In 2018, around one-fifth of 11-year-olds entered year 7 with a mean key stage 2 score below age-related expectations. Five years later, only around one-quarter of those students achieve a grade 4 or higher at GCSE (DfE, 2024).
There may be many reasons why such students do not achieve a grade 4 or higher, but I would argue that a lack of intelligence is not one of them. Talk to a student in a bottom maths set about something they are interested in. They will probably be able to talk knowledgeably and engagingly about it and might show their ability to reason well in their chosen context. There is nothing wrong with their “logic circuits”.
I started in the profession 36 years ago. For all the changes and improvements there have been in that time, there is still an underlying belief that some students “simply cannot do maths”.
Low-attaining students need to be receiving an important message: “We know you are behind with your maths, but secondary school is a fresh start. Five years is a long time, and with our support you are perfectly capable of leaving school with a decent working knowledge of the subject, to equip you for later learning and adult life.”
Fine words, you may say. But how? Through making sure that the structure of the curriculum is suitable for these students’ needs, and applying high quality, patient pedagogy consistently throughout the five years.
Simple? Obviously not. Necessary? Absolutely.
Choosing a scheme for low-attainers
Many schemes of learning, including a number of published schemes, do not serve low attainers well. Do you ever visit a low attaining group in year 7, studying (for example) expanding brackets, and later in the week walk into year 9 and find low-attainers doing exactly the same topic – possibly even using the same resource? It is something I have seen, several times.
Topics taught to bottom sets are often not appropriate for their level of understanding. Challenge is one thing: appropriate challenge quite another. In maths, teaching an algorithm can be easy, but if the students do not really understand what they are doing, it is likely to be forgotten. Hence the oft-repeated claim by their teachers: “They understand it in the lesson, but don’t retain it.”
So much of these learners’ time in maths lessons is wasted doing work they do not really understand because they are not yet ready for it. The topic of expanding brackets is a good example. Simple though it may appear, for it to make sense, and hence for students to remember it, it requires a good deal of prior understanding.
As we know, new knowledge needs old knowledge to “stick to”. That it is not retained should not be a surprise. Teaching students to run before they can walk may mean they never learn to do either.
As a result, low-attainers end up “learning” the same methods time after time without ever truly understanding or mastering them. My motto for schemes of learning is “Do it once; do it well” – but for lower attainers this could not be further from the truth.
Surely it is not beyond us as maths teachers to plot a sequence of learning from well-below-average starting-points to a grade 4? Does effective sequencing of the curriculum not apply to bottom sets?
The importance of pedagogy
How about these four important principles – a “quartet for quality”, if I may?
- Learning gaps: One of my primary specialist colleagues once said to me: “Intervention should begin at the point where the child last experienced success.” There are often so many gaps in learning from the student’s distant past. Do not take anything for granted, and constantly reinforce.
- Calculation: Confidence in using mental methods of calculation is so important in developing understanding of mathematical structure. All students, particularly lower attainers, should be taught and encouraged to use these wherever appropriate.
- Representation is central to mathematics: The way in which ideas are represented, through bar models, graphs, number lines, ratio tables (to name but a few), and using a range of concrete manipulatives, can make a huge difference to students’ understanding, particularly for lower attainers.
- Encouragement: Despite its reputation, mathematics is not just about numbers. It is about pattern. Of course, it uses numbers a lot, but there are many outstanding mathematicians who confess to being poor at arithmetic. Just because students fell foul of the calculation-obsessed primary curriculum, it does not necessarily mean they cannot become very good mathematicians. They need to be told this.
Final thoughts
Perhaps most important of all, low-attainers need to be taught by staff with the best relevant pedagogical knowledge. Diagnosing and remedying significant gaps in knowledge is a very skilled job indeed.
The fact that, after 11 years of compulsory education, there are still students who add or subtract using their fingers, or who don’t know that 37% and 0.37 are the same, should be a matter for national shame. Our low-attaining students do not lack intelligence – we are just failing to meet their needs.
- William Thallon is a secondary maths adviser with HFL Education. Formerly Herts for Learning, HFL Education is a not-for-profit organisation providing services, training and resources for schools. Follow at @HFL_Education. This year SecEd is working with HFL Education to publish a series of subject-specific best practice articles. Find all the articles in this series via www.sec-ed.co.uk/authors/hfl-education
Further information & resources
- DfE: Data set from Key stage 4 performance: Key stage 2 to 4 transition matrices GCSE subjects, 2024: https://explore-education-statistics.service.gov.uk/data-catalogue/data-set/a317ce4a-07cc-4090-9d88-cd4c47527058