An alternative method for obtaining analytical solutions of the time-independent Schrödinger equation (TISE) is developed and applied to 1-dimensional model quantum systems of interest in atomic and molecular physics. The method is based on proposing a wave function that is a product of two functions, one of them an integrating factor. The…

As our world becomes more complex, the skills learned in humanities classes supply our students with the flexibility needed to be successful in a rapidly changing world. Building off this idea, I wanted to take the conversation into a specific area, mathematics. Using a specific case study, I will show the importance of having a strong mathematics…

All differential equations students have encountered eigenvectors and eigenvalues in their study of systems of linear differential equations. The eigenvectors and phase plane solutions are displayed in a Cartesian plane, yet a geometric understanding can be enhanced, and is arguably better, if the system is represented in polar coordinates. A…

The author, Sirin Budak, discusses how to model the problem of a frog climbing out of a well using piecewise functions and GeoGebra.

In this article, examples are shown to demonstrate how open-ended mathematical activities can be used in the classroom. Open-ended activities give students opportunities to apply their understanding in unfamiliar contexts without the pressure of finding one perfect solution.

This study reveals the content and methodological features of professionally oriented training of engineering students in higher mathematics. The authors provide examples of applied tasks for students of different technical specialities. The relevance of this article is determined by the fact that a modern higher educational institution sets…

Two examples of mathematical modelling are explored. Firstly, optimising the distance travelled when jumping from a swing is discussed. The second concerns optimising the distance travelled by monkeys when swinging from branch to branch.

This paper describes a process of developing dance performance based and inspired by mathematical concepts and development of mathematics through history. The performance was included in the manifestation of the May month of mathematics in Serbia and prepared in collaboration with mathematicians, choreographers, dancers, science communicators and…

This curated collection covers a selection of PRIMUS articles published over a roughly 12-year period that focus on modeling and applications. The collection includes sections on individual projects, courses with a significant modeling component, and modeling and applications in extracurricular settings and throughout the curriculum.

In this paper, we extend the notion of noticing during the planning of a lesson to examine what and how teachers notice concerning the affordances of typical problems, such as examination-type or standard textbook questions. Teachers in examination-oriented educational systems generally use these types of problems to develop procedural skills.…

The complexity of understanding unit fractions is often underappreciated in instruction. We introduce a continuum of children's understanding of unit fractions to explore this complexity and to help teachers make sense of children's strategies and recognize milestones in the development of unit-fraction understanding. Suggestions for developing…

The Modelling Dance task is a mathematical modelling task that explores the relationship between mathematics and dance. The authors share the task sequence, adaptations made to support virtual implementation, and evidence of student learning related to learning goals.

As they do their work, physical therapists apply mathematical ideas. Teachers can use some of those applications to inspire students' discovery of new concepts. In particular, the joints of the human body provide a way to represent angles that is accessible to all students and can be understood in the elementary grades. Used with fourth graders,…

In this note, I present an 'easy-to-be-remembered' shortcut for promptly solving the ubiquitous integral [line integral] x[superscript n] e[superscript alpha x] dx for any integer n>0 using only the successive derivatives of x[superscript n]. Some interesting applications are indicated. The shortcut is so simple that it could well be included…

The authors present mathematics problems related to the packaging of sporting goods which they used to motivate and engage their students in the USA. This article reports on a series of questions/problems that were explored in groups by the students in a college class designed for sophomores, as part of a program to prepare them to be teachers at…