In this article, we consider the phenomenon of improvisation by small groups of middle years students while engaged in rich mathematical tasks in a classroom setting. Working from the premise that improvisation comprises a spectrum of behaviour, we propose that there is a range of improvisational behaviours that may be observed as the students…

Out-of-class activities play a crucial role in student learning. However, student opinions on the design of these activities are rarely measured across several different classes. The purpose of this study is to understand students' preferences and attitudes towards new "Engaged Mathematics Labs" in which professors and teaching…

The first calculus course in the province of Quebec (Canada) is taught in the first year of college (17-18 year-old students) before university. Statistics show that this course is the most difficult one for students at the collegial level and that it prompts many to drop out of school. The literature has highlighted the cognitive problems…

The Zen concept of beginner's mind describes how one's level of awareness can open one's mind to growth and possibilities, an attitude that would be beneficial for many mathematics students. In this naturalistic case study, two small groups of middle years students engage in the same mathematical task, one group demonstrating the characteristics…

We discuss teaching and learning situations that surfaced when computer programming and mathematics were brought together in a course where students write computer code to explore mathematics problems. Combining programming and mathematics creates a rich ecosystem which, on top of traditional mathematics activities (writing solutions, proofs,…

Mathematics itself is a living and creative act (Boaler, 2008), and mathematicians themselves often collaborate in their work (Burton, 2004). What, then, is holding school mathematics back? Are educators so conditioned to expect the act of mathematizing in school to proceed in a certain abstract, formalized way that they are neglecting other means…

This naturalistic case study investigates the problem posing patterns that emerge as four small groups of 12 year old students in Western Canada work collectively on a structured mathematics task. A method of data analysis is introduced that blurs the data to create transcript "tapestries" providing visual evidence of collective patterns…

The arithmetic mean is a fundamental statistical concept. Unfortunately, social science students rarely develop an intuitive understanding of the mean and rely on the formula to describe or define it. According to constructivist pedagogy, educators that have access to a variety of conceptualizations of a particular concept are better equipped to…

This submission contains the Proceedings of the 2011 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Memorial University of Newfoundland in St. John's, Newfoundland. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning.…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…