Motivating students to watch pre-lesson videos to prepare for class is among the most significant challenges cited with flipped learning. We demonstrate boosting student preparation by up to 29% by implementing start-of-lesson quizzes. This is shown through the comparison of a flipped control group without the quizzes to flipped experimental…

This article reports on a reconceptualization of the Precalculus course experience at Florida International University. We discuss the details of the redesign process--unified within a faculty learning community (FLC) model--along with a broader change in the course sequence leading up to Calculus. We provide data, including the comparison between…

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…

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…

We derive the additive property of Poisson random variables directly from the probability mass function. An important application of the additive property to quality testing of computer chips is presented.

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 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…

A college mathematics placement test with 25 basic algebra items and 15 calculus readiness items was administered to 1572 high school seniors, and first college mathematics course grades were obtained for 319 of these students. Test results indicated that more than two thirds of the high school graduates were not college ready, and the test…

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…

The standard derivative tests for extrema and inflection points from Calculus I can be revisited subsequently from the perspective of Taylor polynomial approximations to provide additional insights into those tests, as well as to extend them to additional criteria. (Contains 3 figures.)

Group Quizzes using the Think-Share-Write strategy can be very effective in engaging students and enhancing their learning in the classroom. In this article, I describe my experiences in implementing this method in both lower division and upper division Mathematics courses. (Contains 1 figure.)