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Embracing errors in maths: How to move forward after making a mistake

iMaths 3/8/18

Note: iMaths is in its final year and will be discontinued at the end of 2024. If you’re looking for a primary maths resource written for the Australian Curriculum Version 9.0, explore Maths Trek.

Mistakes in maths are common, but many students worry about making them and feel a sense of failure when their work is marked incorrect.

Mistakes need to be recognised for what they are: opportunities for learning and self-growth.

Here are three tips to help your students move forward the next time they make a mistake.

1. Face the challenge with an ‘I can!’ attitude

When students see their answers marked wrong, their first reaction is often, ‘I can’t do it’. Encouraging a shift away from a fixed mindset – where students easily give up – towards a growth mindset – where they try again – is vital.

Developing a growth mindset at a young age helps students understand that an incorrect answer does not indicate a lack of intelligence, it simply means they don’t yet have the skills to tackle a particular problem.

How do we help students change their mindset? By encouraging them to think ‘I can’t do it yet’. When students realise intelligence is learned, and practice increases the brain’s ability to solve problems, they start to:

• build confidence in their own knowledge
• apply prior knowledge to new situations
• make new discoveries
• foster a deeper understanding of concepts
• strengthen their resolve and love of learning.

Provide students with plenty of opportunities to practise problems. You can model some problems and complete them as a class or provide questions for students to practise independently.

As students persevere with problem solving, celebrate their successes in the classroom and encourage them to believe ‘I can do it!’.

Read more about maths and the growth mindset in the article Ability and Mathematics: the mindset revolution that is reshaping education by British educator Jo Boaler.

2. Rethink the strategy

Mistakes are opportunities for students to re-evaluate the strategy they applied to a problem-solving task. Determining where they went wrong can help students identify whether the strategy they used was the best one for the problem at hand, or whether there might be a more appropriate strategy.

Encourage students to ask themselves ‘Why didn’t the strategy work for this problem? Is there a better strategy I could try?’.

While there is no right or wrong way to solve a problem, it’s useful to discuss with the class the various strategies students used for a problem-solving task to see if one was more efficient than another. You could even provide students with a list of problem-solving strategies for them to refer to.

3. Work it out together

When students are tackling difficult topics and wrong answers show they don’t yet fully understand the concept, continuing to work alone doesn’t always result in a breakthrough. Often, what’s needed is a fresh approach.

Small-group work where students apply their knowledge to a real-world project can provide unexpected opportunities to consolidate their understanding of a topic. Working together on a project allows students to:

• apply their own knowledge and draw on others’ knowledge
• discuss strategies and plan
• experiment and make mistakes in a collaborative environment
• understand how a maths concept applies to a real-world context.

Investigations are a great way for students to apply their knowledge of specific maths concepts to extended mathematical problems.

Importantly, investigations give students plenty of time for trial and error as they work towards a common goal. At the conclusion of the investigation, encourage students to reflect on what worked and what didn’t.

We all make mistakes from time to time. It’s what we do with them that counts. With a positive attitude and a supportive environment, students can view their mistakes as learning opportunities and not as learning failures. As the inventor Thomas Edison once said:

‘I have not failed. I’ve just found 10 000 ways that won’t work.’ 

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