Post updated: January 2022

I must start this post with something Dan Meyer said at the MEI Conference 2021 that really struck a chord with me, he said “There are no mistakes or misconceptions, just takes and conceptions.” Dan Meyer mentioned WW Sayer who said:

Most remarks made by children consist of correct ideas very badly expressed. A good teacher will be very wary of saying ‘No, that’s wrong’. Rather he will try to discover the correct idea behind the inadequate expression. This is one of the most important principles in the whole art of teaching.

WW Sayer

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For a starter addressing common misconceptions try the excellent Classic Mistakes resources by Nigel Hopley.

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A superb resource to use in class (or for students to use at home) to address misconceptions is of course Craig Barton’s and Simon Woodhead’s Diagnostic Questions site. The site has many thousands of questions with carefully designed multiple-choice responses to address common misconceptions.

The Insights feature is so helpful for learning about misconceptions, suppose we look at a White Rose Quiz on Algebraic Notation, for example, looking at the Insights we can see for any question the number of responses for each option from the many students who answered this question.

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From NCETM, these videos and resources for teaching Key Stage 3 maths topics include common misconceptions and pitfalls; looking at Directed Numbers for example we find slides and a pdf support document including as illustrated here, “What things typically go wrong?”

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Some years ago a website, counton.org which is now no longer available published a very useful document on misconceptions. In 22 sections, in each section misconceptions are given along with the correct version. Further explanations are also provided and also follow up exercises with answers.

The above pdf document includes all 22 sections. The first 8 of these documents, by Ilan Samson & David Burghes, are on the CIMT website.

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Malcolm Swan’s excellent ‘Improving Learning in Mathematics‘, includes a section (5.3) on exposing errors and misconceptions. An activity suggested there is to let your students become examiners and mark the work of others, this works very well, I have highlighted some excellent resources for this on the ‘Spot the mistake!‘ page.

See for example from Andy Lutwyche, his excellent Erica’s Errors series for Spot the Mistake activities or, also, on TES, Andy’s Clumsy Clive series. Andy’s many Spot the Mistakes resources.

Many of the outstanding resources from the Standards Unit address common misconceptions; see PD2, learning from mistakes and misconceptions.

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On the SERP website before see MathByExample and AlgebraByExample which is a set of Algebra 1 assignments that incorporate worked examples and prompt students to analyze and explain. These resources can provide prompts for discussing common misconceptions.

From this page you can access all the resources.

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From Michael Pershan, see his Math Mistakes site, to quote the Author:

The purpose of this site is to collect, organize and make sense of the mistakes that students make while doing math. I’m also increasingly interested in using mistakes to help us create worked examples that students can learn from.

Michael Pershan

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Steve Blades’ site www.m4ths.com has many excellent resources; on the GCSE page we see under ‘Miscellaneous Worksheets‘, several documents including 18 Common Misconceptions.

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All the examination boards publish helpful material which addresses common misconceptions, such resources can promote very useful class discussion as can examiners’ reports.

From Cambridge University, see Common Errors in Mathematics.

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There is an updated page here.

A great way to get students thinking about mistakes and misconceptions and hence deepen their understanding of topics is to have them mark the work of others. There are some great resources hosted on TES that will allow your students to do just that.

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Particularly excellent resources come from Andy Lutwyche, look at his excellent Erica’s Errors seriesfor Spot the Mistake activities. See also, on TES – further Spot the Mistakes resources from Andy Lutwyche.

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Edexcel’s A Level Teaching and Learning Materials, a growing library of resources offer excellent support for teachers.
The exemplar answers with examiner comments provide a particularly valuable resource. These booklets look at questions from the AS and A level Sample Assessment Materials, which was used in the trial undertaken in summer 2017. Real student responses are shown together with commentary showing how the examining team apply the mark schemes. The commentary includes always useful notes on common
errors. These could be used in class and students asked to find errors.

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TES resources I have come across include:

R Barnard’s Bob’s Ratio Homework 

Craig Barton’s lovely little starter on Algebraic Misconceptions (this one is truly tried and tested – I used it as a starter for a lesson observation and followed it up with a class discussion on what advice students would give to students making the kind of errors here – it went down rather well with the observers!)

Kaszal’s Fractions Mistakes

and Damian Watson’s

Transformations AfL Spot the Mistakes

Enlargement Spot the Mistake Booklet

Fractions AfL Plenary Spot the Mistake Booklet 

Thank you to all the great authors of these resources.

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On the subject of mistakes, the Classic Mistakes website has a gallery of posters of classic errors made in Mathematics. These could be a prompt for a useful discussion starter activity. Note that an audio file is also available for each poster.