Is it a 'number talk'? Or a 'number talk string'?

Number talks are a 5 - 15 minute daily investment that teachers are finding to pay great dividends for the students they work with.

But it's one pedagogical approach on a large menu of maths talk routines being shouted about from the school rooftops. And sometimes there is some confusion about what constitutes a number talk and what doesn't.

This article explains a number talk using its key traits and does so in contrast to a similar, (but different) routine - a number talk string. While both talk routines focus on mental computation to solve number problems, there are some key differences to be aware of.

NB: Some refer to a string of related number problems as number strings. I already understand number strings to be this (a pattern recognition) in mathematics. So I use 'number talk strings' to differentiate this pedagogical approach from that mathematical noun.

1. The number of problems

Number talks focus on, highlight and celebrate a diversity of students' existing strategies in the group. And does so using one, single prompt. The discussion for which lasts anywhere up to 15 minutes.

In a number talk, we focus on one problem for 5 - 15 minutes.

When running number talk, that one problem to spark discussion needs to be 'juicy'; it needs to have the potential to come up with a range of solutions to solve it.

But not just that, the students need to have the existing strategies to solve it. No explicit teaching happens in a number talk - the ideas are generated by the group and drawn out through the questions posed.

Number talks focus on one, juicy number problem with a variety of possible solutions.

A good sign that it's a good fit, juicy problem is when it's difficult to keep to the time limit, as students are eager to keep playing in this creative computation space.

When an older group isn't yet equipped with the mental strategies to solve computation problems, dot number talks are an excellent place to begin. They ensure a high level of accessibility to the talk for all group members, and they provide a great playpit for explaining thinking.

Dot number talks are valuable and interesting for all ages.

This is different to a 'number talk string'

This is different to a number talk string where a set of related problems is presented, one at a time. The purpose here is to develop strategies. The length of the discussion is still limited to 15 minutes so the time spent on each problem is less.

In a number talk string, each problem posed prompts limited strategies. One problem is presented at a time.

2. The use of models

While the teacher chooses the problem, the strategies shared come from students. Number talks are not a time for explicit teaching. Instead, the teacher facilitates the discussion and records the various strategies on the board. They ask clarifying questions about each strategy as needed to ensure that what's recorded does, in fact, honour the students' thinking. If the student's explanation involves the use of a model (like a number line) it gets recorded. If they don't, then no models are used.

Meanwhile, in a number talk string, the teacher will often explicitly connect a student strategy to a model. This connects to the different purpose; developing strategies. So, while the teacher invites strategies in both routines, in a number talk string there's usually a bit of input from the teacher into developing strategies.

3. The format - whole class or small group?

There is much for everyone to gain in a number talk. It's a chance for everyone to be involved in a short discussion around a problem, to be curious about each others' ideas, to practise attentive listening, and to reason mathematically about the strategies generated.

The teacher gains plenty too - not just mathematical insights but also observations on student character and confidence. I often think of number talks as a mathematical equivalent to story-time, where the whole class comes together to connect through story. Only in the number talk, students are sharing their own stories about how they approached a problem.

Number talks strings are often run as a whole class too. However, I have seen videos of number talk strings in action where only a few of the students were engaged because the focus of the number talk was above the appropriate level for most of the group. To me, this isn't a good use of whole-class together time.

For this reason, I have less reluctance about running number talk strings in small groups. Given that their purpose is to develop strategies, it makes sense to differentiate instruction with them. I simply caution, when using small group instruction, against fixed performance-based groupings or other grouping models that look like, sound like or feel like streaming.

I hope this has answered a question or two. Feel free to post further questions or comments below.