Systematic observation is a technique used in studies of classrooms. Observers work out a series of categories and then observe action, coding each sequence as they go. As an example -- if you wanted to see how much students interacted with the teacher you would observe and record a teaching sequence and every 30 seconds make a note of different types of interaction. If the teacher was speaking you would enter a code of 1 (say), and if students were interacting, it would be 2.
Famous studies like ORACLE recorded types of statement made by teachers -- statements or questions. Each type of statement or question was further subdivided (open or closed questions, for example). The result was some quantitative data which gave a better record than the usual kind of rather vague and unfocused classroom observation, it was claimed. For a good account of the origins of the method (and a fascinating application of it to studying policing) try this
So now go and try it in a leisure/sport/tourism context? Examine interaction with coaches in a PE lesson/coaching session? Compare the number of times male and female students get asked to demonstrate a task? Do tourists really interact with locals when they encounter them?
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