Research School Network: I can’t do Maths…yet! Blog 3 How gaps in recall can impact on future learning.

Welcome back to my exploration into how gaps in recall can impact on future learning, giving insight into some of the ideas and methodology that can help address it. We started our journey looking at Transition from primary into secondary and then we explored how Mathematical Talk can help check understanding. I will now conclude this short series by looking at assessment and some of the ways it can be used to secure progress.

In this blog, I will be largely drawing on the EEFs Guidance Report into Improving Mathematics at KS2 and KS3 and Recommendation 1 which is focused on assessment.

Assessment to me is the most important aspect of a teacher’s planning. When I say this, I do not mean the summative assessments but rather the smaller, more discreet techniques that subconsciously reward pupils for their success, whilst helping the teacher know exactly what they know, or more importantly don’t know.

As I have just said, and I purposely repeat, I do not believe there is anything more important in the classroom than assessment. The very ability to judge what the pupils know, what they understand and whether they ultimately remember is key to being an effective practitioner. 

This latter focus is the guiding question for this blog – Can pupils remember what you have taught them? This is also reinforced by the EEF when they say, ​‘Assessment should be used not only to track pupils’ learning but also to provide teachers with information about what pupils do and do not know.’

Problems with recall stem fundamentally from the way mathematics is traditionally taught. As teachers, we assess prior learning, making sure pupils can do any other maths they need that session/​week/​unit, then we model how to ​‘do’ the new maths, normally leaving a clear structure displayed for reference. We then assess that they understand, by using the clear structure they can see. This is normally followed by some kind of extended practice which, because it follows the structure they have just seen, they can successfully do.

If we think about it, it is obvious why this does not lead to long term learning. It is merely a pupil regurgitating exactly what they have just been shown. This in itself is not bad teaching of course, but we must look at ways to assess understanding which is not merely based on a pupil’s ability to ​‘stick to the given structure’. We must consider carefully how at each stage we check pupil understanding. 

In my previous blog on mathematical talk, I discussed how getting pupils to talk was fundamental to their understanding, so when we consider the role of talk in assessment, it is by carefully planning questions that make pupils think; specifying the connections to prior knowledge (whilst drawing out and addressing misconceptions) which are important. 

I personally also use talk and questioning by ​‘cold calling’ to draw in pupils who may get distracted or find it more difficult to grasp a concept or to maintain concentration thus attempting to ensure that they are not left behind.

Here at Etone, I have carefully built the mathematics curriculum around clearly designed Formative Assessment Points and this is having a strong impact for our learners. 

The new knowledge each year is built on connecting knowledge learnt previously. We do this by setting a simple Do Now task to prompt recall. This is then followed up with modelling of new learning, with simple steps, in an I Do – We Do style.

This kinds of activity works well on mini whiteboards but we also ensure that key information or structures are glued into pupil exercise books as a reference point thus starting to engender, or encourage certainly, some independence. 

It is vital that pupil conversation is encouraged throughout the learning episodes, so that this learning is not superficial. We can then really listen in and test understanding and gauge whether students can actually ​‘remember’ and truly understand the mathematical technique and why it works.

Once the teacher has established some sense of understanding, this can then be secured with a longer ​‘You do’ task to start to embed the learning and provide further practice. 

At Etone, these tasks are designed to identify any misconceptions and also contain challenge that can then be assessed using a whole class technique. I favour the hands up traffic light system.

This opens up the opportunity for Targeted Questioning leading into whole class discussion as an effective plenary, openly addressing misconceptions, and further securing pupil understanding.

Each topic ends with a low stakes ​‘Skills Check’ that pupils are guided to mark themselves. As these are designed around end points, it is easy for them to see how to improve. The teacher checks these as part of a book check and where appropriate, plans tasks that close any gaps found.

Although I said I would focus on formative assessment for this blog, it is important that we do consider the role of the more formal assessment.

These assessments should be an opportunity for pupils to showcase what they have learnt, questions should be linked to what they have seen, with challenge to make them think, but ultimately where they have every chance to be successful.

The Ofsted Research Report refers to the dangers of preparing pupils for assessment, in preference to full understanding, often leading ​‘to an acceptance of pupils moving through the mathematics curriculum with significant gaps in their knowledge…in these schools, some pupils would be better served by studying less, but securely learning more.’

As teachers we need to hold back from putting in too much challenge to our lessons, as too much challenge can disengage a pupil, and make them think they are not learning, or worse still reinforce the very thing we are trying to move them away from… That they can’t do Maths! We have to be mindful that we are building a culture where it is okay to ​‘fail’ and make mistakes, but people still need to feel those successes. 

To conclude, the golden nugget that runs right through this series, is to truly know the pupils in front of you on an individual basis. Even with assessment this is key. 

If we know the pupils, we can become better at understanding the best way to gauge their understanding! 

Further reading:

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



Mathematics guidance: Key Stage 3 DFE (2021)



Coordinating mathematical success: the mathematics subject report Ofsted (2023)