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What lessons were like (details)

We used several analytical methods. The first was a grounded analysis of early videos, and our perceptions at that stage of the kinds of things which varied between teachers. Note that our information about small group interactions with the teacher was very sketchy, but we included it because some teachers confined their challenges and supportive remarks to selected groups, while others were much more public.

The second method was to use an observation schedule that focused on issues which arose from the earlier grounded analysis (lesson observation schedule years 2 & 3). This method homed in on details of strategies such as what sorts of questions teachers dealt with quickly and what more slowly; what sorts of questions were posed to the whole class and what to small groups; what general remarks were made about mathematics, if any, and so on. The observer used the schedule and summarised the observations afterwards according to the overarching questions.

The third method developed from the shortcomings of the second, in which the order of events became lost so that content could be seen in more detail. In the third method, generic kinds of mathematical activity were mapped chronologically in a way which showed both presence of certain activities and their pattern throughout the lesson (lesson analysis map). This could complement methods used in the METE project but our focus was on the nature of engagement and activity rather than the nature of the mathematical content.