Learning from mistakes and misconceptions: supporting teachers Feedback is important in guiding any system; in education it is often weak. The method of Diagnostic Teaching has been developed through research to help remedy this, for both students and teachers. It contributes to long-term learning and promotes transfer from the immediate topic to wider situations. This strategy works through focused professional development, with specific activities supported by well-engineered materials.

Where a live professional development program is not possible, some teachers will be able to benefit from the following 'do-it-yourself' alternative strategy.

Learning from mistakes and misconceptions: gaining the skills helps teachers, working in their own classrooms and with colleagues, to expand their teaching style to include the strategies that are at the core the diagnostic teaching approach. The key aspects of this method are the identification and exposure of pupils' misconceptions and their resolution through 'conflict-discussion'. Conceptual diagnostic tests also play a part both in helping pupils to become aware of their misconceptions and enabling the teacher to observe progress.

Research also shows that conventional methods of teaching typically produce short term gains, but with substantial loss over periods of a few months. For related reasons, state tests, and national and international surveys of mathematics attainment, show disappointing levels of achievement and relatively small yearly gains