Differential equations are widely used tools for modelling the world around us, making a course in differential equations a natural place for students to connect concrete mathematical applications to abstract concepts. Since students grasp the concepts better by applying them, introducing differential equations through modelling becomes essential.…

We believe that developing cultural competencies can help students learn mathematics and conversely that learning mathematical content can help students learn about themselves and others. Using frameworks introduced by Rendón (2009) and Gutiérrez (2018), we present a five-part bundle of activities for undergraduate differential equations course…

In the past, my mathematics students have frequently complained at any suggestion that they should communicate ideas through the medium of a written report. This article discusses student responses when they were asked to write a short report for the mayor of a (hypothetical) small town in response to the mayor's plan to eliminate a contagious…

Academic integrity at our small Canadian college is informed by several key frameworks and centred around teaching, learning, and proactive education. Mathematics assessments were quickly moved through various learning environments over the past year, showing that some assessment design strategies were no longer feasible if they instead centred on…

In this classroom note, we describe the use of a wiki to aggregate student solutions to calculation-based mathematics problems. We outline the setup of the wiki used to support this project, the administrative issues involved in running a wiki, and student reaction to the wiki project. We will describe how students participated, and were assessed,…

In this note, we report on an implementation of discovery-oriented problems in courses on Real Analysis and Differential Equations. We explain a type of task design that gives students the opportunity to conjecture, refute and prove. What is new is that the complexity in our problems is limited and thus the tasks can also be used in homework…

A literature review establishes a working definition of recreational mathematics: a type of play which is enjoyable and requires mathematical thinking or skills to engage with. Typically, it is accessible to a wide range of people and can be effectively used to motivate engagement with and develop understanding of mathematical ideas or concepts.…

FOIL is a well-known mnemonic that is used to find the product of two binomials. We conduct a large sample (n = 252) observational study of first-year college students and show that while the FOIL procedure leads to the accurate expansion of the product of two binomials for most students who apply it, only half of these students exhibit conceptual…

Rarely do university departments of mathematics redesign their basic mathematics courses. Through developing an online version of our associate degree in engineering in collaboration with Open Universities Australia, we redesigned the first in a sequence of five engineering mathematics courses. The online cohort proved different to our…