The role of proof in mathematics teaching and The Plateau Principle


  • David Easdown


One of the most difficult learning thresholds for students of mathematics is the concept of proof. The difficulty manifests itself in several ways: (1) appreciating why proofs are important; (2) the tension between verification and understanding; (3) proof construction. The first case study describes a spurious but ‘convincing’ proof and a correct but ‘unconvincing’ proof of a deep result in linear algebra. A brief discussion introduces The Plateau Principle, an unspoken credo for successful research in mathematics, which says simply: ‘look for and be prepared to use a variety of plateaus as starting points for a mathematical investigation.’ The second case study illustrates an underlying ‘proof template’ that assists in the development of proof technique, in much the same way as a sense of perspective is essential for the ability to draw well.