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This paper contains theoretical ideas about open tasks as well as about case studies in lower secondary schools and in in-service mathematics teacher education courses. I distinguish between tasks formulated as questions, problems and commands. Furthermore I set out what I find to be a powerful or vague formulation of a task. The math teachers participating in the in-service education course seemed to want to work with open problem solving. In their own judgments they found it easy to formulate open tasks but in the classroom it was obviously very difficult to do so. The results from the case studies gave inspiration to develop other ways of working with formulation and evaluation of open tasks in an in-service education course, which is described in the last part of the paper. (author’s abstract)
Classification: D53 B50
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