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Lesson structures

Lesson structures were dictated by the flow of mathematical ideas.

Most lessons we recorded throughout the project had whole class introduction, either to language and ideas through discussion or through some kind of activity. Then instructions, then further discussion and/or pairwork, followed by more discussion of ideas relating to what had just happened, followed by further task and further discussion. Most lessons included references to previous or next lessons, or even something met a few weeks before.

Most lessons were 55 minutes or an hour long. Time spent on individual, pair and small groupwork varied from 5 minutes to 50 minutes with the mode between 20 and 25 minutes, usually in two or three chunks. The rest of the lesson was whole class listening, discussion, physical or interactive activity.

In most lessons there was a clear mathematical theme which ran through different stages of one task and across tasks. In four lessons there were at least two disconnected features of mathematics presented. In one lesson there were two unconnected mathematical topics presented but the ways of working on them were explicitly connected. In one lesson there was no maths, only organisational matters to do with folders, equipment and so on (this was with a low set in year 8).

Every lesson was differently structured in terms of how the teacher wove mathematical ideas, challenges and activity together. This fascinated us - how could we capture this diversity? We devised a structured list of types of mathematical activity and began to use it to construct maps of the flow of mathematics in lessons (link to lesson map).

In most lessons, all parts of the list are visited and there is no clear order in which this happens. In one lesson, activity was confined to the top left corner and consisted of low level, repetitive, copying or instrumental tasks. We noticed that lessons taught by non-specialist teachers were just as likely as anyone else's to include a wide range of mathematical engagement, but were less likely to include discussion of the mathematical implications of what had been done in the lesson, or indications of how the ideas connect to other areas of mathematics, or attention to underlying meanings of the work done. Not many lessons contained highly formal reasoning, and those that did were taken by mathematics specialists.

(for more details of six lesson structures click here)