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What habits and purposes of interaction have been established?

Students' experience of mathematics depends on the interactions between them and the teacher, so we identified habits in classrooms to show that our target students had, by and large, a rich and varied environment in which to participate. For PLAS we saw it as especially important that such environments were sustained, since such students often have a more limited experience in which to learn mathematics.

There was rarely a strict 'handsup' code in whole class discussions, and we saw that in several classrooms this meant that a few students could dominate the interactions, but teachers could then ask named people to bring others into the work. Whole class episodes were interspersed with small group and individual group work which avoided sustained exclusion. Teachers would use stricter codes of participation when classes were being particularly difficult. Several teachers started lessons with discussions about the meaning of words. Three teachers used mainly learner generated examples to structure their expositions.

Students generally had time and space to work out how to do things and were expected to:

Teachers were interested in how students did things and the way they thought: