With thanks to Nick Hart, Deputy Headteacher at Penn Wood Primary School in Slough, for this really interesting article on closing the disadvantaged gap in maths.
Part 2 – common gaps in maths and how to address them
In part 1 of this post, I explained the importance of knowing the specific barriers that contribute to low attainment for the disadvantaged children in your schools and classes. Some of those barriers are beyond the school gates while some are generic. The maths specific barriers that I identified in part 1 are the subheadings below and we’ll look at how each one can be addressed in turn.
Insecure knowledge of facts such as number bonds and times tables
If children do not have facts committed to long term memory and are skilled at recalling those facts when needed, then children will struggle when faced with a question like this:
The task requires the child to add 3 of the 5 given numbers and find a combination where the horizontal and vertical numbers have an equal total. A child who has instantly recalls number facts will be able to try out different combinations with ease, focusing on whether the combinations are equal because they are not expending any mental effort in adding the one digit numbers. In contrast, if a child does not have these facts internalised, they will have to count on to find the totals. Because their working memory is being used up with these calculations, it is highly likely that they will be unable to keep in mind the goal of the task – to balance the horizontal and vertical totals. As a result, the child may well just fill in numbers seemingly at random.
The maths curriculum and the pedagogical practices used to get children to learn it should ensure that recall of number facts is a priority. Children can’t ‘just work it out’ – this is simply not an acceptable attitude towards closing the gap. So what is the best way to learn number facts? Concrete manipulatives to model how numbers are related and regular low stakes quizzing to ensure children get quicker and more accurate at recalling facts. Flash cards are good here and this is a good use of TA time – short bursts of quizzing with flash cards and subsequent modelling / explanation if the child has a misunderstanding.
Lack of understanding and fluency of standard calculation methods
Consider a question such as this:
To solve this problem, children need to add the heights of Kilimanjaro and Nevis, then subtract that from the height of Everest: column addition, then column subtraction, assuming that the answer to the addition calculation is correct. Also assuming that the child can figure out what calculations are needed in the first place. The trouble is, if the child’s entire working memory is taken up on the calculating, then they will almost certainly lose their place in their thinking about what to do next. This is why is important to be able to calculate with automaticity, almost without thinking, so that full attention can be allocated to thinking about the problem. Often, we set practice tasks until children get it right. Our most vulnerable children need to keep practising until they never get it wrong. This practice needs to be little and often.
Loses their place in multi-step operations / tasks
A similar problem to the one exemplified above is losing one’s place in a problem that requires multiple things doing. If children’s working memory is exhausted by calculating, then their attention cannot remain focused on the bigger picture of the problem. One solution here is to provide step by step worked examples alongside problems that children are solving themselves. They can use the worked example to make sure that they follow the problem through to the end and by making the problems increasingly varied, the scaffold of the worked example will be less and less necessary.
Poor understanding / quick forgetting of key mathematical vocabulary
If children do not know what a mathematical word means, they have either never come across it before or they have forgotten it. As teachers we know that we have ‘taught it’ but of course that does not mean that children have learned anything. When learning new vocabulary, mathematical or not, children need multiple interactions in order to internalise new words. One of the reasons that children do not remember mathematical vocabulary is that they do not use it often enough. If children learn about angles once a year, knowledge of the names of different sized angles won’t necessarily stick. Very simply, if we want children to use mathematical vocabulary accurately, we have to let them hear it more often and use it more often. Displaying words in the classroom is not the answer – this is just background noise and children learn to tune out. Much better is regular quizzing, particularly of old topics, which is why teachers must have a very good knowledge of what is expected across their year group and feed in revision activities regularly to offset the natural process of forgetting. Flashcards are great here too because they work just as well for prompting children think deeply as they do for simple recall. For example, the prompt on the flash card could be: True or false – all quadrilaterals have 2 pairs of parallel sides. In thinking about and responding to prompts like this, children have to interact with mathematical vocabulary. If working with an adult, there are even more opportunities to elaborate. The adult could ask them to prove it by drawing, annotate the pictures with vocabulary or insist that explanations contain given words. This is a great activity to do if the adult formatively assesses what the child knows and addresses misconceptions there and then.
Poor attitude to maths / gives up quickly
The direction of causation is counter intuitive – we often think that you have to be motivated in order to work hard and be successful and so teacher effort is ploughed into attempting to motivate disengaged children. This can take the form of making the content of the lesson ‘more engaging’, perhaps by using a context closer to children’s hearts, like fidget spinners or slime. Inevitably, children’s ears prick up at this but they’ll probably remember the context and not the maths. Motivation and success work the other way around – children have to experience success in order to become motivated to seek more. Our job then is to set children up for success and then point out those successes to them. Carefully breaking down tasks into manageable chunks and scaffolding tricky bit helps children to get things right. That can then be celebrated. Over time, children experience more and more success and in turn want to do more of the same because they are getting good at something. Familiar tasks are important here, subtly varied over time to ensure a range.
The maths curriculum needs to explicitly spell out what knowledge children need to acquire at each stage of their education. This includes knowledge of facts but also knowledge of procedures – how to do short division for example. Our curricula must be designed in such a way that benefits our most vulnerable children and this design must take into consideration what we know about how children learn and forget. Regular revision through low stakes quizzing with subsequent re-teaching or intervention where necessary is the very essence of what teachers should be doing and when done well, has the potential to close the disadvantaged gap for good.