Teachers, pedagogical skills, and the obstacle of intuition
(PHYSorg.com Mathematics)

When a task calls for intuitive knowledge, as in `subtracting means taking something away,` its complexity often goes unnoticed. However, when intuitions are not mobilized - having to grasp, for instance, that subtracting means `finding the difference` - the task is considered difficult, and seemingly requires the use of specific educational strategies. Researchers at the University of Geneva (UNIGE), Switzerland, have demonstrated that teachers sometimes struggle to understand the difficulties encountered by pupils when attempting to solve apparently intuitive problems that are in fact very difficult. The findings suggest that teachers only use their pedagogical skills when a problem seems to mobilize counter-intuitive strategies. The results, which are published in the journal Educational Studies in Mathematics, stress the importance of training teachers to avoid the pitfalls of intuition so that the seemingly obvious does not get in the way of understanding the difficulties faced by students.