Years of failed attempts to engage my mathematics teacher students in exploration and co-creation led me to radically change my teaching approach. Inspired by literature that uses the jazz improv metaphor for teaching, I derived three tenets based on principles from jazz improv. First, I would bring no more than a single problem-solving task to…

Critical pedagogy for music education (Abrahams, 2005), as influenced by Freire's (1970) conception of critical pedagogy, emphasizes the importance of deconstructing power imbalances between students and teachers, in addition to placing students' musical cultures at the forefront of learning. Though the Orff Schulwerk teaching approach is similar…

Instrumental music practice has been conceived and investigated from the perspective of self-regulated learning (SRL), i.e. how students acquire the tools necessary to take control of their own learning. SRL processes depend on variables such as ways of studying (method), time invested in practice and behavioural and social/cultural factors. Thus,…

This paper aims to examine how specific aspects of Bakhtin's theoretical perspective might inform our understanding of improvisation. Moreover, it outlines the possible educational implications of such a perspective. Specifically, a sketch of a Bakhtinian conception of improvisation is proposed, a sketch which emphasizes the cultivation of an…

This article presents practitioner research dealing with improvisation in solfege as a creative alternative for the development of music perception. Solfege practice, conceived as a personal construction of a melody, requires an attitude that embraces aural sensitivity to the spatial and temporal dimensions of a melodic line, identification of…

This paper explores the phenomenon of mathematical understanding, and offers a response to the question raised by Martin (2001) at PME-NA about the possibility for and nature of collective mathematical understanding. In referring to collective mathematical understanding we point to the kinds of learning and understanding we may see occurring when…

The argument examined in this paper is that music--when approached through making and responding to coherent musical structures, facilitated by multiple, intuitively accessible representations--can become a learning context in which basic mathematical ideas can be elicited and perceived as relevant and important. Students' inquiry into the bases…