Child A enters school with limited number sense and spatial reasoning.
Child B enters school with some number sense and spatial reasoning.
What do we do to enable both children to succeed?
Perceived wisdom seems to be that the children are parallel tracked from their earliest experiences. Child A needs simpler and less to feel successful. Child B will be provided with more and richer mathematical experience.
If we turn that argument on its head we might argue that Child A needs more and richer mathematical experience to achieve a greater equity with Child B. Then Child A will feel successful through their own endeavours.
Some children will always need more though they may not be the same children depending on concept, stage and external contributing factors. More time, more focus, more practice. I’d argue that what they don’t need is less.
Imagine the two children as they journey through school. What will the differences between the children be by the time they reach Year 6? My experience is that if the first model of delivery is pursued, less is expected of these A children by their teachers. The work in their books has some telling characteristics. The following represents my finding from work scrutinies and lesson observations where schools have asked me to look to find reasons why a group of children are not making the learning gains they could. These are broad characteristics and do not represent every child A or B, sometimes there is a mathematical difficulty that is holding back Child A and once diagnosed and addressed new gains and confidence often follow.
However, over time a practice and experience deficit begins to build up which exacerbates the gap, meaning that by Y6 this is much more difficult to close. Think of a child in your class that completes a lot of practice, is hungry for more and a child that never seems to complete practice and sometimes you wonder what they were doing all lesson. Looking through books in every year group we can identify the pupils for whom this is having a negative impact on their ability to keep up. Over time less output is expected of those children – so they produce less. They expend less effort on the learning and if you expend less effort you are not as likely to imprint it into long term memory. Conversely, the children who complete more have more expected of them and as long as the practice is of the right kind, they become more successful and often expend more effort. In some cases this can be very stark. When looking at groups of children who did and did not score 100+ on the KS2 SAT 2018 it was apparent we could predict those who did and did not just by looking at the work that was produced in the Spring Term.
Why does this matter?
Practice is crucial in any discipline. The risk of not completing enough of the right kind of practice is that children will not have necessarily secured the procedural automaticity, made connections and explored concepts needed for future mathematical work. They don’t have enough bricks to build with.
So doing less than others overtime can exacerbate the gap. But also what I notice is the simpler tasks are given to (or sometimes chosen by) A children. Often these are also over-scaffolded and/or supported by an adult on almost every occasion. This leads to parallel mathematics curricula existing in schools. For a few learners this may be entirely appropriate, however, my experience is that there are a large number of children (often from the disadvantaged cohort) for whom we should proceed a little differently.
What follows are examples of how we can boost success and prime learning.
- interspersing practice with worked examples to discuss and then use to complete further similar (but not necessarily the same) type of examples
- fading scaffolding over time so that it is all visible/accessible at first but then gradually reduced passing over the effort to learners
- identifying prior learning necessary to future learning and using this to track up to new learning
- pre-teaching so that core facts, skills are more automatic before new learning
- identifying specific areas of difficulty i.e. not just they don’t understand place value but they haven’t secured place value equivalence for example one hundred tens are equal to 1,000 or understanding what a unit is; then intervening to address
- reviewing high value learning beyond the teaching in ‘Everyday Fluency’ sessions to allow children to ‘remember’ what they learnt and further imprint into the long term memory
The Herts for Learning KS1 mathematics fluency project was interesting in that one group stood out in particular as making the greatest gains in automaticity when practice was increased, regular and focussed. This was the disadvantaged learners. Once more time was devoted to them rehearsing quite specific skills/facts the outcomes showed that they were then able to deploy these accurately in deciding on strategies to solve calculations mentally. In every round of the project the disadvantaged pupils closed the gap between themselves and those identified by their teachers as competent calculators by the end of the project, even though the competent calculators also improved. What is more, teacher surveys after the projects identified that teachers had reviewed the way they perceived their learners. They had higher expectations of all children as a result. Children in the group teachers identified as weaker calculators, were also cited and observed to be more confident and enjoyed trying out different strategies by the end of the project. Success bred further effort and effort is of course necessary for learning.
A number of times throughout the blog I have referenced the ‘right practice’. This is because even though one child may be more effortful than another it doesn’t mean they are practicing the right things. Child B therefore may not get there either. If children are only rehearsing using many randomly chosen standard examples a + b = c for example then they may develop inflexible knowledge that leads to difficulties later with examples such as c = a + b or c – b = a. This is because the examples may not have focused on the equality between a + b and c but on the computation only. An earlier blog discusses this in relation to KS2 assessment outcomes: KS2 reasoning papers: an uphill struggle?
Some schools have cracked this and the results speak for themselves; children who talk the maths talk, who want to practice, who reason and solve problems applying connected learning, who are proud of their successes, who can walk the walk when assessed and who are taught by teachers with high expectations for them.
To sum up, I see that if we can increase effortful learning by putting the right practice into place and provide the space for some children at any time in the journey to have more, more, more and to specifically address any underlying difficulties then the deficit can be minimised.