Teaching approaches have been shown to be an important aspect of teaching in school or higher education. Although differing approaches to teaching may play a role in the outcome of professional trainings, they have not yet been further studied in this context. It is first necessary to determine whether the existing approaches to teaching construct…

In this article, Mark Colyvan argues that formal mathematical notation is more than just the language of mathematics. He gives examples of where notation plays a role in extending mathematical theory and in delivering explanations. He concludes that good mathematical notation, in both mathematics and empirical domains, helps us to think,…

In this paper, Richard Ollerton presents two alternative approaches to proving the six standard trigonometric angle sum and difference identities. They are suitable for students who have an understanding of rotation matrices.

This manuscript outlines the possible benefits of nonconscious behavioural mimicry (NBM) to Physical Education (PE). The identification of NBM as an unexamined phenomenon in PE will be explored, as well as factors mediating its occurrence. Further, this manuscript will discuss the speculated origins of this phenomenon within the human species.…

The authors consider in this critical paper that claims that human agents experience things-in-the-world as the same are deeply flawed as these accounts misconstrue and fail to appreciate the phenomenology of embodied subjectivity. To overcome these complex problems they outline how phenomenology can reach beyond positivist and standardised…

This article provides a detailed guide for Physical Educators with limited volleyball knowledge to teach the sport with a tactical approach, hopefully resulting in more skilled students.

Creativity plays an important role in mathematics, but it can be overlooked in undergraduate courses. This article describes three ways an existing first-year math seminar was modified to increase its focus on creativity: introducing readings and discussions related to creativity, drawing connections to creativity in other disciplines, and adding…

To design and improve instruction in mathematical proof, mathematics educators require an adequate definition of proof that is faithful to mathematical practice and relevant to pedagogical situations. In both mathematics education and the philosophy of mathematics, mathematical proof is typically defined as a type of justification that satisfies a…

Research on productive failure suggests that attempting to solve a problem prior to instruction facilitates conceptual understanding compared to receiving instruction prior to problem solving. The assumptions are that during the problem-solving phase, students activate their prior knowledge, become aware of their knowledge gaps, and discover deep…

To avoid cultural appropriation, music educators need to take the time to explore the source culture and approach the traditions of others in a respectful manner so the people and musics studied are neither demeaned nor exploited. Students can be part of this exploration and share what they learn from their research with the class.

The use of photography representing human distress in higher education warrants moral attention, owing to the imperative that we avoid objectifying the vulnerable communities who are often represented in those images. Assuming the fundamental Kantian precept that we should always treat others as ends and never merely as means, I extend this…

Skills in discussing substantive issues are vital in any job or civic role--and even in family life. Anne Vilen and Ron Berger, leaders in the Expeditionary Learning Schools network, detail how Casco Bay High School and other EL schools have established structures and programs to ensure courageous discussions are a regular part of learning for…

Psychologist Wendy Ostroff explains why using dialogue in learning with elementary-age students is a win for everyone, especially for learning. Young students are inventive questioners and naturally divergent thinkers, and they are engaged and empowered by exercising their voices. Teachers will benefit from Ostroff's guidance about fitting…

This paper is a revised version of a plenary prompted by the upsurge of interest in the role of pragmatics in teaching, learning, and assessment, and has as its purpose to take a fresh look at recent developments in the assessment of target-language (TL) pragmatics in spoken language. The first issue considered is the question of whether to…

This article represents a first attempt to analyze and synthesize the theological, hermeneutic, and educational insights of Joseph Sander Lukinsky, who was one of the foremost Jewish educational thinkers and master practitioners of recent times. Particular attention is paid to Lukinsky's theology of revelation, to his educational theory, his…