Graduate teaching assistants (TAs) are an important group of math instructors whose practice deserves to be supported and studied. In this action research study, I lead a customized regimen of professional development (GQuesT model) for a cohort of first/second-year calculus TAs and study their teaching practice. This study focuses on how the TAs…

On a typical day in a university precalculus classroom, as students arrive, they settle into their small groups and begin sharing their ideas and questions from the homework assigned the previous night. It can be quite challenging to create a learning environment in which students engage in mathematical thinking outside class and are prepared to…

Most word processors, including Google Docs™ and Microsoft® Word, include an equation editor. These are great tools for the occasional homework problem or project assignment. Getting the mathematics to display correctly means making decisions about exactly which elements of an expression go where. The feedback is immediate: Students can see…

We describe recent attempts by the University System of Georgia to develop and pilot a system-wide online Precalculus course for credit. The course was based on full online delivery, using an emporium model for learning. We experienced moderate success with the course, with a completion rate of 61-76% compared with the 4-7% for Massive Open Online…

The teaching of probability has changed a great deal since the end of the last century. The development of technologies is indeed part of this evolution. In France, continuous probability distributions began to be studied in 2002 by scientific 12th graders, but this subject was marginal and appeared only as an application of integral calculus.…

Guessing, for Pólya, is an important way of getting an initial handle on a mathematical problem. An argument can be made to place guessing in any one of the first three steps of the four-step approach to problem solving as described in "How to Solve It" (Pólya 1945). It could be a part of understanding the problem, devising a plan, or…

We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque…

Throughout the school year, AP Calculus teachers strive to teach course content comprehensively and swiftly in an effort to finish all required material before the AP Calculus exam. As early May approaches and the AP Calculus test looms, students and teachers nervously complete lessons, assignments, and assessments to ensure student preparation.…

Making the transition from calculus to advanced calculus/real analysis can be challenging for undergraduate students. Part of this challenge lies in the shift in the focus of student activity, from a focus on algorithms and computational techniques to activities focused around definitions, theorems, and proofs. The goal of Realistic Mathematics…

The flipped classroom is becoming a popular course structure in many academic disciplines, but particularly in STEM disciplines, including mathematics. Considerable research has addressed potential advantages and challenges of teaching a flipped course, as well as examining students' attitudes towards the flipped classroom. Studies on students'…

In this paper I discuss the motivation behind using an introduction to Fourier series as a method to unify the topics of integration techniques and series calculations in a Calculus II course.

Student understanding of integration has become a topic of recent interest in calculus research. Studies have shown that certain interpretations of the definite integral, such as the area under a curve or the values of an anti-derivative, are less productive in making sense of contextualized integrals, while on the other hand understanding the…

Research on the test structure of the Force Concept Inventory (FCI) has largely ignored gender, and research on FCI gender effects (often reported as "gender gaps") has seldom interrogated the structure of the test. These rarely crossed streams of research leave open the possibility that the FCI may not be structurally valid across…

The use of web based software for learning opportunities abound, but what impact do they have on students' mathematics learning beyond the initial experience? This 2-phase, 17-month case study of 50 freshmen investigates the use of web-based learning and face-to-face lecture on students' future academic achievement in mathematics. First, the study…

Large foundational courses delivered in lecture halls are disadvantaged in eliciting participation from all students and maintaining engagement throughout the class session. We introduced a question-driven method facilitated by an audience response system, namely TopHat™, that allows the instructor to engage students in solving Calculus problems…