Pre-service teachers' free and structured mathematical problem posing

This exploratory study examined how pre-service teachers (PSTs) pose mathematical problems for free and structured mathematical problem-posing conditions. It was hypothesized that PSTs would pose more complex mathematical problems under structured posing conditions, with increasing levels of complexity, than PSTs would pose under free posing conditions, because the structured posing condition would guide PSTs to more closely consider the mathematical relationships in a posing situation. Sixty-five PSTs – 61 participating in a written assessment and 4 participating in task-based interviews – responded to problem-posing tasks under free or structured posing conditions. Two-way independent samples t-tests and chi-square tests were used to test the hypothesis, along with a qualitative analysis of the task-based interviews. We found that while the task format had limited impact on the complexity of problems posed, PSTs in the structured-posing condition may have more closely attended to the mathematical concepts in each task, and may have also impacted their process of posing problems than those in the free posing condition.