Specific Learning Difficulties Network: developments in dyscalculia science

Publication Date
Dr Silvia Paracchini
Dr Michelle Luciano
Professor Brian Butterworth

Specific Learning Difficulties refer to difficulties in acquiring skills in reading (Dyslexia), mathematics (Dyscalculia), and writing (Dysgraphia). These differences are very common and can be observed in up to 10% of children, varying in degree of severity.

On Friday 16 June the SLDN met for an exhibition and public talk from Professor Brian Butterworth to learn more about the academic and policy work being done by the Specific Learning Difficulties Network and hear from those with experience of specific learning difficulties and how this research applies to them. This was followed by a panel discussion featuring Fran Foreman from Education Scotland and Youth Ambassadors from Dyslexia Scotland, Emma and Rachel.


The SLDN is a new initiative bringing together researchers from across the UK to coordinate the research agenda better and raise awareness for specific learning difficulties, established by Dr Silvia Paracchini, FRSE (University of St Andrews) and Dr Michelle Luciano (University of Edinburgh). By working with families, teachers, charities, and policymakers the SLDN aims to make research useful to those with specific learning differences.


Dr Silvia Paracchini

Good evening, everybody. Hi, everybody. Thank you for being here. So my name is Silvia Paracchini.

I’m a reader at the University of St. Andrews. And together, with my colleague, Michelle Luciano, I’m the founding co-chair of the Specific Learning Difficulties Network. I really wanna tell you what was our motivation to set up this network. So really, this comes from our personal experience. I’ve been working in the field of this dyslexia genetics for almost 20 years, and it’s absolutely clear that if we wanna make progress in understanding the neurobiology of dyslexia, both in improving assessment and management plans, we need to work as part of large and interdisciplinary teams. We cannot make progress as individual research team. But also, is absolutely necessary that when we do these huge large-scale research, we do research that is actually useful. And what we don’t wanna do is to have our big project and then try to fit them in somewhere, but we wanna engage with the key stakeholders from the beginning of the design of these research projects. So really, our two motivation, we are coordinating research, by starting this dialogue with the stakeholders so that we could deliver impact where it matters.

So the network was launched in November, and we were hosted here at the RSE. And it was 40 of us, and we had a great time, and we’ve been absolutely delighted by the reception and enthusiasm of researcher, clinicians, educator, charities, and policymaker.

And as an highlight, for the very first time, we’ve been able to bring in the same room representative of the two cross-party groups from Holyrood and Westminster. This discussion also showed importance of having a cross-nation approach. Because some of these education and health are devolved, that might be good, but we also need coordination at a bigger level. So we had great talks, great engagement, we’ve been lovely to each other, but something that we were determined to do is absolutely not leaving the room until we had plans on how to channel this enthusiasm and taking some of these idea forward in a very pragmatic manner. So I’m gonna pass you to Michelle now, who’s gonna tell you a little bit more

of what we have set up to do. So, Michelle,

Dr. Michelle Luciano

Great. Thanks, Silvia. So, I’m Dr. Michelle Luciano. I’m a reader in psychology at the University of Edinburgh. And I’m going to briefly describe five of the working groups that were established as an outcome of this inaugural network launched last November. So, just very briefly, the first working group is on setting research priorities. So here we’re going to be generating research questions that aren’t just important to scientists but also to stakeholders and those with lived experience of specific learning difficulties. Our second working group is on improving education resources, and the main aim here is to develop tools for teachers so that they can better identify children with dyslexia/dyscalculia as early as possible. And to this end, this afternoon, we had the working group leads facilitate a focus group with teachers and others from education to get some feedback on some early ideas for a resource in this area.

The third working group is mapping available data cohorts. And this is involving looking through existing UK cohorts and even those worldwide that are accessible for data or information that’s relevant to specific learning difficulties and can help us answer the questions we’re interested in. It might be that there’s insufficient data and that we need to seek funding to create new data cohorts that can answer these questions.So our fourth working group is on terminology. So here, our members are mapping definitions that are currently in use, and they’re looking at points of similarity and differences. And the long-term goal here is to agree on definitions that will be useful for research and for practice.

And our final working group is on technology. So here, we want to take advantage of developments in AI. So how can machine learning multidimensional analysis, for instance, aid our research? And importantly, how can we help people make the most of technology?

