This submission contains the Proceedings of the 2015 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the Université de Moncton in Moncton, New Brunswick. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of…

In a recent issue of "Australian Senior Mathematics Journal" there has been published an interesting article by Galbraith and Lockwood (2010). In that article the problem of finding the most favorable points for a shot at goal in Australian football is considered from different points of view. A similar problem was considered by…

This study examined the utility of brief academic assessments to identify effective generalization procedures for individual students. Specifically, the study built on the proposal that brief assessments of antecedent and consequence manipulations can identify the most effective generalization strategy for individual students. The design was an…

Retaining mathematical knowledge is difficult for many students, especially for those who learn facts and procedures without understanding the meanings underlying the symbols and operations. Repeated practice may be necessary for developing skills but is unlikely to make conceptual ideas stick. An idea is more likely to stick if students are…

An analysis of one-step equations from a cognitive load theory perspective uncovers variation within one-step equations. The complexity of one-step equations arises from the element interactivity across the operational and relational lines. The higher the number of operational and relational lines, the greater the complexity of the equations.…

This paper explores the role examples play in mathematicians' conjecturing activity. While previous research has examined example-related activity during the act of proving, little is known about how examples arise during the formulation of conjectures. Thirteen mathematicians were interviewed as they explored tasks that required the development…

Deictic linking gestures, hand and arm motions that physically embody links being communicated between two or more objects in the shared communicative environment, are explored in a cross-cultural sample of mathematics instruction. Linking gestures are specifically examined here when they occur in the context of communicative analogies designed to…

Summer vacations interrupt the rhythm of learning and may result in a loss of knowledge and skills. This study investigates summer learning losses in an Austrian sample with nine-week summer vacations. The results show losses as well as gains for students in lower secondary education (182 students between 10 and 12 years old). Students experienced…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) identifies the strategic use of appropriate tools as one of the mathematical practices and emphasizes the use of pictures and diagrams as reasoning tools. Starting with the early elementary grades, CCSSM discusses students' solving of problems "by drawing." In later…

Linear algebra is one of the most challenging topics to learn and teach in many countries. To facilitate the teaching and learning of linear algebra, priority should be given to epistemologically analyze the concepts that the undergraduate students have difficulty in conceptualizing and to define their ways of reasoning in linear algebra. After…

Our aim is to discuss how school mathematical activity is modified when students' everyday situations are brought into the classroom. One illustrative sequence--7th grade classes solving problems that required proportional reasoning--is characterized as a system of interconnected activities within the theoretical perspective of activity theory. We…

This study aims to investigate plane geometry problem-solving strategies of prospective mathematics teachers using dynamic geometry software (DGS) and paper-and-pencil (PPB) environments after receiving an instruction with GeoGebra (GGB). Four plane geometry problems were used in a multiple case study design to understand the solution strategies…

A visual representation, such as a diagram, can be a powerful strategy for solving mathematical word problems. However, using a representation to solve mathematical word problems is not as simple as it seems! Many students with learning disabilities struggle to use a diagram effectively and efficiently. This article provides a framework for…

This study used participant observation to explore students' thinking when learning the concept of factorial functions. First-year university students undertaking a mathematics methodology course were asked to find the number of ways in which five people could sit around a circular table with five seats. Using grounded theory as a qualitative…

Formative assessment is the process by which teachers and students gather evidence of learning and then use this to adapt the way they teach and learn. I describe a design research project in which we integrated formative assessment strategies into lesson materials that focus on developing students' conceptual understanding and their capacity to…