Maths difficulties: Understanding where the problem lies

Maths difficulties are still poorly understood and often have many causal factors. While specific early interventions can and do work well for learners – is it time to consider whether our broad approach to maths teaching is contributing to the problem in the first place?

Many children (and adults) in the UK struggle with maths. Exactly what label is applied to this is currently under some debate. The prevalence of Dyscalculia, a specific learning difficulty, has been estimated at 3-7% although academics are divided on causal mechanisms, definition and diagnosis. Many think of it as one end of a continuum that includes broader maths difficulties and even maths anxiety.

The drive to recognise some of the innate and very specific biological reasons behind maths difficulties is worthy and indeed essential. However, we shouldn’t lose sight of the significant impact that other factors such as teacher-pupil relationships, socio-economic factors and unconscious bias have to play. 

And there is, of course, another dimension, which is the method of teaching maths itself. In the UK we often still teach maths in a way that places heavy emphasis on rote learning, including drilling sequences, rules, processes and formulae, from early years right the way through to GCSE. Sometimes we overlook other, deeper routes to understanding that don’t place such a high demand on working memory which puts some learners at a disadvantage.
 

The social and psychological factors can aggravate maths difficulties

In order to understand the root causes behind why some children struggle, it is important to recognise the role that social factors and teacher-pupil relationships play. 

These include;

• Unconscious bias. This is particularly well documented in maths. A study conducted in the US found that when maths teachers were asked to rate pupils’ overall ability they were more likely to judge white pupils as higher achievers than their black or hispanic peers. This is despite previously marking entirely or partially correct answers to an 18-question test without any evidence of bias. Similarly, in a study carried out in Ireland, female primary school teachers were more likely to rate nine-year-old boys as ‘above average’ compared to girls, despite similar academic ability. Bias often means we lower expectations of learners, who then don’t feel supported and fall behind in a self-fulfilling prophecy.
  
  “Groupthink” can also negatively impact how we assess and support learners. Researchers from the University of Maryland have demonstrated that such ‘communities of practice’ can result in groups of teachers discarding a more methodological approach to assessing needs, in favour of naturally supporting each other’s beliefs, especially those that place the locus of deficit with the learner.
• “Boffin blinkers.” Some teachers are such experts in maths that they cannot remember what it was like to acquire concepts and end up teaching it in a way that misses out key steps.  In this situation, the ‘expert in subject matter’ can systematically underestimate the difficulty of the subject matter for the learner – they have their “boffin blinkers” on.

• Maths anxiety. It can take only one or two negative experiences with maths – perhaps when a pupil felt put on the spot – to provoke lasting maths anxiety, which has been shown to overwhelm working memory. Some teachers, particularly those working in Primary schools, can also be anxious about maths, making them gravitate more towards rote learning methods. Students who lack confidence in their teacher’s ability to do maths may also be more likely to suffer from anxiety themselves.
  
• Socio-economic factors. According to a study in the US, by the time they reach four, children from poorer socio-economic backgrounds may have had considerably less exposure to maths at home than their peers and already. Several UK studies have had similar results (see Fisher et al 2020). Some researchers have pointed to the potential impact of social class on executive functioning as a potential contributing factor to maths difficulties, while others also highlight its link to reading ability and the more verbal aspects of maths.
   

Is our current approach to maths teaching making difficulties worse?

When it comes to the innate causes behind difficulties, we now know that working memory deficits (including verbal, spatial and visual dimensions) play a significant role. Sometimes the way we teach maths in school places a great deal of cognitive load on precisely these weaker skills, without providing other routes toward gaining maths understanding.

Maths learning works through scaffolding; which essentially means that pupils with working memory difficulties can get stuck on the early foundational levels, unable to move up to the next rung of the ladder.

Here are some common issues with maths teaching in many schools, particularly those following the British or US curriculum:

 

1. ‘Rote’ learning versus teaching for understanding

Memorisation does have a role to play in maths and there is good grounds for encouraging its use. A study published in Nature Neuroscience, for example, found that memorising the answers to simple maths problems is a key step young children take when developing from counting on fingers to doing more complex sums.