So these were five really important working groups and outcomes of our inaugural network meeting, but another equally important outcome was to hold a public engagement event. We want to raise the awareness of specific learning difficulties, and that’s why you’re all here today. So thank you for your interest. So in choosing a speaker for today’s event, we decided to focus on dyscalculia. So charities like Dyslexia Scotland, the British Dyslexia Association, have done a tremendous job in raising the awareness of dyslexia. But prominent scientists, such as Professor Maggie Snowling here, who is part of our network, is urging schools to move beyond dyslexia. And just last week, we see a news article highlighting the significant number of people who struggle with maths. So you are going to hear from Professor Brian Butterworth, the most recent science about dyscalculia. So before we move on to Brian’s talk, I’d like to thank Dr. Sinead Rhodes, who’s going to be chairing the next session. So Sinead Rhodes is a senior research fellow in the Centre for Clinical Brain Sciences at the University of Edinburgh. She has an interest in understanding the cognitive factors underlying behaviour and learning, and she’s gonna be chairing the next session. So thank you, Sinead. – So it’s really my great pleasure to introduce and chair this session, and introduce you to our speaker, Professor Brian Butterworth. Brian is emeritus professor of cognitive neuropsychology at the Institute of Cognitive Neuroscience at University College London. As you’ve heard, he researches learning difficulties, ranging from dyslexia, but also, importantly, to include dyscalculia, which he’s going to talk about this evening. And he’s done this research in different education systems across the world. And indeed, in reflecting that, he holds professorial positions beyond UCL, in Taiwan and at Melbourne University, where he’s currently working on the neuroscience and the genetics of mathematical abilities and disabilities. He’s led two European networks, Neuromath and Numbra, that promote multidisciplinary research on mathematical cognition. He founded the Centre for Educational Neuroscience, which has a particular focus on children with special educational needs. He is an advocate for people with learning difficulties and is really actively engaged, also, with policymakers. He’s also a prolific writer and has published a number of books in this area, going back to his bestseller, “The Mathematical Brain” in 1999. His most recent book covers the neuroscience of mathematical abilities and has the intriguing title, “Can Fish Count?” Tonight, Brian is gonna talk about developments in the science of dyscalculia. And, yeah, please join me to welcome Brian, our speaker tonight.

(audience applauding)

Professor Brian Butterworth

All right. Well, thank you very much for inviting me. The Specific Learning Difficulties Network is a very important initiative. We don’t have the equivalent in England. I wish we did. Maybe in the future, we will. OK, so I’m going to try and put recent developments in the science of dyscalculia into a context. A context that I talked about last year at the first meeting of this network. And when there’s something new, it’ll say “development.” Where it doesn’t say “development,” this is stuff that’s already been established. So first point to make is that dyscalculia is important for individuals and nations. And nations. So the impact on individuals is considerable. It can reduce lifetime earnings by £114,000. That was in 2008. So you have to take into account inflation, and you’ll see that actually it’s quite a large number now, a larger number now. And it can reduce the probability of achieving five or more good GCSEs by 7% to 20%. Compare this with dyslexia, which can reduce lifetime earnings by £81,000 in 2008 and reduce the probability of achieving five or more GCSEs by about 3% to 12%. This comes from a government report called “Mental Capital and Wellbeing,” and this was a really important report for a whole range of different topics in mental capital, in mental abilities, and mental disabilities. And that was initiated under a Labour government, and, of course, it’s now been completely forgotten. So it’s more of a handicap in the workplace than poor literacy. And men and women with poor numeracy have poorer educational prospects, earn less, and are more likely to be unemployed, in trouble with the law, and be sick, both mentally and physically. So the impact on nations. Okay. So the long-term cost of the lowest 6% in numeracy in England was £2.4 billion a year. This is back in 2010. This is a report commissioned by the government and carried out by the accountancy firm KPMG. Most of the cost was in lost direct and indirect taxes. So if dyscalculics are not earning as much, they’re not gonna be paying as much in taxes, either directly or indirectly. 6% will include some individuals who are not actually dyscalculic, just very bad, but most of them will be dyscalculic. So there’s also costs for justice, because they’re more likely to be in trouble with the law. Medical costs because they’re more likely to be ill, both physically and mentally. But the really shocking point, to me, even back then, was that the amount of money that was spent on trying to help people with dyscalculia was just 10% of the total. I mean, there are figures there which are about special needs support for numeracy, both in primary and secondary schools, but beyond that, there was very little money spent actually trying to help people. Now, the second kind of impact on nations comes from an OECD report. And what they found was that if you could raise the lowest attaining 15-year-olds, that’s those who are at or below Level 1 in maths, to a PISA minimum level, that’s Level 2, this would increase GDP growth in the UK by nearly 0.5% a year, and that’s actually quite a lot. Increasing standards in maths by 20 PISA points, which is a 1/4 of a standard deviation, would increase GDP to 2090, by about over $6 billion US dollars using PPP. And, again, that’s from a quite independent analysis. So dyscalculia is not just being bad.

