The Teacher’s Role in Supporting Students’ Connections Between Realistic Situations and Conventional Symbol Systems

We use the notion of focusing phenomena to help explain how a teacher’s actions were connected to her students ’ interpretations of a linear equation. This study was conducted in a high-school classroom that regularly emphasised dependency relationships in real-world situations. Seven interviews revealed a majority view of y = b + mx as a storage container—a place to insert b and m values—rather than as a relationship between x- and y-values. Classroom analysis revealed how the teacher directed attention away from functional relationships with increasing frequency as she moved from realistic situations to conventional representations. Current reform efforts in algebra instruction in several countries emphasise mathematical modelling, the use of realistic problem situations, and a pedagogical approach toward functions based on the notions of change and dependency (Fey, 1990; Kaput & Nemirovsky, 1995; Kieran, 1993). According to the Australian Education Council (1990), the study of functions should begin with modelling activities that draw upon students ’ daily experiences with variation. Similarly, algebra standards in the USA call for middle- and high-schoo