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…

The pedagogical discussion between the merits of traditional learning versus online learning provides much discussion from both camps. Following the Coronavirus of 2019 pandemic in the spring of 2020, undergraduate students enrolled in the freshman Single Variable Calculus course at the United States Military Academy at West Point were forced to…

Over the last 10 years faculty members in the Department of Mathematical Sciences at the United States Air Force Academy have incorporated individual oral exams into mathematics courses. We have experimented with various approaches, shared results and ideas with other department members, and refined our techniques. We have found that this…

There are many details to consider when designing a capstone experience. Expectations of students, faculty workload, resources, logistics, and timing all play a part in the value of this endeavor. We discuss the experience of creating a research capstone experience from scratch including the components of our current course as well as lessons…

This project served as a capstone event for the United States Military Academy sophomore Calculus II course. This multi-disciplinary problem-solving exercise motivated the link between math and biology and many other fields of study. The seven-lesson block of instruction was developed to show students how mathematics play a role in every…

This project is one of four that were issued to first semester sophomore undergraduates at the United States Military Academy as part of an integrated learning experience at the end of their Calculus II course work. This project was used during a short, seven lesson block of instruction that was intended to capitalize on their recent academic…

We discuss approaches to develop and improve habits of mind in our students. Several illustrations and strategies are offered and we demonstrate how popular culture and mystery can be used to motivate students. We offer an approach to assessing the work ethic efforts of our students based on an historical approach used at the United States…

We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

Two years ago I implemented a basic outline of each class for my students to take notes on for Calculus II at the United States Military Academy. The outline provided students with a shell of the class material for each day of class. Their job was to fill in the shell as we went through the material. The outlines provided students an easy method…

The United States Military Academy (USMA) has a four course core mathematics curriculum that is studied by all students. The third course is MA205, Calculus II; a multivariate calculus course filled with practical applications. During a Problem Solving Lab (PSL), students participated in a hands-on exercise with multiple vector operations,…