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 survey paper, we describe the state of the field on linear algebra research. We synthesize themes, questions, results, and perspectives emphasized in the papers that appear in this issue, as well as a selection of those published between 2008 and 2017. We highlight the extensive base of empirical research detailing how students reason…

In sports, it is very common to see athletes performing jumps, where they impose rotations to their own bodies' elements and intentionally change their moment of inertia around the centre of mass (CM). When this occurs, weird effects are observed in the body's trajectories. In this work we study a jump called "Grand Jeté" of a ballerina,…

Australia has used SI metric units for measurement for decades now, although the conversion of measurements from the earlier Imperial units--known as metrication--commenced subsequently in 1971, and was not completed until 1988. All Primary and Secondary schools were using only metric units in school lessons by 1973, and it became illegal to teach…

In this paper, we derive the result of the classical gambler's ruin problem using elementary linear algebra. Moreover, the pedagogical advantage of the derivation is briefly discussed.

Mathematical problems and puzzles that require commitment and perseverance to solve can help foster deep mathematics understanding in students. In this brief, the author describes factors that influence productive struggle, shares four examples of how teachers often respond to their students' productive struggles, and offers four strategies to…

Using "live editing" it is possible to write code that can be run a section at a time. This makes it easier to spot and correct errors. It can also be used to create an interactive mathematical story. This brief article shows how MATLAB software can be used to take the user on a mathematical journey with historical connections.

The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In…

Using the simplest possible quantum system--the qubit--the fundamental concepts of quantum physics can be introduced. This highlights the common features of many different physical systems, and provides a unifying framework when teaching quantum physics at the high school or introductory level. In a previous "TPT" article and in a…

The main objective of this paper is to propose a didactic framework for teaching Applied Mathematics in higher education. After describing the structure of the framework, several applications of inquiry-based learning in teaching numerical analysis and optimization are provided to illustrate the potential of the proposed framework. The framework…

Mathematical conventions -- which account for the choices of mathematics community regarding definitions of concepts, their names and symbols -- are the focus of this paper. We introduce the task of unpacking, that is, offering plausible explanations and arguments for the choice of conventions. Using responses of four prospective teachers to the…

Students often struggle with concepts from abstract algebra. Typical classes incorporate few ways to make the concepts concrete. Using a set of woven paper artifacts, this paper proposes a way to visualize and explore concepts (symmetries, groups, permutations, subgroups, etc.). The set of artifacts used to illustrate these concepts is derived…

The adoption of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) has caused a shift in the expectations for student learning, with implications for teaching. It has also introduced a new kind of standard focused on the way that students think about content in the form of the Standards for Mathematical Practice (SMP). The SMP…

The technique of "group-averaging" produces colorings of a sphere that have the symmetries of various polyhedra. The concepts are accessible at the undergraduate level, without being well-known in typical courses on algebra or geometry. The material makes an excellent discovery project, especially for students with some background in…

Robust and fast methods for chemical or multiphase equilibrium calculation are routinely needed by chemical-process engineers working on sizing or simulation aspects. Yet, while industrial applications essentially require calculation tools capable of discriminating between stable and nonstable states and converging to nontrivial solutions,…