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Proof is back in the national curriculum! Across England, Wales, Northern Ireland and Scotland pupils should be developing skills in mathematical proof. This book, born out of classroom research by a secondary school teacher, argues the case for proof. Details of approaches and pupil responses are given. Pupils will start thinking about proof in primary lessons, working through 'Proof Levels' to formal proof for some pupils towards the end of secondary school. Over 70 proofs are considered together with common fallacies. The book is full of ideas on how teachers can build proof into their teaching programme.