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Tool Learning from mistakes and misconceptions: PD materials


These tools support leaders of professional development for a research-based method of teaching for long-term learning by exposing and working on students´┐Ż mistakes and misconceptions. These professional development courses for teachers provide an introduction to the method of Diagnostic Teaching. Materials are provided for key mathematical topics that trouble students from late elementary grades through early high school.

The tools include diagnostic assessment and instructional material for teachers that will help students who have difficulties in mathematics to identify and deal with their mistakes and misconceptions.

Benefits and adaptations

All students gain from the robust long-term learning. Teachers gain from this and from the reduced need for repeated review of topics already 'learnt'. Strategy Redefine the roles and expectations of teacher and students helps students take more responsibility for their own learning. Leadership will find the atmosphere of these sessions enhances the professional development climate in general.


£10 (about $30 inc. shipping) per topic:
  • Number Operations
  • Functions and Graphs
  • Algebra
  • Geometry.

The General Introductory Course; the "Decimals and Fractions" topic course and additional materials for professional development courses will be available free from this website in the near future.

Evaluative evidence

There is research evidence that shows, across a range of topics, that the diagnostic teaching approach leads to much better long term learning than standard "positive only" methods, which avoid analyzing and understanding misconceptions.

This is summarized in the strategy Strategy Introduce diagnostic teaching and in
Askew, M. and D. Wiliam (1995). Recent Research in Mathematics Education 5-16. London, HMSO.

Design and development

Malcolm Swan, Alan Bell and the Shell Centre for Mathematical Education, University of Nottingham.


Strategic applications