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High Learning Potential (HLP) in Maths

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The subject of kids with high learning potential (HLP) in Maths is one which is close to my heart, having my own child who falls into this category. HLP, or ‘giftedness’ as it may once have been called, is a very emotive word and seems to conjure up strong opinions (even on whether one can use the word or description at all). But it is so often misunderstood, and in my experience is usually only fully appreciated by people who either have their own HLP child, or know someone who does. It is a subject I feel very strongly about, as I feel it isn’t generally well catered for in state schools (obviously there are some wonderful exceptions) and comes with many challenges commonly associated with SEN children (and again, I feel qualified to comment on this as I also have a child with SEN).

What does it mean to have HLP?

First, let me set the scene on HLP (in any subject, not just Maths). As with those who are naturally fast runners, or pitch perfect, or brilliant swimmers, there is an innate ability over and above the ‘average’ which, whilst it can be honed with practice, is there nonetheless. Whilst of course applauding dedication to one’s field – a talented violinist still needs to practice their pieces for a concert and is rightly commended for their performance – these abilities in whatever form are talents that a person is born with. So – in my opinion – they are not something one can boast about, or in any way feel superior about. We are all made differently – thank goodness – and that should be celebrated.

The charity Potential Plus is an excellent resource for those investigating HLP. This page gives a brilliant overview of what it means for a child to have HLP. Here you can clearly see that there is no one-size-fits-all profile, and HLP can come in many different forms.

What does HLP in Maths look like?

What does it look like for a child to have HLP in Maths? As with most things, this will look different for every child. I’m an expert on my child, so I can tell you what I’ve seen. But there will be children far more advanced than this, so this isn’t by any means a benchmark. Please bear in mind (and maybe I’m over-sensitive due to judgement over the years) that I’m saying this with the view that this is the way my son has been made, not something amazing that I have done or something that I am boasting about. Here are a few things that made me think my child might be quite ‘mathsy’:

  • When he was 1, he was counting to 20, recognising all the numbers to 20 and could put them in the right order. When we were on holiday on the beach, he wanted to draw numbers with a stick in the sand, and was only happy stopping when he felt he had mastered the numbers to 20.
  • He learnt to read when he was 2 and by aged 3 was reading chapter books. He was writing book reports in nursery.
  • When he was 2, he enjoyed counting in hundreds. He loved puzzles – before he was 2, he was doing 24 piece puzzles and was up to 50-100 pieces before he started nursery.
  • Before he started pre-school, he had an analogue watch and could confidently tell the time. I remember his nursery teacher telling me that Friday afternoons went very slowly as he would say ‘Shirley, it’s 5 to 3 now. Shirley, Shirley, it’s 3 o’clock now. Shirley, it’s 5 past 3 now…’. At the same nursery, my son was asked to put away puzzles that the nursery staff were struggling to put back together (he was 2).
  • When he was 3, he liked playing with magformers – magnetic shapes. However, his favourite thing to do with them was not to build structures, but to work out times tables (though he wouldn’t have known to call them this). When I had left him alone for a bit, I came back to find he had worked out the 3 times table with squares. He also liked to build big rectangles e.g. with 36 squares and then work out all the different ways that he could make a 36-rectangle (e.g. 18×2, 6×6 etc). He similarly loved working out patterns of square numbers, and triangular numbers.
  • Also aged 3, he became very interested in prime numbers. He worked out that prime numbers were rectangles that couldn’t be rearranged in any way. He liked working out new ones, and hypothesised that the density of prime numbers decreases as numbers get larger (a simplistic analogue of the Riemann Hypothesis, although obviously he didn’t know that!).
  • When he started nursery, he was asked what he was most looking forward to. He said that he hoped he would learn some maths and he wanted to learn the 8 times table as it was the only one he hadn’t mastered yet.
  • From aged 3, one of his favourite games was to start on a number and keep doubling it in turn. We’d get to many hundreds of thousands, and then my brain would get tired and forget what number I was doubling, so he nearly always ‘won’ (though he graciously considered it a team effort!).
  • For fun, he loves squaring and cubing numbers, and working out as many multiplications as he can. When he was waiting for something recently, he decided to work out all the times tables up to the 39 times table, just for fun!
  • Now he’s in year 2. He loves algebra and solving linear equations. He likes finding the highest common factor and lowest common multiple of two numbers, playing with indices, and working out lateral thinking puzzles. He likes working out the square root of a number to 1 decimal place in his head. He also enjoys sudoku. When you talk maths to him, his eyes light up and he’s fascinated.
  • He believes he’s never studied maths in school. We go to advanced maths sessions for fun in the holidays and he loves them.

As you can probably tell, my son has therefore struggled with the pace of Maths in school. It’s very hard to be doing number bonds to 10, when you self-discovered number bonds to 100 a few years before. Hence also my views on Maths Mastery in primary schools not meeting the needs of HLP children (see Maths Mastery in Primary Schools).

What are the challenges?

So what are the challenges that my son faces (and many like him)?

