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Tool Learning from mistakes and misconceptions: classroom materials


This package provides material for supporting teachers in developing diagnostic teaching skills. It includes diagnostic assessment and instructional material for helping students who have difficulties in mathematics to identify and deal with their mistakes and misconceptions. These tools will enable teachers to help their students use common mistakes and misconceptions constructively in the classroom to promote more effective learning of mathematical concepts.

These materials, and the detailed suggestions for their use, focus on common difficulties within a number of mathematical topics. They support lessons that helps student identify their own and others' errors and, through discussion and reflection, understand and correct the misconceptions that underlie them.

Preparation and help

This tool is designed for use by teachers, preferably working with a colleague or two. Since diagnostic teaching goes beyond traditional expository teaching, live professional development support is helpful. The parallel tool Tool Helping teachers gain diagnostic teaching skills is designed for such courses.

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 ‘learned’. Strategy Redefine the roles and expectations of teachers and students helps students take more responsibility for their own learning.


The General Introductory Course and the Decimals and Fractions
modules will be made available free-of-charge on this website in the near future.
£10 (Approx $30 including shipping to US) per topic.

Topics are:
  • Number Operations
  • Functions and Graphs
  • Algebra
  • Geometry

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 Gain diagnostic teaching skills and in
Askew, M. and D. Wiliam (1995). Recent Research in Mathematics Education 5-16. London.

Design and development

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

Contact Person Malcolm Swan or Organization The Toolkit Team for details.


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Strategic applications