On 24 June 1994 at Fairchild Air Force Base, during practice for an air show, a low-flying B-52H aircraft banked its wings vertically and crashed. Emphasizing the activity of modeling drag and gravity, these notes examine the possibility of recovery with several models. First, with algebra, historical data lead to a model where in a free fall near…

The subject of mathematics is important for many other subjects, including physics. The questions we ask in physics often need a mathematical translation to be graphically interpreted and transformed. Students learn physics when interacting with physical questions; questions from physics also give insights and discoveries in mathematical problems.…

Modelling roles of mathematics in physics has proved to be a difficult task, with previous models of the interplay between the two disciplines mainly focusing on mathematical modelling and problem solving. However, to convey a realistic view of physics as a field of science to our students, we need to do more than train them to become fluent in…

Working with approximations is a common practice in physics. This paper presents an exploratory study of student understanding of some of the elementary aspects of approximations encountered in college physics. For this purpose, a questionnaire (a set of 14 multiple-choice questions) was developed to probe how students dealt with these aspects in…

Physics and mathematics represent closely intertwined fields, wherein physicists employ mathematical modeling to address intricate problems. A challenge encountered by physicists involves bridging conceptual understanding with mathematical equations, a task that educators can facilitate by supporting students in navigating these two realms of…

This paper describes two examples of teaching situations in which the idea of infinity arises, and supports the conclusion that infinity is not a physical reality but a very powerful and useful mathematical device which facilitates modelling and the solution of problems in physics.

We present a complete, soup to nuts, modeling activity of a falling column of water. Many colleagues have used this material in teaching applications of first order separable differential equations. We describe how the material can be presented with students collecting their own data from online videos. One can then either offer the differential…

Optimization is a component critical to method development. Mathematical modeling of physical phenomena enables an efficient search for the parameters and conditions that optimize methods and systems. Here, optimization of methods in sonoelectrochemistry, electrochemical separations, electrochemical education, and assessment of diabetic status are…

Much has been written about Adaptive Learning, but does its implementation alone guarantee success? We have found that integrating an Adaptive Learning Strategy with diverse didactic techniques gives better results. The objectives of this exploratory study were to know the impact of the Adaptive Learning Strategy on students' learning and…

Relating mathematics learned in the classroom to real situations increases student motivation and enhances learning. In this paper, we provide an example of a classroom application of calculus to physiology in two courses: "Differential Equations" and "Calculus I for Biology and Medicine." We designed and implemented a project…

We explored the mediating role of prior knowledge on the relation between intelligence and learning proportional reasoning. What students gain from formal instruction may depend on their intelligence, as well as on prior encounters with proportional concepts. We investigated whether a basic curriculum unit on the concept of density promoted…