Research School Network: I can’t do Maths…yet! Blog 2! How gaps in recall can impact on future learning – the importance of mathematical talk

In this blog I will continue to delve into how we can support pupils to minimise gaps in their learning that may have a long time impact on confidence and ultimately progress. In the first blog in this series, I looked at how we can support pupils with the transition process, through shared curriculum planning, understanding pupils, avoiding narrowing the curriculum and effective intervention. I am now going to look at how mathematical talk can allow us to link and embed learning by developing pupil understanding.

Maths classrooms have changed dramatically over the years. Pupils seem to no longer have the attention spans or motivation to sit doing prolonged extended practice. In fact, Bo Brusco writes ​‘it’s empirically evident: attention spans are shrinking’ due to the changing tech driven world we are in. (Journalistic Learning Initiative, 2024).

Recommendation 3 from the EEF’s guidance report into Improving Mathematics in Key Stages 2 and 3 (2022) says that we need to teach pupils strategies for solving problems. Now problem solving itself is a very human skill, so what we must do is guide our pupils so they know how to apply this skill within mathematics. It is important that they can see the full process – dissecting the problem, considering which mathematical techniques to apply, the execution (using a logical approach), and the review – making sure the solution fits the initial problem. This is vital as a specific problem may only be seen once, whereas the techniques selected can be applied in a wide range of settings.

One way this can be achieved is through mathematical talk. The TOLD model gives us a framework to promote this high-quality talk. It emphasies the importance of pupils taking part, providing opportunities to work on shared problems encouraging collaboration, linking pupils’ different responses allowing the development of understanding and promoting debate.

When we focus on dissecting the problem (and providing these opportunities) is where mathematical talk really comes into play. This is an excellent opportunity to develop oracy, with mathematical language, and it can also be where pupils can develop the ability to turn text into visual representations.

In my own practice, I often use the mantra ​‘If it’s tricky, draw a piccy!’ I did not come up with it myself, but more adopted it. It’s a bit cheesy, but the pupils remember it. This gives us as teachers a way in to see the level of understanding and to use open questioning to develop it further. Craig Barton summarises it nicely in his book ​‘Reflect, Expect, Check, Explain’ when he says that mathematical thinking is made up of three elements: the role of the task; the role of the student; and the role of the teacher. Of course, to have mathematical talk, you must first have this mathematical thinking, so we must carefully consider these elements.

I have previously written about using worked examples to promote high-quality mathematical talk.

Worked examples can allow us to create talking points in a lesson, where effective questioning can be used to check understanding. It also allows pupils to consider different methods, and go on to share their own ideas, developing mathematical connections. As teachers we must be careful not to dismiss ideas but more guide pupils towards a valid route, ideally using their own thought processes. Recommendation 4 reinforces this when it suggests teachers should ​‘provide regular opportunities for pupils to develop metacognition by encouraging them to explain their thinking to themselves and others’.

In the example below we can see how different methods are displayed side by side, demonstrating the mathematical connections that link both. Teachers can model the thinking processes that led to each answer and include students by careful questioning to explore the links. 

Recommendation 5 reinforces this idea of explaining thinking further when it states ​‘Provide regular opportunities for pupils to develop metacognition by encouraging them to explain their thinking to themselves and others.’ However, it adds in the important warning ​‘Avoid doing too much too early.’ Pupils must be introduced to new ideas at a suitable pace, allowing them time to build these connections, practice with these skills and to develop their own ideas. This is where pupil independence comes in. You can consider ​‘thinking time’ before collaboration of ideas, as it is a pupil’s own thoughts that they rely on within assessment to secure their progress. This can be developed further with independent activities that rely on the pupil using these new-found connections. It is only when a technique is fully embedded, that they should be introduced to further ideas.

To summarise, well-planned talking points can allow pupils to demonstrate their understanding, and build vital mathematical connections that can support their recall of vital knowledge.

In the next blog, I will be looking at how effective assessment and feedback can help to identify gaps in learning and allow us, as teachers, to plan activities that support and guide pupils towards closing those gaps.

Further links and reading: 

Blog 1: I can’t do Maths, yet!

Subramanian, K.R., 2018. Myth and mystery of shrinking attention span. International Journal of Trend in Research and Development, 5(3), pp.1 – 6.

Henderson, P., Hodgen, J., Foster, C. and Kuchemann, D., 2022. Improving Mathematics in Key Stages 2 and 3. Guidance Report. Education Endowment Foundation.

Using Worked Examples to Promote High-quality Mathematical Talk EEF (2023)

TOLD: Four Evidence-informed principles to promote high-quality talk in Maths EEF (2022)