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…

The present study explores students' understanding of calculus-based kinematics (henceforth, CBK), in which argumentation is taken as the sequence of the modes of fostering reasoning and problem-solving. The investigation stresses the importance of arguments students bring to the learning situation of CBK and recognizes the active construction of…

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…

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…

The calculus concepts of concavity and inflection points are critical for a complete understanding of quantities' behavior, making them important topics of research for those interested in the intersections of STEM disciplines. This study seeks to provide insight into this area by reporting on trends in students' concept projections of these…

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…

The fundamental theorem of calculus (FTC) plays a crucial role in mathematics, showing that the seemingly unconnected topics of differentiation and integration are intimately related. Indeed, it is the fundamental theorem that enables definite integrals to be evaluated exactly in many cases that would otherwise be intractable. Students commonly…

The literature emphasizes the interest and need to learn the concept of continuity with understanding, although this meaning it is not consensual nor specified how it may emerge and be developed in the learning process. In this paper we report the results of a study aiming to analyse Brazilian preservice mathematics teachers' understanding of the…

This paper gives a blueprint for reacting to the various issues that an instructor will face in their day-to-day life as the manager of a Mastery-Based Testing (MBT) classroom. For example, I created a rubric to compare traditional testing with MBT, adapted my office hours to accommodate more retake opportunities, and required effort between…

Common student errors and misconceptions can be addressed through the method of classroom voting, in which the instructor presents a multiple-choice question to the class, and after a few minutes for consideration and small-group discussion, each student votes on the correct answer, using a clicker or a phone. If a large number of students have…

Understanding students' readiness for precalculus and calculus at the community college level is critical not only because of the key role community colleges play in higher education but also because calculus remains a gateway course for students in advancing to higher level mathematics. The Algebra and Precalculus Concept Readiness Assessment for…

This article uses action-process-object-schema theory to study the mental constructions about the limit of series during a Calculus 1 course at a university. The researchers also used the theory's teaching methodology to teach the topic. A plethora of research on the limit concept is available and suggests that the concept is on record as being…