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In the present study, we investigated pre-service mathematics teachers’ problem-formulation performances, which is a kind of problem-posing, in terms of being related to the existing problems, mathematical validity, and strategy types. Thirty-eight participants responded to a paper-and-pencil test wherein they formulated mathematics problems in as many ways as possible. We analyzed the problems formulated in the paper-and-pencil test according to our theoretical framework of problem-formulation strategy types and determined whether they were task-related and mathematically appropriate. The results indicated that most of the formulated problems were task-related and mathematically appropriate. The pre-service mathematics teachers tended to use strategies that involved making changes to the surface features of existing problems rather than the structural features of existing problems. The pre-service mathematics teachers used the strategy of replacing the given and requested information and generalizing strategies the least among the structural strategies. We also found that their problem-formulation tendencies changed according to the problem type.

An Examination of Pre-Service Mathematics Teachers’ Problem-Formulation Performances