From 'uh-oh' to 'ah-ha!' - fostering intuition in the classroom

Inquiry-based learning; problem solving; challenging tasks; student-centred learning; active learning: These terms are commonly used for an approach to learning mathematics which sees the student develop their own understanding as they work through a mathematical problem, and such approaches are - quite rightly - widely promoted in our classrooms.

These approaches give students better chances to experience authentic mathematical experiences as they attempt to model real life problems and data. The exact nature of the inquiry can vary greatly, from a more traditional confirmation inquiry where the teacher frames questions for the student, usually with a specific pre-determined outcome, on to structured and guided inquiry with decreasing levels of scaffolding, through to open inquiry, where students formulate their own research question(s).