an online environment became more challenging in the midst of the COVID-19 pandemic. With limited or no face-to-face interaction with students, lecturers had to explore alternative ways to recreate aspects of an engaging and supportive face-to-face learning environment. This article focuses…

Mathematics faculty created a model for intermediate algebra integrating principles from the science of learning. The redesigned curriculum revolved around two big ideas (solving and graphing) and provided students with information about the formation of long-term memories, the benefits of distributed practice, the impact of physiological aspects…

Income inequality is a central social justice concern, and hence excellent motivation for real-world applications in mathematics classrooms at every level. We describe the "Mathematics for Social Justice" course at Saint Michael's College, giving a specific example of one of the typical social justice projects for the course, and showing…

During the Spring 2020 semester, universities transitioned to online instruction to slow the spread of COVID-19. During this time, mathematics support/tutoring centers also moved their services online. We discuss best practices for online tutoring from the literature and the shared experiences of 28 tutoring center leaders who transitioned to…

As a consequence of the COVID-19 pandemic and measures to secure public health, many processes have moved to the online space. The educational process is not an exception. Our main goal, which is presented in this article, was to re-design the educational process from face-to-face to distance learning in the Mathematics 1 course at the Technical…

In this paper we report on a survey designed to test whether or not students differentiated between two different types of problems involving combinations--problems in which combinations are used to count unordered sets of distinct objects (a natural, common way to use combinations), and problems in which combinations are used to count ordered…