Number talks - nurturing and normalising mistakes
Updated: Jul 17, 2021
'We learn from our mistakes'. 'Mistakes help us to learn'.
These phrases are use and heard commonly enough. But I think they are really very token in a world where perfectionism and anxieties (performance anxiety, social anxiety and maths anxiety to name a few) are rife. I've spent a good deal of time navigating these myself and understand how disabling they can be. It's incredible how entrenched fear of failure is in our culture.
One of the beautiful things I love about number talks, and other maths routines that adopt similar pedagogies, is the way that they nurture and navigate mistakes to pro-actively normalise them. This post lists five little practices that I see as adding up, pedagogical nuances I've developed or learned from others, to help build a safe space for risk-taking during number talks. Some of them transfer nicely to other maths learning and teaching contexts.
These are my current practices - as a personal approach to number talks and maths teaching generally is ever-evolving. If you have other ideas or perspectives to add, please do join the discussion.
Start with dot formation prompts - for all ages. Very young grades will typically use free dot formations and dots on a ten frame in their number talks. But dot number talks are powerful for creating that safe space where more people will feel comfortable verbalising and sharing their ideas. It's also a really lovely way to demonstrate the variety of ways for seeing and approaching a problem - to build norms around valuing different strategies. And demonstrating how efficiency can look different for different brains.
2. Expect more than one answer. In number talks, one of the protocols is to collect all
answers before inviting strategies. Repeated consistently over time, this step can help to create a space where it's safe and normal to have multiple answers.
3. Leave undefended answers on the board. In their latest book, Humphreys & Parker (
(page 20) call out that uncomfortable feeling that many teachers have of leaving multiple answers of the board and finding themselves wanting to agree on what's correct. They recommend that we 'accept all answers and that they try not to indicate whether answers are right or wrong'. (It's a brilliant book, written mostly for teachers of years 3 to 10. And there's a dedicated chapter on Mistakes).
I personally practice adding 'proof strokes' under the answer that has had a clear strategy support it, emphasising the stacking evidence for that answer. With
this visible clarity, it feels even more unnecessary to remove those other answers which are inferred as incorrect.
4. When students change their answer, aim to keep it visible (but ultimately leave it up to them). This practice was raised by my friend and fellow primary teacher Gabi - the importance of keeping mistakes visible to highlight their role in the process and help normalise the presence of mistakes on the maths learning journey. It's an important point, especially as I think that it can feel quite counterintuitive not to erase something once we know it's 'wrong'.
Having dabbled in different approaches over time my currently approach is this:\ In order to keep it a safe and comfortable, let the contributor choose what happens
with their ideas. When a student wants to change their answer, the approach I'd use early on to help form this as a student-owned protocol is to ask:
Would you like me to leave it up to remind us what happened in the process? Or would
you like me to put a strike through so we can still see it? Or would you like it removed?
Once this protocol is formed, we can have a short version of the question, one that becomes a normal part of maths conversations, while it's relevant:
Shall I leave it up, strike through or remove?
5. Nudge towards a mistake spotlight. This is a one- or two-pronged strategy that uses
specially designed dot formation prompts. I like using these help overcome reluctance to share answers which might be a mistake, as well as strategies that help explain the mistake.
a) Choose a dot formation prompt that has the potential for miscounting dots. You might have spotted an example in the image above with the overlapping dots where 12 might be seen (instead of 10) by counting two of the dots twice. Here are a couple of other examples. Access these images and more as a PDF here.
b) Even if we choose a formation that has a potential miscount built-in, it doesn't mean that a miscount will happen. If it doesn't happen, and I want to work on normalising mistakes, I will introduce a theoretical mistake after the initial
sharing of student strategies with this question: How might someone see 15 (instead of 13)? And we can explore it then, theoretically.
That's all from me for today. I'd love to hear any strategies or pedagogical stories you have for nurturing and normalising mistakes in number talks, or in maths teaching generally :)