Order of operations: On convention and met-before acronyms

In our exploration of the order of operations we focus on the following claim: “In the conventional order of operations, division should be performed before multiplication.” This initially surprising claim is based on the acronym BEDMAS, a popular mnemonic used in Canada to assist students in remembering the order of operations. The claim was voiced by a teacher and then presented for consideration to a class of prospective elementary school teachers. We investigate the participants’ understanding of the order of operations, focusing on the operations of multiplication and division. We report on participants’ ways of resolving a cognitive conflict faced as a result of relying on memorized mnemonics.     

Stuck on convention: a story of derivative relationships

In this article, we explore the responses of a group of undergraduate mathematics students to tasks that deal with areas, perimeters, volumes, and derivatives. The tasks challenge the conventional representations of formulas that students are used to from their schooling. Our analysis attends to the specific mathematical ideas and ways of reasoning raised by students, which supported or hindered their appreciation of an unconventional representation. We identify themes that emerged in these responses and analyze those via different theoretical lenses—the lens of transfer and the lens of aesthetics. We conclude with pedagogical recommendations to help learners appreciate the structure of mathematics and challenge the resilience of certain conventions.     

Irrational gap: sensemaking trajectories of irrational exponents

Educational Studies in Mathematics - We investigate how students make sense of irrational exponents. The data comprise 32 interviews with university students, which revolved around a task designed...     

Reducing Abstraction: The Case of School Mathematics

There is a growing interest in the mathematics education community in the notion of abstraction and its significance in the learning of mathematics. Reducing abstraction is a theoretical framework that examines learners behavior in terms of coping with abstraction level. It refers to situations in which learners are unable to manipulate concepts presented in a given problem; therefore, they unconsciously reduce the level of abstraction of the concepts involved to make these concepts mentally accessible. This framework has been used for explaining students conception in different areas of undergraduate mathematics and computer science. This article extends the applicability scope of this framework from undergraduate mathematics to school mathematics. We draw on recently published research articles and exemplify how students behavior can be described in terms of various interpretations of reducing abstraction level.