In this work we critically examine a mnemonic designed for the pedagogy of first-order ordinary differential equations. The particular mnemonic takes the form of the SHIELDS acronym. We perform a critical analysis on mnemonics, outlining some of their benefits and limitations from the literature. As a result, we propose a general mnemonic model…

How should our students think about external forcing in differential equations setting, and how can we help them gain intuition? To address this question, we share a variety of problems and projects that explore the dynamics of the undamped forced spring-mass system. We provide a sequence of discovery-based exercises that foster physical and…

Solving systems of linear equations is of central importance in linear algebra and many related applications, yet there is limited literature examining the symbolizing processes students use as they work to solve systems of linear equations. In this paper, we examine this issue by analyzing final exam data from 68 students in an introductory…

This study examined the genre of undergraduate mathematical proof writing by asking mathematicians and undergraduate students to read 7 partial proofs and identify and discuss uses of mathematical language that were out of the ordinary with respect to what they considered conventional mathematical proof writing. Three main themes emerged: First,…

The purpose of this mixed-methods study was to explore how undergraduate students in an applied calculus course used the written curriculum (i.e., textbook, online homework system, and previous exams). The study design included three phases: (a) an online survey, (b) individual observations, and (c) student interviews. Students' survey responses…

This paper describes a research project implemented in a course of Real Analysis II. The aim of this project is to analyse students' comprehension of the limiting behaviour of a function from "R"[superscript 2] to "R" at a point "P"[subscript 0] focusing on the formal definitions. Alternative definitions and other…

Although there is extensive research on attrition in gatekeeper courses and students' cognition about calculus concepts, there is one population in introductory calculus that remains understudied: those who failed their initial course and chose to repeat it rather than change majors. These students can provide insight into overcoming poor…

The following research focuses on Game-Based Learning (GBL) for assessment through the lens of designing and validating a stealth assessment for the calculus game Variant: Limits™. The process of using Evidence-Centered Design (ECD) to create a valid assessment is highlighted through the development of a competency model and scoring rubrics. A…

We describe the use of student-generated video content to assess students' engagement with, and understanding of, problem-solving skills. In this framework, students are tasked with using technology to create videos that show them working through, and explaining solutions to, challenging calculus exercises. The videos are then posted online,…

At the college level, it can be difficult to engage students outside the classroom through the use of effective homework assignments. Although it is straightforward to create assignments that test the ability to carry out computations as discussed in class, it is more challenging to create assignments that encourage students to think more…

Governmental and educational organizations have pointed out that students coming into the biological sciences require stronger skills in statistics and data modeling that are not usually addressed in typical engineering-based calculus courses. Our work here documents how faculty in biology and mathematics addressed this issue at a large urban…

This article describes the revision of a Business Calculus course at a medium-sized, northwestern university. The purpose of this manuscript is to describe the need for a redesign of the Business Calculus course, conversations among math and business faculty about the course changes, the development of the new course, and the addition of a…

Over the past 9 years, we have implemented, developed, and refined a novel student-centered teaching method called Extreme Apprenticeship in university mathematics context. In this paper, we report the theoretical orientation behind the method, as well as its practical implementation. We also reflect on our experiences gained from using it in our…

In this article, the authors propose a department-level curricular committee structure, called Strand Committees, as a mechanism to facilitate oversight and enact significant change to policies and practices in specific courses. The primary goal of the Strand Committees is improving both student success and instruction while upholding a high…

What do you do when a change in enrollment policies leaves you with more than 600 students in a first-term university calculus class, three-quarters of those students had a failing mark in mathematics in the pre-enrollment test, you planned a series of remedial activities for the second term, and the COVID-19 pandemic shuts the university down…