One of the great pleasures of being a mathematics teacher lies in experiencing that very special buzz in the classroom that occurs when every single student is thoroughly engrossed in the task the teacher has set them. The teacher knows that in those precious moments genuine learning is taking place, however noisy and chaotic it may appear to an…

A proof's potential to promote understanding and conviction is one of the main reasons for which proof is so important for students' learning of mathematics. Unless students realise the limitations of empirical arguments as methods for validating mathematical generalisations, they are unlikely to appreciate the importance of proof in mathematics.…