The two questions I am often asked by head teachers and subject leaders at this time of year, when they are reflecting on outcomes and writing action plans is; how can we improve progress in maths? Or, how can we improve attainment in maths? Some school want both, others are focusing on one more than the other.
As the lead for the ‘Improving progress in mathematics’ project, run by HfL, these questions form the basis for our work on the project. Although we say that there is no magic wand, silver bullet or easy answers, maybe there are a few (fairly basic) things, which if done well, can have significant impact.
When you narrow it down, there are usually pupils in any cohort who are key to either the attainment or progress measures (or both): The pupils who struggle to make the progress they are expected to make across Key Stage 2, and sometimes the same pupils who are also at risk of not reaching the expected standard.
To pause for a moment on why this is important; I’m sure we all believe that all children deserve good teaching, to make progress, enjoy their time at school and feel secure in their learning. We know that children who attain the expected standard at the end of Key Stage 2 generally, statistically, fare better through secondary school and go on to achieve better GCSE grades than those who begin secondary school below the expected standard. And we want all children to have a range of options open to them beyond their GCSEs.
So, the three main suggestions I make below are hinged on good teaching provision for all children, which allows them to make progress, as a direct result of securing learning. It is really important to state that these are not new ideas. Most schools would say they are trying one, two or all three of them. My challenge would be; how well are you doing them? Do children secure learning as a result? Because to do these well, with whole school consistency, is challenging.
To give a brief background to the thinking: Making progress is essentially about accumulating learning. If you are learning more within a subject, you should be making progress. Right? (Providing the learning is of appropriate content, including relevant and age appropriate knowledge and skills).
Ofsted’s latest school inspection handbook, May 2019, says;
182. Learning can be defined as an alteration in long-term memory. If nothing has altered in long-term memory, nothing has been learned. …In order to develop understanding, pupils connect new knowledge with existing knowledge. Pupils also need to develop fluency and unconsciously apply their knowledge as skills. This must not be reduced to, or confused with, simply memorising facts.
I really like this link between learning and memory and the obvious implication that children need to remember their learning (though this is by no means the only definition). This helps us when we think about constructing our teaching and considering our provision. Do our lessons (and curriculum) promote the remembering of the knowledge and/or skill/s being focused on? And does what wraps around our lessons also promote this?
And so to the three suggestions. If done well, I believe that together they could have a significant impact, with more pupils securing learning, which in turn would address questions around attainment and progress.
The group of children who are likely to benefit most from these are the children who are sitting just below what is considered ‘age related’ and those struggling to maintain ‘age related’, often affecting attainment and progress.
1. Fading scaffolds and support, to build pupils’ independence: Moving children from ‘guided’ to ‘independent’ in a structured way. Vygosky’s work suggests that if we can do something well independently we are securing or have secured the learning, more so than if we continually require guiding and support.
2. Addressing learning quickly, if it is not yet secure: Noticing if a child has not secured the key learning from that lesson (with reasonable independence) and acting on this, so that the child is not expected to move on with the next lesson based on an insecure understanding. Developing an approach to our teaching of keep-up rather than catch-up.
3. Building in opportunities to develop fluency, including spaced retrieval practice: Again, focused on securing learning, but this time the focus is on the remembering and manipulation of the learning. Some maths can end up being taught in small isolated chunks, for example shape vocabulary, telling the time, Roman numerals, each taught usually for a few days out of an academic year. Children can then struggle to remember the learning, if they do not need to use it for a period of time. We need to arrest the forgetting of learning which was previously secured but has not been used for a while.
In reality each of these could be a blog on their own, but sharing them together feels like a more holistic approach to securing learning. There is huge a amount available on all three areas, but I think it is their application in a combined way which is the key to impact.
In slightly more detail and with examples from my own work and experience;
Fading scaffolds and support, to build pupils’ independence:
When a child is struggling with their learning, guiding them is entirely appropriate. Supporting them through a process helps them to see and achieve the outcome. Many children work with teachers and TAs in ‘guided groups’ all over the country to enable them to access and achieve learning. So, what’s the problem? In my work with lots of schools I suspect that there are some children who become over-reliant on this support. They lack independence and then you find they don’t remember the learning. Do adults needs to develop strategies to fade the support? By gradually reducing the scaffolding, the child builds independence and confidence, and as this happens they are also likely to be building memory.
A slide I have been using with both teachers and TAs shows this process:
I find this strategy works particularly well for fairly procedural areas of learning such as written methods. There are many variables, such as how many maths questions might you ‘guide’ before you drop down to ‘prompting’ and then ‘observing’. This will be dependent on the child. Pointers would include; be prepared to move back a step or two if necessary, for example, if you reach the point of ‘observe’ and the child struggles, you may need to go back to ‘guide’ to address this. Is it also helpful if the pitch does not increase very much (or at all) between questions, because the focus is this case is on building independence.
The aim is to reduce the reliance of the child on the adult (or other scaffolds and supports) over time as part of the process of the child really securing the learning for themselves and so remembering it.
It comes with the caveat that if you can’t move on from ‘guiding’, then the learning is not appropriate for the child at that point and so learning will not be secured.
