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Secondary Magazine - Issue 92: Focus on...

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 05 October 2012 by ncetm_administrator
Updated on 24 October 2012 by ncetm_administrator


Secondary Magazine Issue 92Question mark cookies by Scott McLeod some rights reserved

Focus on...learning from mistakes and misconceptions in mathematics

When pupils make mistakes in their mathematics it can be for different reasons. Some of these mistakes are made because they are not concentrating or trying to work too quickly however some mistakes are made as a result of a misconception; the pupil is thinking about their work but has not understood a concept correctly which is leading to incorrect responses. It is important to be able to distinguish between errors and misconceptions and have the tools to deal with them in the classroom.

There are some teachers who think that it is a mistake to draw attention to misconceptions but there is also a wealth of research evidence, which suggests that paying attention to misconceptions, building them into teaching episodes and drawing pupils’ attention to them can be a valuable teaching technique. The resources highlighted on this page will give you the opportunity to make that decision for yourself.

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The NCETM departmental workshop Use of mistakes and misconceptions to deepen understanding is designed to encourage you to make effective use of the common mistakes and misconceptions students make during lesson time. It explores some of the reasons students make mistakes and how you can use these to enhance students’ learning. The workshop models how you could begin to address some algebraic misconceptions. This approach to developing lessons focusing on misconceptions could be replicated with other areas of the mathematics curriculum.

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The Mathemapedia entry Misconceptions, Partial Conceptions & Errors: Mistakes – are they essential to learning? may give you something to apply in your own classroom.

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The National STEM Centre eLibrary hosts the materials From Level 3 to Level 5 in mathematics – tackling misconceptions. Each of the four resources gives a sample of some pupil work with a commentary indicating the possible misconceptions, some test questions and an activity designed to work on possible misconceptions in that specific area of knowledge. The four areas covered are fractions and decimals, multiplication and division, area and perimeter and algebraic notation.

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Improving Learning in Mathematics has a series of professional development resources which includes a module on learning from mistakes and misconceptions.

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Finally, Mike Askew and Dylan Wiliam in their Recent Research in Mathematics Education 5-16 (Ofsted, HMSO Publications 1995, ISBN 0 11 350049 1) make the following points regarding the use of misconceptions in mathematics:

One of the most important findings of mathematics education research carried out in Britain over the last twenty years has been that all pupils constantly invent rules to explain the patterns that they see around them.

Overcoming these kinds of misconceptions presents the teacher with a dilemma. When teaching multiplying whole numbers by ten, in order to present pupils with examples where adding a zero does not work, it would be necessary to stray far from the original topic and it may involve mathematical ideas that are, for the time being, beyond the pupils’ capacity to understand.

The model of simple through to more complex examples can also lay the foundations of misconceptions.

It seems that to teach in a way that avoids pupils creating any misconceptions (sometimes called “faultless communication”) is not possible, and that we have to accept that pupils will make some generalisations that are not correct and many of these misconceptions will remain hidden unless the teacher makes specific efforts to uncover them.
(Askew and Wiliam Recent Research in Mathematics Education 5-16, pages 12 and 13).

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30 October 2012 22:57
I hadn't...thank you for signposting me there.
By brunoreddy
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24 October 2012 13:53
Your Simpsons resources are lovely, Bruno!

Have you seen the current 'Getting better at teaching' thread in the Maths Cafe community, which is about misconceptions, errors and mistakes?
By mary_pardoe
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23 October 2012 16:13
Exposing misconceptions head on is something I like to focus on for entire lessons but it's a fine line between making pupils feel bad about their misconceptions and helping pupils to learn from them.
So I've started attributing the classic mistakes that I see pupils making to Simpsons characters. This has created a safe way for us to talk about the errors and seems to work.
I've uploaded the resources I developed on misconceptions around powers, factors and multiples here: http://mrreddy.com/blog/2012/09/classic-mistakes-brought-to-you-by-the-simpsons/
By brunoreddy
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