This article explores the process of finding the Fermat point for a triangle ABC in three dimensions. Three examples are presented in detail using geometrical methods. A delightfully simple general method is then presented that requires only the comparison of coordinates of the vertices A, B and C.

This article focuses on designing and conducting action research in diverse settings. Action research is a collaborative approach to problem solving. It involves consultative problem identification, reflects context, encourages reflexive examination, and ultimately encourages and empowers beneficiaries for desirable change. In that regard, it puts…

The importance of professional skills teaching and assessment within veterinary education has recently been highlighted in the veterinary education literature. This academic discourse follows the acknowledgement by both veterinary employers and graduates themselves that new graduates often lack the professional skills and attitudes needed for…

It is not typically the bent of infrastructure to be continually responsive in a way that is expansive and inclusive; instead, for newcomers or those with alternative histories, aims, vision, values, and perspectives, the inertia of infrastructure is more likely to be experienced as infrastructural breakdowns. We ask: "What might wisdom look…

How can a cognitively demanding real-world task such as the Seven Billion People problem promote productive struggle "and" help shape students' mathematical dispositions? Driving home from school one evening, Jaclyn Murawska heard a commentator on the radio announce three statements: (1) experts had determined that the world population…

Computational Thinking (CT) is pervasive in our daily lives and is useful for problem-solving. Decision-making is a crucial part of problem-solving. In the extant literature, problem-solving strategies in educational settings are often conveniently attributed to intuition; however, it is well documented that computer programmers might even have…

The ability of novice instructional designers to become skilled problem-solvers, who select and apply appropriate instructional design (ID) models in their work environments, are key competencies generally sought after in introductory ID courses. Yet, the proliferation of ID models, coupled with varied philosophies and practices about how ID is…

The Math Teachers' Circle (MTC) model is a widely implemented form of professional development that invites teachers to become practitioners of mathematics, thereby developing their fluency with mathematical practices. This article presents comparative case studies investigating the self-reported experiences of several MTC-participating teachers…

The Research Skill Development (RSD) framework was devised in 2006 to articulate what educators do when they facilitate student learning through active exploration in ways that enable their skills to grow in sophistication and rigour. This special issue of JUTLP comprises eight articles that focus on the critique, adaptation and application of the…

Rich mathematical modeling activities are crucial to giving students agency and making mathematics meaningful. Proportional reasoning and transitional algebraic reasoning are the primary topics in the prealgebra curriculum, so a need exists for meaningful modeling activities using proportional reasoning in addition to geometric modeling. In…

One of the central goals of modern science and chemistry education is to develop students' abilities to understand complex phenomena, and productively engage in explanation, justification, and argumentation. To accomplish this goal, we should better characterise the types of reasoning that we expect students to master in the different scientific…

Accurately modeling individual students' knowledge growth is important in many applications of learning analytics. A key step is to decompose the knowledge targeted in the instruction into detailed knowledge components (KCs). We search for an accurate KC model for basic equation solving skills, using data from an intelligent tutoring system (ITS),…

As in the rest of the world, teachers' roles have been changing in the Turkish educational system. In this process, their roles have been redefined as technical and social roles. In their technical roles, they focus on regular educational core tasks while in their social roles they dwell upon a wide range of social tasks besides teaching. However,…

The current industrial revolution demands a revolution on teaching methodologies at all levels, particularly for higher education. Here, we present an efficient model to teach technologies associated with Industry 4.0 (I4.0) in undergraduate engineering courses. The first step was identifying the main skills required for an I4.0 practitioner and…

The author discusses how to teach students to extend economic models using in-class scaffolding assignments, supported by discussions and workshops. Methods include discussions of a model's strengths and weaknesses; small group, in-class assignments that provide steps toward model extension; informal presentations of the work resulting from these…