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What is a mathematical problem and how is it different from a mathematical question?

Way back in 1982, Cockcroft stated, “The ability to solve problems is at the heart of mathematics. Mathematics is only ‘useful’ to the extent to which it can be applied to a particular situation and it is the ability to apply mathematics to a variety of situations to which we give the name ‘problem solving’.

Often students expect to be told what to do rather than think about a problem for themselves so how can we, as teachers, offer support without doing the thinking for the student?

Giving students the right problem, at the right time, is important. A good problem for a student is one they can access given their confidence and achievement but cannot immediately see a solution, yet is sufficiently challenging for them to feel a sense of satisfaction from making progress. We also need to ask the right questions to guide the student along the way. Probing questions that encourage the student to think about their own progress with a problem, that avoids quickly giving structured and direct help.

We’ve developed a half-day (or shorter) event, a Problem Solving Booster event, to encourage and support A level students in developing skills and confidence in problem solving. It’s aimed at students who haven’t already attended our Higher Level Problem Solving events, or STEP, MAT or TMUA courses. The event is suitable for Year 12 or early Year 13 A level Mathematics students. If you’d like a bespoke event arranged for your students, please get in touch with your local Area Coordinator.

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