It is well known that there is a unique circle passing through three specified points if and only if they are non-collinear. We show that there is also a unique circle passing through the endpoints of diameters of three specified circles if and only if they have non-collinear centres.

The role of the teacher, specifically teacher craft, is central to engaging students in effective reading instruction. However, the science of reading has revealed that the content taught is also important to reading acquisition. Although the science of reading was aggregated some two decades ago to result in what became known as the five big…

A standard problem for physics students is to calculate or measure the acceleration of an object down an inclined plane. Additional information can be obtained by measuring the angular acceleration as well as the linear acceleration. An experiment is described where a billiard ball was filmed as it rolled down an inclined plane at different…

Is the natural number 7 rational? Is it complex? We argue that the answers to these questions relate to the ways numbers are taught. Commonly, a new kind of numbers is presented as an expansion of a previously familiar kind of numbers, which results in a nested image of the relations between number sets. In this article, we introduce an…

What do a short car trip, a pandemic, the wood-wide fungal web, a challenging learning experience, a storm, transport logistics, and the language(s) we speak have in common? All of them are systems, or multiple sets of systems within systems. What happens in any set of circumstances will depend on a mix of initial conditions, complexity dynamics,…

To explain successful subject matter learning with digital tools, the specification of mediating cognitive processes is crucial for any empirical investigation. We introduce a cognitive process framework for the mechanisms of learning with digital tools (CoDiL) that combines core ideas from the psychology of instruction…

Building on the original work of Bunker and Thorpe and their Teaching Games for Understanding (TGfU) approach to physical education, there is now a proliferation of Game Based Approaches (GBA) in the research literature (Bunker & Thorpe, 1982, A model for the teaching of games in secondary schools. "Bulletin of Physical Education,"…

Field experiences are often considered by researchers, leading organizations, and accrediting bodies as a critical component of special education teacher preparation. Yet, much remains unknown about the types or numbers of field experiences that will best prepare special education teacher candidates. Given the ongoing changes in the field of…

This study employed a sequential mixed methods explanatory research design to explore the influence of mentoring in the self-efficacy-forming experiences of primary school teachers who participated in a variety of professional development projects on science teaching. In the quantitative phase, survey data drawn from primary school teachers…

The increasing use of digital resources has changed the way of teaching, where platforms such as YouTube offer large repositories of educational videos. There are many theoretical studies that analyse the digital competences of teachers, but to a lesser extent on the behaviours and use that the teacher makes of this multimedia platform. Thus, the…

Purpose: It is now considered commonplace to teach in a multigenerational higher education classroom that is made up of Baby Boomers, Generation X, Y and Z students. To ensure that all students, regardless of their generational identity, are successful in the classroom, educators must teach purposefully, with an understanding of the variables that…

Students' valuing of academic content impacts their engagement in learning and plays a pivotal role in shaping their future academic and career choices. Fortunately, practicing educators can integrate many readily applicable strategies into teaching to enhance students' valuing of academic content. Drawing from expectancy-value theory, Eric M.…

When the current generation of K-12 learners has the opportunity to improve global issues and quality of life, they are inspired to advocate for worthy and ethical causes. Thus, we consider moving beyond the perspective of STE(A)M education from a workforce and global economic focus towards empathy-oriented STE(A)M learning as a humanistic pursuit…

In a span of about three days in the spring of 2023, the author's Instagram feed became inundated with mentions of artificial intelligence (AI), including Chat GPT, text-to-image models, and much more. She would turn on the radio and hear about the controversy surrounding AI, or look at her cousin's social media posts about the injustices of her…

Live cell imaging is a standard technique in experimental biology that enables the observation of isolated cells and tissue slices in real time and the testing of cellular responses to changes in buffer composition. However, most live cell imaging devices require the use of dedicated microscopes and/or specialised stage adaptors, and come at a…