From process to object in teachers’ introductory algebra discourse

Abstract

Generalization is one of the core aspects of algebraic thinking, and research literature points to the importance of objectification when generalizing mathematical discourses. To increase the field’s understanding of the objectification process in various algebra discourses, our study analyses Grade 6 teachers’ use of words, symbols, routines and narratives when they introduce various algebraic concepts. Our results show that there exist instances of objectification in the teachers’ discourses, but these are all implicit, which can make them difficult for students to notice. Thus, teachers need to be made more aware of the importance of making the objectification process explicit. Furthermore, our results show that instances of objectification are tightly connected to the use of formal algebraic symbols. This highlights the importance of the transition from concrete/iconic to formal/arbitrary representations.