Well, for starters, he is very bored in school. He is in a local state school where the teachers are lovely, but struggling with very limited resources to teach 30 children of very wide-ranging ability. This means he can mess around and feel frustrated in Maths lessons. He is also not building up any resilience. He’s so used to finding everything painfully easy, that when he reaches more challenging problems he hasn’t got the emotional tools to deal with not seeing the answer straight away. This is something that we have had to work on at home, and a reason that I provide stretch for him outside of school. I teach my students that making mistakes in Maths is how you work out how to do something and a vital tool in learning, but to make mistakes you have to be willing to have a go. This is what I am working on with my son. When he is given ‘Greater Depth’ challenges at school, so often these are just more sheets of the same thing, or with slightly bigger numbers. Once in a blue moon he tells me he had to stop and think about something, but mostly it’s not providing any challenge. Similarly he had to sit through phonics lessons in year one when he had been confidently reading for 3 years and already read to the end of the primary school book band levels.

This might sound like a ‘nice problem to have’. But it comes with emotional and behavioural consequences that seem to compound as time goes by. I’ve seen increasingly negative emotions relating to school in my son, as well as increasingly disruptive behaviour as he faces no challenge. Other parents with similar children talk of the problems when this isn’t addressed. Many have taken their kids out of school and home-schooled them. Others move them to independently selective schools. But for a lot of parents, these options are not available. This article provides a good summary of some of the SEMH challenges that an HLP child can face –

A common problem for children with HLP is something called ‘asynchronous development’. This means that whilst they might be very advanced in one area, they are merely average or even below average in another. In other words, they have a ‘spiky profile’. Although a trivial example, I remember having a conversation with my son when he was 2 about some complex area of mathematics, and seconds later he was having a complete tantrum over his carrots being cut into cubes rather than cuboids! His emotional intelligence was not remotely on a level with his cognitive ability, and the results could often be confusing with the juxtaposition of events like this. Have a look at to see another example.

The other challenges can be for the parents. So often parents of children with HLP feel that they need to downplay their children’s ability so as not to make others feel bad in some way (I’ve definitely been guilty of this), but actually in some ways this perpetuates the feeling that these children are superior. Parents can also feel judged to be ‘pushy parents’, or accused of thinking their ‘average child is a genius’, or ‘far too focused on academic success’. Teachers can bristle against the mother that asks for extension work, or talks about a child feeling bored, or they may fail to recognise the cause of a child’s ‘bad’ behaviour. All of these are understandable reactions. But they miss the fact that most HLP parents think that all children are wonderful gifts, with their own unique talents, and being very good at Maths doesn’t make your child any better than any other child who no-doubt has greater abilities in other areas.

As I mentioned, I often downplay or hide my son’s ability to avoid other people’s reactions. Don’t get me wrong, lots of people have been very supportive and find it fascinating to see what he can do. But with teachers I’ve mostly been met with a lack of understanding, and a feeling that I must be a relentless slave driver at home who doesn’t let her poor son play. When he was doing a series of exams recently to move schools, my son cried when they were over as he had enjoyed them so much and asked if he could do the 8+ exams next year (absolutely not!). This was the first glimmer of understanding I saw from the teachers as they realised the motivation came from him, not me, and were really surprised by his reaction. I don’t blame the teachers. They are over-worked and under-paid, and have to meet the needs of 30 children. And no doubt there are parents who push their children past the point that is necessarily healthy for them. But I’m not sure there has been much education and acceptance that some children are just born like this.

Another challenge for parents is in the actual parenting of the child with HLP. They are endlessly curious, ask lots of questions, very sharp and – when you’re tired at the end of the day – pick up on any inconsistencies in things you say. It can be exhausting. And there is the constant guilt of whether you’re doing the right thing – are you stretching them enough/too much, have you imagined their abilities, why do you want to stop them asking so many questions when you should be encouraging their curiosity (but are simply exhausted!). This page puts it brilliantly.

The more I have found out about HLP, the more I realise that this is something I share with my son. And it has certainly come with challenges for me. I find that I am constantly masking – I consciously try not to appear cleverer than people I’m with so that I can blend in. I have struggled with perfectionism and having to be the best at everything I do. I don’t like doing something I’m not good at. I’m very self-critical. There are other things as well, and all this has taken its emotional toll.

What can be done?

I would love to see more education of the wider population – especially those involved in teaching children – of what HLP looks like and how to recognise and support it. I would love HLP to be something that can be openly talked about and celebrated, in much the way that it doesn’t seem taboo to talk of your child’s sporting successes. I would love those with HLP or parenting a child with HLP to be better supported, and to understand the resources they have access to in charities such as Potential Plus.

In Maths in particular, I would love to liaise with those involved in delivering Maths Mastery to work out how it can work for children with HLP, and how to teach a classroom of 30 children where some cannot do 2+10, and others can cube 17 in their heads. In my post Maths Mastery in Primary Schools, I make it clear that I don’t think mastery works for HLP children. I’d love to change that. I would love those in primary education to understand that treating children equally means recognising their differences, and provide for much greater differentiation by ability.

I would love parents of children with HLP, and those with HLP themselves to be confident to talk about it, and share the wonderful way in which their brain works so we can all share and benefit from whatever their area of expertise is. Surely this is good for everyone?!

2 Responses

  1. Jen says:

    Really interesting Claire! This is an issue so often brushed aside when it appears, and the difficulties that the child (and parents!) face as a result are overlooked. Great, informative article.

  2. Julia says:

    Wow Claire – fab read!
    There is a lot of attention given to pupils with learning difficulties and I feel the same attention should be given to those who are finding it too easy. Funding is obviously a problem, but I think awareness is a start. Thanks for telling us 😊

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