## EEF Blog: Integrating evidence into mathematics teaching – Minimising Misconceptions

This new monthly series supports teachers and maths leads in implementing the evidence from the EEF’s Improving mathematics in Key Stages 2 and 3 guidance report. The second in the series of seven focuses on misconceptions.

What are your existing beliefs and assumptions about misconceptions in mathematics?

• Are misconceptions the same as mistakes? Or something different?
• Is it better to address misconceptions ‘head on’ or wait until they become a problem?
• Are you confident that you are aware of common misconceptions in mathematics, how they arise, and why they might persist?

If all teachers of mathematics in your school were asked these questions, would there be broad agreement in their answers?

One of my favourite classroom moments happened in a colleague’s lesson on averages. After correctly identifying the median of 4 and 5 as 4.5, the class were asked what they thought the median of 5 and 6 might be. Spotting a pattern, one child confidently predicted the answer to be 5.6, and a productive classroom discussion ensued about why the actual answer was 5.5.

The pupil’s logic here is clear, and is correct based on their experience to date, but has been extended beyond its usefulness. This misconception was caught before it became embedded, but other common misconceptions, such as ‘multiplication makes bigger’, can be many years in the making and can prove much more persistent.

Given that mathematical misconceptions are numerous and commonplace, how should we look to minimise them in our classrooms? As always, it is helpful to consider the evidence base in order to guide our thinking. Our guidance report, based on an extensive review of the evidence on teaching KS2 and 3 mathematics, found that:

• Knowledge of common misconceptions can be invaluable in planning lessons to address errors before they arise
• It is important that misconceptions are uncovered and addressed rather than side-stepped or ignored
• Teachers should think about how misconceptions have arisen and consider counter-examples in challenging pupils’ beliefs
• We should use assessment of pupils’ strengths and weaknesses to inform our choices of classroom tasks, and these should be used to address misconceptions
• Using examples and non-examples of concepts can help

While there are some practical approaches we can take in the shorter term, a longer-term view, with planning at its heart, is likely to prove most beneficial.

REACTing to misconceptions

The REACT planning framework prompts us to consider upcoming teaching through an understanding of common misconceptions and the planning of classroom tasks which aim to minimise these.

It prompts us to:

• RESEARCH common misconceptions

We might consider published sources of common misconceptions, discussed and enhanced through team meetings, and ways of assessing any existing misconceptions our pupils might hold (for example, through multiple-choice diagnostic questions).

• EXPLORE why they persist

Considering at which point in the learning journey a misconception has arisen can be beneficial in identifying ways of addressing it. Providing convincing counter-examples can help: for example, illustrating the position of fractions on a number line for pupils who think that a larger denominator means a larger value when using fractions.

• ADDRESS the misconceptions head on

Is there opportunity to collaborate as a team, possibly through discussion of common misconceptions in team meetings? This is likely to support less experienced colleagues who have not yet experienced misconceptions first-hand in the classroom.

• CONSIDER possible future issues

The language we use in the classroom is of particular importance, and avoiding problematic phrases or unhelpful shortcuts – even if they seem useful at the time - could minimise the development of future misconceptions. For example, highlighting something which will be studied in future which might ‘break’ the patterns now seen could help in stopping misconceptions from emerging down the line.

• Plan TASKS that could help

Effective tasks which provide examples and non-examples of concepts, discuss and compare different solution approaches, build conceptual knowledge in tandem with procedural knowledge, and provide opportunities for pupils to investigate mathematical structure and make generalisations can all be effective in minimising the impact of misconceptions.