So turns out that the dyscalculics and the double deficit group are significantly less accurate and slower on addition, subtraction, and multiplication than those with reading difficulties, and the controls, who are the same. The dyscalculics and the double deficit group are slower on timed dot enumeration than those with reading difficulties and the controls. And there’s no difference between dyscalculia and those with reading difficulties on any of the tests. So the double deficit doesn’t make you worse. And those with reading difficulties were as controls on our number tests. So here’s another way of testing number sense. This was done by Manuela Piazza, a former student of mine, where you have to select the panel with the most dots. And dyscalculic 10-year-olds are worse at selecting the panel with the larger numerosity when the proportional difference is small. So, you know, if they’re close together, in nine versus 12, as opposed to nine versus three. And there was another study here by Karin Landerl, and she used a very similar method. And she found these are the controls, these are those with reading difficulties, those are dyscalculics, and that’s the double deficit group, and this is reaction time. So the reading difficulty group are just the same as the controls, but the dyscalculics and double deficit group are significantly slower. And there’s been a very recent study by Decarli in Marco Zorzi’s lab in Padova, and he tested, or they tested, number sense at 12 months. So these are babies, really. And they found that the ability to discriminate numerosities at 12 months predicts math scores at four years. So it’s something that’s really congenital, really inherent in your condition because if you’re not very good at four months, I’m sorry, 12 months, you’re still not gonna be very good at four years. And another interesting study from Marco Zorzi’s group, he used a maths-to-sample paradigm. So what the subject has to do here, the subject will see a number of dots and then has to pick out the same number from a choice of three. And what he found was that dyscalculic learners are less accurate and are slower on this very simple task, with either large or small numerosities. I’m just gonna tell you briefly about a study which I talked about before, which is using dot enumeration in kindergarten in Australia, it was a Melbourne study. So these poor kids were tested seven times, 20 cognitive tests a time, from ages 5 1/2, when they were in kindergarten, to age 11. And we did a number of additional tests like item-timed calculation, which is very important educationally, and also an IQ test. And here, we use a different statistical method from the ones that you often find in the literature. So instead of saying, “Well, the dyscalculics are the bottom 5% or the bottom 10%, the bottom 3.5%,” what we said was, “Is there a cluster of individual kids who look different from the rest?” So we used a statistical method called cluster analysis. And what we found were the three clusters, which we’ve named slow, medium, and fast. And so, this is in the slow group at six years up to 11 years. And what you may be able to see is that these kids are slower on all these ages from the medium group and the fast group. The slow group was about 7% of the total sample. Then we looked at what’s called the subitising range, the number of objects that somebody could accurately report up to about four items. So in the subitising range, individuals are generally very fast

