Six US first-year university students in humanities or social science degree programmes were interviewed while solving 4 tasks on continuity and asymptotes in a required mathematics course. The focus was on how the students referred to the definitions or to the concept images when solving the tasks and if partial understandings appeared. Partial…

In a series of group activities supplemented with independent explorations and assignments, calculus students investigate functions similar to their own derivatives. Graphical, numerical, and algebraic perspectives are suggested, leading students to develop deep intuition into elementary transcendental functions even as they lay the foundation for…

Translating an informal mathematical argument into a proof which conforms to the norms of the mathematical community in which it is situated is a non-trivial task. Here we discuss several types of products, other than the initial informal argument and its direct formalisation, which we observed students generating in a master's level analysis…

In recent years advanced undergraduate students have developed projects for our redesigned Calculus II classes. Our student designers create new mathematics projects and present their work at conferences and in local talks. They are often mathematically early in their college careers, and so we can involve students of all levels in research…

The main purpose of this study was to present a simplified view of model metabolic cycles. Although the models have been elaborated with the "Mathematica" Program, and using a system of differential equations, the main conclusions were presented in a rather intuitive way, easily understandable by students of general courses of…

The goal of this report is to shed light on how counselors view the persistent attachment to calculus in college admissions. This report examines how high school counselors interpret admissions offices' expectations, driving their advice that students maximize calculus opportunities. The conclusions are based on a survey and interviews conducted…

In this article, we report the results of research that explores the intra-mathematical connections that high school students make when they solve Calculus tasks, in particular those involving the derivative and the integral. We consider mathematical connections as a cognitive process through which a person relates or associates two or more ideas,…

The present study details the implementation of an improvement process for a gamification activity from a Calculus course for undergraduate students aimed to develop mathematical modeling competencies. The improvement process was studied taking into account three types of data: the results of the students' performance assessment, the…

The purpose of this research was to develop a valid, practice and effective a bilingual scientific-worksheet of the indefinite integrals. This research is development research with 1) Preliminary investigation phase, 2) Prototyping phase, 3) Assessment phase. Data were collected from test and questionnaire and analyzed to examine validity,…

In this paper we report a study in which we have developed a teaching cycle based closely on Bloom's Learning for Mastery (LFM). The teaching cycle ameliorates some of the practical problems with LFM by making use of the STACK online assessment system to provide automated assessment and feedback to students. We report a clinical trial of this…

At Florida Polytechnic University, a STEM University founded in 2014, Calculus I is the first mathematics course required by students in every major. In order to ensure students received the support necessary for Calculus I, an online Primer course was developed. The course, which is housed in the online platform CANVAS, targets specific topics…

This paper reports observations and reflections from a pedagogic intervention intended to enhance mathematics students' learning of course content in a course in multivariable calculus. The intervention design required students to structure, practice, and deliver an oral presentation that was a synthesis of the teacher's weekly lectures, for the…

The purpose of this dissertation is to investigate the relationships between student persistence and students' attributes or perceptions of instructional pedagogies, as well as to examine whether the identified relationships are moderated by three different instructional settings. Improving student persistence in science, technology, engineer, and…

In the context of an analytical geometry, this study considers the mathematical understanding and activity of seven students analyzed simultaneously through two knowledge frameworks: (1) the Van Hiele levels (Van Hiele, 1986, 1999) and register and domain knowledge (Hibert, 1988); and (2) three action frameworks: the SOLO taxonomy (Biggs, 1999;…

Addressed toward course coordinators and departmental leaders interested in redesigning an undergraduate mathematics course, we highlight the steps our team at the University of Maryland, College Park has taken in bringing active learning to our Precalculus course. We provide examples of ways in which we have coordinated active learning across…