Mistakes matter — five practices to empower maths learners

Have you ever wondered why, in a world that professes 'we learn from our mistakes,' so many of us are paralyzed by the fear of making them? 

This common discrepancy between words and actions reveals a critical flaw in our approach to education. With more and more students unable to attend school, there is a real sense of urgency around helping the world to access kinder maths learning opportunities. 

This article is one small contribution for thoses looking for positive and playful strategies for navigating, nurturing and normalising mistakes.

Take what you like and leave what you don’t — the goal of this article is to provide some tangible ways of meeting students where they’re at and helping them extend themselves and each other.

#1 Actively expect mistakes

Mistakes are an inevitable part of learning, and building positive responses around them can transform them from a source of frustration or shame into powerful learning moments. 

Actively expecting mistakes is powerful for communicating that they are valued and accepted as part of the learning process. 

A clear message that we can change an answer at any time is important too.

Consider how mistakes are navigated in this short (3 minute) video. 

• What do you notice/wonder?
• If you were the teacher what would you do differently/the same and why?

#2 Model curiosity and invite reasoning

By modelling curiosity about answers and how they come about, this curiosity will rub off on students.

Knowing that there’s more than one way to solve a mathematical problem opens up a whole new and creative world for sense-making, decision-making and experimentation — key features of play, a safe space for mistakes and ‘failing forward.’

When we have a go at explaining “how we know” or “how we worked it out” there’s a good chance we will reach one of two outcomes: 

Scenario A: We provide a convincing argument to ourselves and others that yes, the strategy we used gave us a correct answer. Hooray!

Scenario B: We realise, through the explanation, that we made an error. This is the perfect opportunity to fix it and just goes to show how explaining our approach out loud can help us be precise. Hooray!

See how a reasoning routine can support precision through this small group number talk. 

• What do you notice about it? What do you wonder? 
• What do you find valuable about this process?

#3 Celebrate mistakes and their unique role

Embracing errors means embracing growth and the opportunity to deepen our understanding and extend our skills. 

Hearing language that supports this way of being can be very powerful.  For instance:

One of my favourite things about noticing a mistake I made, is being able to fix it. 

Here are some other language examples for normalising and celebrating mistakes: 

• It’s good that we aren’t sure of the answer. It means we’ve really got something to think about and make sense of here. 
• Did you know that mistakes actually grow our brain? Each time you notice an error, new connections in your brain form and get stronger… So cool. 
• If making mistakes is a sign we are learning, then mistake-free work must be too easy. 
• Mistakes are the portals of discovery (James Joyce)

#4 Give space for self-correction and struggle

Giving time to struggle is important too. One of the hardest things for many helpers to do is to “hold back from telling”. It’s a practice I continue to work on! 

Of course, there are times when stepping in or “lowering the entry point” is necessary… Teaching is an art and it takes time to develop an approach that gives enough space and support. 

Starting with open-ended questions like What do you notice? What do you wonder? before questions that seek an exact answer can be a great strategy for building up confidence before the challenge.  

In this 4 min video, notice the struggle that the students navigate through before finding their error.

• What do you notice/wonder? 
• What would you do the same/differently to the teacher leading this conversation? 

#5 Model being wrong

Modelling curiosity about our own mistakes with a think-aloud can be powerful. For instance:  

I see I’ve added these numbers incorrectly...I wonder where I went wrong. 

Fake mistakes have their place in strategic teaching and I use these from time to time. When our mistakes are genuine and occur in the moment, these are a gift as they can be the best ones to model being wrong and inviting student help with. 

It not only demonstrates humility and vulnerability which fosters positive and productive relationships, it also shows students that making mistakes is a natural part of learning.

Hopefully something here has been useful to your situation. By drawing on these five practices — expecting mistakes, fostering curiosity, celebrating errors, allowing space for struggle, and leveraging our own vulnerability — I’ve seen learners of all ages (including myself) quickly repair their relationship with mathematics, and move from avoiding or just surviving mathematics, to thriving in it.