The retention of fundamental mathematical skills is imperative to provide a foundation on which new skills are developed. Educators often lament about student retention. Cognitive scientists and educators have explored teaching methods that produce learning which endures over time. We wanted to know if using spaced recall quizzes would prevent our…

Most teachers of mathematics think that regular practice is essential for success. In face-to-face instruction settings, regular practice requires doing homework, which has to provide students with feedback in order to be useful. Online homework allows teachers to assume the workload involved in providing feedback to a large number of students…

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…

Specifications grading is a version of mastery grading distinguished by giving students clear specifications that their work must meet, and grading most things pass/fail based on those specifications. Mastery grading systems can get quite elaborate, with hierarchies of objectives and various systems for rewriting and retesting. In this article I…

Research across five countries has identified inability to pay attention to mathematical detail -- the discipline of noticing -- is an issue in senior secondary school mathematics teachers. The test and questionnaire completed by an Australian cohort further identifies a reluctance to employ non-routine questions in assessments, with teachers…

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…

The Advanced Placement® (AP®) Program offers high school students the opportunity to take rigorous coursework in high school and receive college credit for AP Exam scores that meet or exceed the requirements of their attending institution. Students receiving AP credit are typically exempted from an introductory level course or series of courses…

Calculus courses often present a large number of difficulties to undergraduate students of scientific studies, especially in engineering degrees. These difficulties are sometimes related to teaching and assessment strategies. In this paper, a teaching innovation experience is presented within the framework of the Universitat Oberta de Catalunya.…

As STEM educators, we know it is beneficial to train students to think critically and mathematically during their early mathematical lives. To this end, the author teaches the College Algebra/Precalculus course in a flipped classroom version of an inquiry-based learning style. However, the techniques described in this paper can be applied to a…

This paper describes investigations in visualizing logpaths of students in an online calculus course held at Florida State University in 2014. The clickstreams making up the logpaths can be used to visualize student progress in the information space of a course as a graph. We consider the graded activities as nodes of the graph, while information…

High failure rates in calculus have plagued students, teachers, and administrators for decades, while science, technology, engineering, and mathematics programmes continue to suffer from low enrollments and high attrition. In an effort to affect this reality, some educators are "flipping" (or inverting) their classrooms. By flipping, we…

This paper describes the results of a two-semester-long study of the effects of student-centered instruction on Precalculus courses. We also describe our teaching approaches centering around students, which include a mixture of lectures, student presentations, group work, discussion, and guided investigations. Students were taught with either the…

In this study we aimed to understand who was struggling in freshman calculus courses, and why. Concentrating on the Fall sections of the class, the best predictors for success (R[superscript 2] = 0.4) were placement test results, the student's own appraisal of the quality of mathematics teaching they received in high school, and the Motivated…

Videos have been used in classrooms for decades, but student-produced video has recently become a viable, economical option to enhance learning. Students were asked to create videos to be used for their exam review in two different undergraduate mathematics courses: Differential Equation and Complex Analysis. Students were then surveyed about…

Partial fraction decomposition is a useful technique often taught at senior secondary or undergraduate levels to handle integrations, inverse Laplace transforms or linear ordinary differential equations, etc. In recent years, an improved Heaviside's approach to partial fraction decomposition was introduced and developed by the author. An important…