Nerding out over number talks (at MathsConf 25)

Five years ago, I didn't yet know what number talks were. What sparked an investigation into them was an opportunity to visit another school. Since discovering them, my own approach to teaching maths began to transform.

These days I enjoy opportunities to spread the word about number talks - their life-changing potential and power. So I enjoyed the opportunity to share recent learnings at MathsConf 25. There was a passionate, curious and like-minded group in attendance who submitted fantastic questions and ideas that helped drive the session. Here are some of the big ideas we talked about.

What number talks are

A number talk is a 5 to 15 minute routine that brings a whole class together to focus on mental strategies for solving number problems - and talk about that. Number talks are an opportunity to really push on and develop our ability to think about and make sense of numbers without pencil and paper.

Number talks are stand-alone events that don't have to connect closely to our main lesson. Regular use of them in the maths classroom (e.g. 1-3 times per week) allows us to have a safe and ongoing learning conversation where big and important number ideas like place value, additive thinking and multiplicative thinking are drawn upon and applied.

I'd describe number talks as an incredibly rich approach since, over time, they can have an impact on various aspects of maths learning: from helping to build positive maths norms and mindsets as well as deeper understandings in Number and improved fluency. For me, powerful pedagogical habits that developed seeped into maths teaching contexts beyond number talks.

How a number talk runs

1. Students are presented with a prompt

The prompts in a number talk are dot formations or number problems. The first step is for the teacher to reveal the prompt and verbally emphasise the thinking task. In our MathsConf 25 session, we started by exploring this dot formation prompt.

2. Students have think time - time to solve the problem mentally

The group are given think time to work out the total in a way that makes sense to them.

There are no mini-whiteboards or notepads. The group's attention is on the prompt and what's happening in their minds.

Students use subtle hand protocols to indicate where they're at with their thinking - this helps the teacher get a sense of how much time is needed by the group to access and make sense of the problem.

I love how number talks move away from the idea of being 'done' with a maths problem. In a number talk, students are encouraged to make full use of the think time by looking for additional ways of counting or making calculations. I see this aspect as a powerful way for creating habits that support mathematical precision, as students are mentally checking their work by looking for other strategies for solving the problem.

3. Collect all answers from the group

Collecting all answers is an important step that is completed in full before moving onto sharing strategies. This is where, as the teacher, we put our no-judgment poker face into action and accept all answers, no matter how out-of-the-ball-park they seem.

By visibly adopting a default expectation that there will be multiple answers, mistakes are seen as normal and as a part of the process. With multiple answers to 'defend' when sharing strategies, we can create genuine opportunities to think about and learn from strategies that didn't quite work.

When launching number talks with a group, it usually takes a little time to delineate answer-sharing from strategy-sharing. At first I wondered why it was so important to separate these steps - why couldn't we let students share their answer and strategy together? I then realised that, by having a clear step where we collect ALL answers, we can avoid situations where a correct answer is 'defended' and interferes with the cultural learning norms that the sharing-all-answers step is helping to build.

An abandoned practice

For a while, I invited students to use the 'I agree' or 'me too' hand signal to indicate if they got the same answer as any which are shared during this answer-collecting step. I've since abandoned this practice since reading this excerpt in Ruth Parker's 'Confessions of a Learner' (page 78) in Digging Deeper: Making Number Talks Matter Event More:

Here's what's going on for some of us in the midst of showing hand signals. We're asking ourselves, If I give the "me too" signal for a wrong anwer, is everyone going to notice that I don't get it? Even if I'm confident, are there others our there who are feeling put on the spot? Who can I watch so I can piggyback into their response and just do the same thing, since I trust they do get it? What if I disagree with nearly everybody - do I dare suggest a different answer? Am I being assessed right now? Forget about thinking; our brains are in search of safety!

There are various pedagogical nuances that help to keep number talks a safe space for all students. This perspective from Ruth is just one example informing these.

4. Facilitate sharing of student strategies

The sharing of strategies step is where the 'talk' in 'number talk' happens! As the visual breakdown here aims to show, this is the main event of a number talk and is what most of the time is spent on.

The are various jobs going on at this stage. We (teachers) put our skills to the test with careful listening and asking questions that draw out precise explanations. We're also recording student thinking on the board for the benefit of the group.

I love how the job we have as 'recorder', creates a natural expectation on students to provide precise explanations so that we can share their thinking accurately on the board.

One of the challenges we have here is to ensure we avoid assumptions about student thinking. Using clarifying questions is important to honour student thinking e.g. 'Do you mean like this? Or do you mean a different way?'

This image attempts to capture how number talks create time for individual thinking so that all members of the group have the chance to generate their own ideas. It's also a highly collaborative event where the group benefits from the sharing of different strategies. I am so often surprised by a strategy or way of seeing by a student that I hadn't predicted would come out.

A common challenge of number talks is that they can easily run well over-time. I don't worry to much at the start, when number talks are new, as the reason for running over-time is often because students are just so engaged and excited to share!

After the first couple though, my go-to strategy is to use a timer. When the timer goes, and students still want to share, encouraging them to do so with someone nearby can help as we transition to the next task. Keeping number talks short makes it more likely that they'll be energising and sustainable for students for the long term.

An abandoned practice

In 2018, at a conference, I was in a session where 'equity sticks' were used in a number talk. When we entered the room, we were given a popsicle stick to write our name on. Then these were drawn out of a cup randomly to decide who would share their strategy. I quite liked how this meant that choosing people to share wasn't a teacher decision - I was already aware that we are subject to unconscious biases when inviting student contributions and this seems like a clever tool to avoid that.

Another reason put forward at that session about their usefulness was about keeping students accountable to engage. I tried using 'equity sticks' in a Year 1 classroom subsequent to that session and abandoned it soon after. Again, Ruth Parker offers valuable insight on this:

Popsicle sticks are sometimes called equity sticks, but I believe they are inherently inequitable because not all students have the same level of comfort with being called on randomly. I know that [it's] intended to make sure that all students are engaged. But I'm not at all convinced that this practice results in higher levels of engagement; quite the contrary... We might be able to make students participate (even if it's only by saying "I pass"), but we can't make them engage. Engagement comes from being curious and wanting to figure things out. It comes from wanting to be part of a conversation - whether or not you talk.

'Number number talks'

With only one hour at MathsConf 25, we didn't dive too deep into 'number number talks' but we did take a few minutes to explore what these can look like. We follow the same steps as listed above but the recording looks a bit different.

We could spend several dedicated sessions just on 'number number talks'! I allude to their power and importance in this personal learning reflection.

If you have number talk experiences or strategies to share I'd love to hear them!