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.…

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.

This paper questions the idea that there are two opposing paradigms of educational research, often called positivist versus interpretivist. It argues that the 'paradigm' term has been used to avoid philosophical discussions about the nature of educational research. This has been done by understanding 'paradigms' to reflect metaphysical positions…

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…

The purpose of this article is twofold: (a) to present the results of a study examining the current status of performance evaluations for school psychologist and (b) to use those findings to inform future directions. A content analysis of a national sample of 36 performance appraisal rubrics was conducted to examine their alignment with the…

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…

The aim of this article was to evaluate the use of alternatives to traditional language sample analysis (LSA) measures with bilingual preschool-aged children. A database of 184 bilingual preschool children, including children with developmental language disorder (DLD), was used in this study. The goals of the study were to establish the convergent…

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.

Research approaches are general techniques that researchers follow when conducting a study. Employing research approaches in information research is noted to vary from one researcher to another based on the investigator's choice as well as the nature of the topic under investigation. The differences in the use of research approaches in information…

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…