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Strategy Learning from mistakes and misconceptions: supporting teachers


Many students who appear to understand a topic at the end of the teaching unit, do not retain that even for a few months. Better long-term learning depends on developing a robust understanding with many connections to other topics and applications. Diagnostic teaching achieves this by helping students to learn to detect, understand and correct misconceptions in their own and their fellow students work. This strategy and its associated tools will help leaders to provide teachers with effective support for developing the extra pedagogical and mathematical skills involved.

Applicable tools

Planning essentials

The planning is much the same as for any sequence of professional development sessions. The resources give explicit guidance on each session and how the sequence may be paced, giving time for work in the classroom in between but avoiding too-long gaps. As always, it is important to get to know the associated teaching material.

Budget issues

These are standard, including costs of the session, teacher time and the classroom materials.


  • 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  Redefining the roles and expectations of teacher and students helps students take more responsibility for their own learning.
  • This makes the teachers’ daily work more rewarding and effective.
  • The discussion helps students to build a well-connected body of knowledge, integrating the newly corrected knowledge with the rest of their understanding of the subject.
  • Leadership will find the atmosphere of these sessions enhances the professional development climate in general.

Implementation pitfalls

  • Teacher-student and student-student discussion of the mathematics will present a new challenge for many teachers. (This professional development support will help greatly. Linking the outcomes from successful diagnostic teaching to improved scores will, as usual, encourage persistence)
  • The students have to learn how to engage in meaningful discussion of key points, being willing to expose their understanding, even if they fear it may be wrong. They need also to learn to listen to other students and to appraise what they say, without antagonism.

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 download for this strategy.

Design and development

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

Contact Person Alan Bell or the Organization Toolkit team for details.

Challenges addressed

Complementary strategies