So in the subitising range, individuals are generally very fast and very accurate. So the slow group could only subitise two items. The medium group could subitise three items. And the fast group, even at the youngest age, could subitise four items, which is about the adult level. They all ended up being able to subitise four, but in kindergarten, there were these significant differences. And the cluster at kindergarten predicts age-appropriate arithmetic to 10 years. So this is the slow group, this is the medium group, and this is the fast group. And you’ll see the fast group are much more accurate than the slow group. This is two-digit arithmetic at 9 1/2, and again, the slow group are significantly less accurate on these tests, and the other two groups are more or less the same now. And three-digit arithmetic at 10 years, and the slow group is still miles behind. So, conclusion. There’s a small cluster, as I said, about 7% in this sample with poor ability to enumerate sets: that is a core deficit in number sense. This core deficit persists from kindergarten to 11 years. It predicts who will and who will not have trouble learning arithmetic, at least to the age of 11 years. The implication of this study is that you should use this test in kindergarten, or year one, so that you know which children are likely to have difficulty. We also use a similar test in a very large-scale study in one district of Havana. We started with 11,500 children from six to 16, and we used randomised stratified sampling of tests they already did in school, because they do a standardised arithmetic test every year, and then we tested nearly 2,000 individually, and one of the tests was item-timed dot enumeration. But here, what the child had to do was, on a keypad, if it’s five dots, press the digit five. And the results were that the prevalence of dyscalculia, inefficient dot enumeration, and poor arithmetical fluency was 3.5%. The predictive value for the educationally relevant Gold Standard of arithmetical fluency, this is really what teachers and parents of children want to know about because this is the educationally relevant task, the sensitivity was 27%. That is, there are lots of other reasons for poor arithmetic, as I’ve said. The specificity, the true negative rate, was 98%. That is few learners have a core deficit and good arithmetic. So if you’ve got a core deficit, you’re in trouble. And the negative result was very good at reassuring that a child does not have dyscalculia. So the negative predictive value was 86%. So if you’re okay on this very simple number sense test, you’re very unlikely to have dyscalculia. Let me say something about the brain here. These are the areas in the brain that are specific to number sense, these two areas here. This is top view of the brain, and this is a slice, round about there. And these two areas in the intraparietal sulcus left and right, are part of the arithmetic network. And this arithmetic network is bilateral, that is it’s in both the right and left hemisphere. There’s a slight developmental change, becomes more left-dominant as you get older. And as you can see, in these adults, you’ve got more areas in the brain, in the left hemisphere, this is the left over here, and so these number sense areas are part of the arithmetic network. In dyscalculia, you find abnormalities in this area. So you find reduced grey matter. So these are the areas, again, these two

So these are the areas, again, these two little bits here. This is a study from a Swiss team who found reduced grey matter in children in the right hemisphere. This is the classic study by Elizabeth Isaacs, who found in adolescents,reduced grey matter in the left intraparietal sulcus. And this is a study not yet published by my student, Ashish Ranpura, and it’s exactly the same coordinates as Isaac’s, and the original study of number sense in the brain. There’s a persistent reduction in grey matter in the IPS

looking at longitudinally over four years, or two samples over four years. So this difference persists in children. And there’s also reduced white matter in the superior longitudinal fasciculus, which is the white matter, the axons that go from the parietal through to the frontal lobe. And you also get activation differences. So the relevant areas are not as active in dyscalculics as they are in normal.So one question that is important here is, is dyscalculia heritable?

Well, we don’t really know, is the answer to this.If you look at twin studies,you find heritability estimates for dyslexia,is about 40% to 50%. This is large-scale studies. But that’s for dyslexia. For maths, but not for dyscalculia, specifically, it’s about 30% heritable. What I mean by 30% heritable, I mean that doesn’t mean that for each individual dyscalculic, 30% of the problem is inherited. What it means is if you look at a lot of twins, 30% of the variance looks as though it’s due to heredity. It’s also more common in boys than in girls. This is from the Havana study. There are also X chromosome disorders, like, for example, in Turner’s Syndrome, there have been several studies here. And I think every Turner’s Syndrome female, these are just females… So Turner’s Syndrome, females have one complete normal X chromosome, and the second X chromosome that they should have is either abnormal or missing. And it’s not heritable because Turner females are infertile, but it’s congenital, that is you’re born with it. And all the ones that have been properly tested are dyscalculic. Certainly, all the ones that we’ve tested are dyscalculic. There’s also a condition called Fragile X, which has been tested by an Italian group. And another X chromosome condition, called Klinefelter syndrome, also by the same Italian group. But candidate genes for dyscalculia so far identified are not in the X chromosome. In so far as we know where they are, they don’t seem to be there. And in so far as it’s been claimed, Silvia Paracchini and her group have found that that study wasn’t replicable. Practical diagnosis. So, as I said before, use simple number sense tests early. So a specific test for dyscalculia, not just for poor arithmetic, based on number sense. It must identify the core deficit in number sense using both time and accuracy. So it’s the efficiency of the system which is both, you must do it quickly as well as accurately. And we developed something called the Dyscalculia Screener, (2003), which uses dot enumeration time, which we adjust for basic processing speed ’cause we want to know that the individual is slow on number tasks, not slow generally. And this seems to be the only standardised dyscalculia-specific test that’s easily available. There haven’t been any more properly developed, and better tests should be developed because this was done a long time, 20 years ago, and things have moved on a bit, and we need new tests standardised on different populations. Ours were standardised on an English sample of kids, and so, you know, must be used with care. We’ve also been working on interventions for dyscalculics, and we have certain intervention principles. So the key to understanding arithmetic are sets and operations on sets, i.e. number sense. So this will come as no surprise for primary school teachers. Therefore, the key to supporting dyscalculic learners in schoolwork is linking sets to the familiar symbols, counting words, and digits.