Addressing learning quickly, if it is not yet secure:
When sufficient learning has not taken place in any maths lesson for a child (or group of children), this learning needs to be continued. If it is a large number of the class then the next lesson can be used to address this. However, if it is a child or small group, that has not secured the learning sufficiently to be ready for what comes next, for example if there are errors in their work which suggest incomplete understanding, or if they have not had sufficient practice, then they need further. Sometime this needs to be supported by an adult.
Many teachers use ‘same day’, ‘rapid’ or ‘immediate’ intervention to give a name to this. Meaning that they catch that child or group, to consolidate that learning before it moves on in the next lesson. This might be a further 10-15 minutes with the teacher or TA to further practice what was being learned that day, focusing on the key skill or knowledge, so that the child is able to keep up when the next lesson’s learning moves on. This relies on the adults noticing day-on-day how the child copes, and intervening within and between lessons when needed. The focus is very much on keep-up rather than catch-up.
For some schools, this is replacing some of the more traditional interventions: Where previously adults might have taken pre-planned groups of pupils to work on a pre-planned focus, they are now responding more to what has happened that day in the lesson – who needs the extra input and what specifically do they need to secure now to be ready for what come next? Then you come back to and combine this with the first strategy given above, where guiding needs to be faded to independence.
A really basic example to model the point would be in the Autumn of Year 3 when children commonly learn formal column addition layout with 3-digit numbers. Children should be able to regroup when this is necessary, so 247 + 138 = 385
If in the main lesson a child (or small group) could complete the layout, but clearly struggled with the regroup element (where 7 + 8 = 15, what happens to the ten within the 15), where the rest of the class had largely succeeded, would it not be obvious that the child/ren need some further support and rehearsal?
The aim for catching the learning within and/or between lessons is to allow the child to keep up, rather than needing to catch up later when lots of small gaps have accumulated and led to them falling behind their peers.
The measure of whether this is happening (or not) in your school already might be to look at the books of the children who sit just below age related expectations:
- Is their learning pitch at / building towards age related expectations?
- When they struggle (if answers are incorrect), what happens?
- Is there any evidence that they are supported with their learning within or between lessons in order to maintain pace and understanding with their peers?
- When you look at the learning in their books, do you suspect they will remember the knowledge and skill/s over time? Have they have sufficient practice and has there been some varied practice, such as changes in layout or application of the learning?
- Have they developed independence?
Building in opportunities to develop fluency, including spaced retrieval practice:
The third suggestion also relates back to the Ofsted quote used earlier, but focuses on the memory retrieval and fluency elements. In maths, some things are commonly taught in isolation, for a few days out of a school year. The examples given earlier were shape vocabulary, telling the time, Roman numerals. It is probably true that, a few days learning something out of a whole academic year may mean that although children learn it at the time, they may not remember it weeks or months later. Other areas of maths might include conversion of measures, rules for rounding numbers and long division, these have been learned but need a workout so that children can bring them more easily into the working memory.
To address this issue, many school are working on building ‘fluency’ opportunities into their timetables. Whether these are called maths meetings, fluency session, daily fluency or something similar, the idea is broadly the same: small amounts of time are protected, say 3-4 times per week (or daily), for around 10-15 minutes, in addition to the maths lesson. These short sessions are used to address several areas of prior learning in maths briefly to allow pupils to retrieve and apply this learning.
An example for Year 4, covering 5 chosen areas in the 10-15 minutes, so spending 2-3 minutes on each might include;
- reading an analogue and digital clock to decide if the times match
- discussing strategies for calculating 2583 + 4762
- working out 3800ml in litres and then 1.04L in millilitres
- converting 243 into Roman numerals
- Describing similarities and differences between a kite and parallelogram (with images given)
Teacher are likely to select recent or prior learning which might, if not rehearsed, be forgotten. The next session would keep the same 5 focuses, but change just one small thing about each question. The aim being to build the memory and retrieval, the confidence and fluency within those areas. After 2-3 weeks, when the children are fully confident with those areas, they are gradually changed. So Roman numerals might be dropped and rehearsal of the recently taught written division method might replace it. The caveat here is that it cannot be new learning as the sessions, although adult led to keep the questioning and pace, are not for ‘teaching’.
To help schools reflect on this idea of fluency, it is helpful to ask: For the children who sit just below age related expectations, how do they cope with retrieving learning? How would they cope with a ‘test’? Would they benefit from opportunities to rehearse their learning (and apply it in new ways), in regular slots which are planned to retrieve learning which is not the current maths lesson focus?
Taking all three strategies into account, between them there is probably plenty for any school to reflect on, when considering addressing progress and/or attainment in mathematics. The final note is about the leadership of all three; to ensure consistently good practice is embedded across the school. Within the leadership of this there is the need to monitor and give feedback. Looking at books, talking to children, watching fluency sessions and reviewing data all play a part in building the picture. Does the picture suggest that more pupils are securing more of their learning? Is this likely to lead to the improved progress and/or attainment that the school is aiming for?
Senior leaders and maths subject leaders might like to ask themselves:
When looking in the books of children where there are attainment and/or progress concerns; do you see pupils being well supported day-on-day, but becoming independent, and so securing learning? If the child makes errors what then happens and is there evidence of this?
When the same children are asked to retrieve prior learning, including in a ‘test’ situation, how do they cope? Can they retrieve the learning which the teacher would say, at the time they taught it, was secure?