Shunning algebraic formalism: Student teachers and the intricacy of percents

Abstract

This paper investigates primary and lower secondary school student teachers’ use and mastery of algebraic formalism in solving the task of determining the rate of increase of a square’s area when the square’s side increases by p%. The empirical material consists of a video-recorded small-group session where a triad of student teachers was solving this task (with teacher interaction). Notions from the theory of didactical situations in mathematics and semiotic theory are used as analytic tools. The analysis shows how percent notation complicated the task, and how algebraic calculations were avoided. It is further shown how an evolution of the milieu gave rise to creation of manipulatives that provided the student teachers with representations from a different semiotic register, that of plane geometric figures, which were transformed into percent notation that enabled them to produce a solution to the task. Didactical implications are discussed regarding design of such a task on the one hand, and teacher education on the other hand.