Misconceptions in Mathematics

classic mistakes 2

Nevil Hopley’s excellent Classic Mistakes site.

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

Diagnostic Questions - Algebra


A superb resource to use in class (or for students to use at home) to address misconceptions is Craig Barton’s and Simon Woodhead’s Diagnostic Questions site. The site has over 1700 questions with carefully designed multiple choice responses to address common misconceptions. For further details see these posts.


Count On Misconceptions

Count On – Misconceptions

From Count On comes a very clear series of  documents on common misconceptions. For each topic an explanation of how the misconception arises is given, together with some exercises aimed at reinforcing the correction needed.

One of the new year resolutions I suggested was to reread Malcolm Swan’s excellent ‘Improving Learning in Mathematics‘, this 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.

Many of the outstanding resources from the Standards Unit address common misconceptions; see PD2, learning from mistakes and misconceptions. See also the resource hosted by STEM Learning – you will need to create a (free) account to view the STEM Learning resources.



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

Examination boards often publish helpful material which address common misconceptions, such resources can promote very useful class discussion as can examiners’ reports. From AQA for example, have a look at the Feedback documents on each unit available here (scroll down the page and look in the section on Teaching Resources) and another resource here.

Great questions can be used to expose misconceptions, diagnostic questions have already been mentioned above; for further sources of questions see Rich Questions.


Spot the mistake!

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.

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.

sim eq

Edexcel’s A Level Teaching and Learning Materials, a growing library of resources offer excellent support for teachers.Edexcel Model Answers
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.

Edexcel Model Answers example

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.

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.