Treating symptoms vs addressing causes: Developing a deeper understanding of maths difficulties

Many children (and adults) struggle with Maths. Government statistics suggest that 49% of working-age adults in England have the numeracy level that we expect of primary school children, and that the opportunity cost of poor numeracy skills for the UK economy may be as high as £20 billion per year[1].

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As teachers, we often use curriculum-based tests to help us understand what learners can and can’t do, and how this measures up against expectations for their age and stage. This information is then used to plan support and interventions for learners who are struggling. While often effective, this approach sometimes means that we end up addressing the symptoms of the difficulties rather than the underlying causes.

For example, a test may identify that a learner is struggling to accurately subtract 4-digit numbers. To address this, we re-teach the procedure for subtraction and provide lots of additional practice. In the short-term this appears to have some impact, but over the longer-term the benefits seem to fade, particularly when the learner needs to recall skills that haven’t been recently practiced or apply them in unfamiliar situations.

What may have been missed in this analysis is that this learner is in fact lacking some of the underlying knowledge and skills required to successfully learn and understand what we are trying to teach them. Without addressing these underlying gaps, they will continue to struggle to make progress and may be turned off maths entirely..

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Thinking back to our earlier example, a flexible and fluent understanding of place value is crucial to success in subtraction but is often not given the time and attention that it requires. If learners can tell us that 367 has 3 hundreds, 6 tens, and 7 ones we often say that they ‘understand’ 3-digit place value, and we can move on to other areas, but how secure is their understanding really? For example, how easily can they:

  • Tell us what number we would have if we added or removed a ten – do they immediately see the answer, or do they have to count forwards or backwards in steps of 1 to work it out?
  • See that adding 4 tens or removing 7 tens would also affect the hundreds digit, and quickly work out how it would be affected?
  • Understand that we could also think of this number being built in different ways – for example – 2 hundreds, 16 tens, and 7 ones?

The strategies in SNAP Maths, our new diagnostic tool for identifying specific maths learning difficulties, provide a range of activities and approaches that can be used 1-1, with small groups, and with whole classes to support this deeper understanding. One of our most effective (and popular) games is Target Number. In Target Number, everyone starts from zero and is trying to get as close as they can to the target number – for learners new to place value, this could be a 2-digit number like ‘76’.

You take it in turns to roll a dice – whatever you roll you can add or remove that many tens or ones to try to get the target number (though as you start at zero, on your first turn you can only add). For example, if I rolled a ‘5’ I’d need to decide if I wanted to take 5 tens (for 50) or 5 ones (for 5). Once I’ve decided what I want to do, I can either write my number (a more abstract version of the game) or build my number using manipulatives (useful for learners who are still developing their understanding of place value).

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On my next turn, if I rolled a ‘3’, I’d then need to decide what would get me closest to 76 – do I want to add 3 ones for 53, or 3 tens to get to 80? Observing what learners decide to do in this type of situation is very revealing – those with a less secure understanding of place value will tend not to ‘see’ the possibility of going over the target number and only be able to think of continually adding ones to get closer.

As learners develop a more flexible and fluent understanding of place value, they will be able to apply this across their maths learning.

Find out more about SNAP Maths.

Tags

Intervention and SEN, Maths, primary maths, SEN, SENCO, SEND

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