That being said, what we understand as purely rote learning should be balanced with approaches that encourage a deeper relational understanding i.e. knowing why a mathematical rule works. Researchers from the Medical University of Innsbruck in Austria have shown that different parts of the brain are used when pupils are asked to just memorise maths facts, as opposed to working through various strategic approaches to absorb them.

Exploring ways to do maths that rely less on simply drilling maths facts can help level the playing field for those who have working memory deficits.

This particularly applies to how we approach sums. Providing learners with pages of calculations such as 14+9 = 23 will not cultivate a rich maths understanding and generate overreliance on the ‘counting on’ method. Rather we should also be challenging them to approach sums using more of an algebraic approach, getting them to place the equivalent, or equals signs and the numbers in missing boxes, in order to complete the sum.

The example below shows what this might look like;
 

Similarly, at a more advanced level, approaches that promote a visual, less formulaic understanding of things like quadratic equations have recently made headlines and proved popular with some teachers and students.

2. Prioritisation of speed and accuracy over creativity

We have a tendency to praise speed in maths. Often by putting learners on the spot, either by asking for answers to sums in class or using timed tests, we create anxiety which can derail working memory. Yet many of our top mathematicians were not particularly speedy at school, nor are they even as adults. They are however very creative and often highly visual thinkers who were encouraged to explore multiple routes to solving problems.

3. Too much emphasis on arithmetic and not enough on spatial thinking

In 2020 researchers Sorby and Panther found that the performance of fifteen-year-olds on PISA tests correlated highly with their scores on spatial cognition assessments. The researchers concluded that ‘improving spatial skills could be an overlooked strategy to improve student performance.’

Learners with maths difficulties may lack skills in spatial thinking. However the good news is that (contrary to previously held belief), recent research, such as that carried out by academics at the University of Toronto, has found these skills are malleable and can be taught.

4. Lack of confidence and knowledge to select alternative approaches

Many teachers feel like they lack the specific skills to help those with maths difficulties. Training may have been non-existent, or merely scrape the surface when it comes to things like evaluating interventions. This creates uncertainty about bringing more creative solutions into the classroom. Yet having a rotation of different teaching techniques and maths games can have a huge impact on learners; we’ll be investigating this further in later blogs.
  

Final thoughts

A better understanding of the genetic causes behind maths difficulties should not leave us blind to the influence of social and psychological factors, in particular, teacher-pupil interactions.

The way maths is typically taught throughout the Western world is simply not working for all learners. Many countries, including the UK, have recently attempted to address some of the problems outlined above by adopting the so-called ‘mastery approach’ to maths, used in countries like Japan, Singapore and China. This involves teaching for understanding and intervening as soon as problems are encountered, repeating each small unit of learning until it is securely understood. Although countries like the UK are now encouraging this approach, the extent to which this is uniformly understood, applied and genuinely embedded into teaching approaches varies considerably.

Having a good working understanding of maths is a gateway to higher earning potential and a broader scope of career opportunities. Unfortunately, the routes to achieving this are still blocked by the prioritisation of skills like calculation and memorisation, which can be incredibly demoralising for students with maths difficulties. 

What we now know is that there are many more important and creative skills, such as spatial thinking, that go into making a great mathematician and that these skills can be nurtured. 

As Marcus du Sautoy, professor of maths at Oxford University writes “even for those with dyscalculia it’s important to remember that mathematics is not simply sums.” Rather, he reminds us, maths is “the language of the universe and it’s one we can all learn to speak.”

Learn more about how to help children with maths difficulties..

Real Training is now offering courses for Primary and Secondary Maths Teachers, TAs, SENCOs and specialist practitioners/teachers/assessors to help build their knowledge and skills to assess and support learners with maths difficulties. Find out more about our courses that help you understand the theory behind maths acquisition and teaching methods and gain the skills to become a specialist maths teacher.