Teachers’ Orchestration of Mathematics for Different Groups of Students

Abstract

Class composition for secondary mathematics lessons in England is often decided by measures related to prior attainment, with students grouped with others of similar ‘ability’ and referred to as ‘setting’. Research suggests setting does not raise overall attainment and disadvantages students placed in lower attaining sets, with those students experiencing an impoverished curriculum, such as more ‘drill and practice’ (Wiliam and Bartholomew, 2004). This classroom-based video study explores mathematics teachers’ practice in ‘typical’ classrooms and changes that come about when they teach sets with different attainment profiles. The Orchestration of Mathematics Framework (OMF) was developed to interpret classroom activities; this framework integrates a range of theoretical perspectives, including variation theory (Marton and Pang, 2006) and classroom norms (Cobb et al., 2009). The application of the OMF in different settings demonstrated it facilitated cross-class comparisons, and while further research is needed, this evidenced the potential of the OMF as an analytical tool. Three teachers participated in this study; for each teacher two sets with different attainment profiles were studied. When the findings were analysed, a complex picture of teachers’ practice emerged. There were differences between sets, but many facets of teachers’ practice were relatively stable across classes. Some differences reflected previously reported characteristics associated with low attaining sets, such as tighter control over classroom talk (Kutnick et al., 2006), but others were absent; for example, there were no discernible shifts to ‘drill and practice’. One common thread was the low frequency of attention being drawn to mathematical concepts beyond that provided by examples. One question raised is whether students in higher attaining sets are those better placed to read the implicit mathematical meanings available in the act of ‘doing’ tasks.