Mathematical practices (commonly used by mathematicians) in mathematics teachers’ solutions to algebraic problems

Abstract

A teacher of mathematics knows mathematics as a teacher and as a mathematician. Whilst the existing research on teacher knowledge contributes to our understanding of the ways of knowing mathematics as a teacher, little is known about ways of knowing mathematics as a mathematician. Guided by the conceptual framework of mathematical practices (MPs) (commonly used by mathematicians), this case study aimed to contribute to fill this gap. The study examined solutions generated by two secondary teachers of mathematics to a set of algebraic problems to determine which MPs are apparent, or not, in the teachers’ work. Data were content analyzed deductively. Findings reveal that both teachers consistently demonstrated three practices: seeking to find patterns; creating models for mathematical ideas; and using symbolic representations of ideas, whilst two practices: using precise definitions of objects; and having fine distinctions about language were less present in either teacher solutions. More high-level practices such as characterizing objects based on structure and using logical arguments as sources of conviction were manifested in routine problems but absent in nonroutine problems. It is anticipated that teacher training experiences and curriculum contexts have influences on teachers’ MPs in doing mathematics.