This article recounts the life of mathematician Leonhard Euler and discusses the use of Graph Theory in student learning.

In this article we show that the electrostatic field intensity of a uniformly charged straight line equals that of the corresponding arc of a circle charged with the same linear density. This new method greatly simplifies the calculation of the electrostatic field of a system consisting of uniformly charged straight lines.

Student success across environments requires professionals and families to intentionally use collaborative behaviors, such as active listening, team problem solving, and recognizing individual families' backgrounds and priorities. Engaging in collaboration can be difficult to enact within schools because educators may not be provided adequate…

Seven "habits of mind" -- ways of thinking -- create strong school cultures that invite new and veteran teachers into professional conversations to improve teaching. These habits are: remaining open to continuous learning; thinking about thinking; figuring things out; communicating; creating, imagining, and innovating; taking responsible…

US colleges and universities have long been the envy of the world. Institutional autonomy has fostered creativity among faculty, students, and staff. But this autonomy means that colleges tend to create their own solutions for every need. As a result, higher education suffers from costly redundancies that drive tuitions ever upward, putting higher…

One hundred years ago, Paul Weiss and Ludwig von Bertalanffy independently proposed that living organisms interact with their environment through systems. In the century that has followed, systems thinking and modeling have grown in tandem with discovery of the vast complexity of the universe at microscopic through astronomic levels. As our…

In this article, the author will demonstrate how gestures--often used in combination with offloading information on scratch paper--can be used to help students with difficulties in mathematics succeed with secondary level algebra. The authors will provide key examples from three studies of the algebra learning of students with mathematics…

Conflict management is one of the most stressful and frustrating aspects of a school leader's job. An inability to overcome conflicting viewpoints, ever more palpable in today's polarized climate, stymies innumerable school reform efforts. Yet, the subject is rarely examined in graduate-level leadership preparation programs or in-service…

Japanese early childhood teachers use the "mimamoru" approach, in which teachers let children develop their sense of right and wrong in a group-oriented environment where they are accountable to others. Cultural in nature, the "mimamoru" approach is based on teachers' beliefs that children are truly autonomous beings who can…

'Mathematical sophistication' behaviours are often exercised by mathematicians in their work. In this article, the importance of mathematical sophistication will be discussed and three mathematics problems that activate mathematical sophistication behaviours will be presented.

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.

Herein, we present a program implemented in Python that utilizes a simple complete-search algorithm to determine the geometry of a lanthanide-substrate (LS) complex. The program serves as a practical project in a programming course for chemistry students, specifically aimed at illustrating fundamental concepts such as decision-making, repetition,…

Whereas hackathons are widespread within and outside academia and have been argued to be a valid pedagogical method for teaching interdisciplinarity, no detailed frameworks or methods are available for conceptualizing and organizing educational hackathons, i.e., hackathons dedicated to best achieving pedagogic objectives. This paper is dedicated…

Purpose: This tutorial reviews the complexity of issues and definitions around topics of diversity. The impact of diversity and cultural responsiveness are presented in the context of ethics in the practice of speech-language pathology, audiology, and speech-language-hearing-swallowing sciences. Method: Concepts discussed include culture, cultural…

In this article, the authors introduce and illustrate a new activity that involves "follow-up equations," which are equations that follow up on ideas children have already expressed when solving fraction story problems. Specifically, teachers pose story problems and purposely attend to fraction ideas that arise in children's strategies…