And this can be done in two ways. Guidance for teachers, especially teachers of dyscalculic learners, with manipulables. So using manipulables as long as they’re needed. Don’t just get rid of them at the end of year one. Keep using them for those who need them. And we’ve published a book saying how teachers should use manipulables. And digital games. So I’m gonna talk a bit about digital games in a moment. And both ways of approaching the problem should follow the standard pedagogical prescriptions. Build new tasks on what has been learned, adapt each task to be just challenging enough, and construct solutions to enable learners to compare their actions in relation to the goal. This is prediction-error learning. So no multiple-choice questions, that just encourages guessing. So we’re very keen on this constructionist approach. So I’ll just show you one of the games that we’ve developed. It’s called NumberBeads, and it involves constructing and deconstructing sets. So here, what you have to do, is you have to construct that target. And you can do it in two ways, you can split a set. These you will recognise as Cuisenaire colours. That’s there, split it. Or you can join them together to make the target, then you get a little reward. And the teacher could set how many correct versions you need in order to get onto the next level, or we could set it. And you then progress from this arrangement to an arrangement where each set is accompanied by the appropriate digit. So here you’ve got a three and a three keeping the same colour, so if you join those together, you’ll make a target. But the next level, we get rid of the colours. And this may encourage counting the beads, which is fine, but you have to rely on that rather than the colours in order to make the solution. And then, the final level, this part of the game, is where you’ve got digits alone, and you can click on the digits, and it’ll split into two parts to make the target. So a very simple game. No bells and whistles. You have to construct the answers. Everything on the screen is relevant to the task in hand. There’s no irrelevance, there’s no other numbers around, and no birds tweeting or music playing, and this enables the child not to be distracted from the task you want them to do. And we’ve done a number of effectiveness studies. So there are lots and lots and lots and lots of maths games on the web, and the question is, are they any good? And the answer is, we don’t know because they’ve never been properly tested. Here, we’ve done proper tests. I’m not saying this is the only game you should use, but I’m saying that this is a game that’s had proper testing. So this is a study by my former student, Inés Zerboni, in a small sample in London. And what you see here are the errors. This is the dyscalculics using NumberBeads, there are only eight of them in this sample, and the number of errors went down significantly. This is typical learners, and here, they didn’t use NumberBeads, and their errors went up. And there’s a dyscalculic control group, just had normal teaching. There were only three of them, fortunately, and there, the number of errors went up a lot. We don’t really know why. The next study we did was done in Italy, and this is a much larger study. We used this game played at home. So the parents were instructed how to set the game up, and that’s it. And we had typically attaining and also, low attaining,

We’ve seen that there’s some evidence for tests at 12 months for kids who are gonna have trouble later. We need better recognition by educational authorities and governments, leading to support for dyscalculic sufferers. We need a awareness by parents and teachers. Training for professionals, that is teachers, educational psychologists. And we need policymakers to make policy. So official recognition should involve an official definition. For example, Scotland’s definition will do, at least, for the moment. And requirement for special support for sufferers, that should be part of government policy. And in the USA and in Italy, there is laws that require it. And we need funding for more ways of doing assessment, more methods of intervention, properly evaluated, special training for teachers and educational psychologists, and funding for further research. So there’s what I’ve called a virtuous triangle. So policy depends a bit on what science shows. Recognition depends on what science shows and what policy actually spells out. And, of course, all of these things work in a coordinated way. So conclusions, very briefly. Dyscalculia: where we are. A deficit in number sense, the core capacity to process the numerosity of sets, the basis of arithmetical learning. And it’s easy to identify and distinguish dyscalculia from other causes of poor arithmetic using simple timed tests of numerosity processing. The neural basis of dyscalculia is revealed in abnormalities in numerosity-processing parts of the brain. “Developmental dyscalculia is currently the poor relation of dyslexia, with a much lower public profile. But the consequences of dyscalculia are at least as severe as those with dyslexia.” Where we need to be. We need good, cheap or free, properly standardised, easy-to-use screener. So my screener is not free, and it’s not cheap, though it is quite easy to use, we need a better screener. I mean, that’s all you’ve got at the moment, but we need something better. You need effective specific interventions based on the core deficit in number sense and the best adaptive pedagogy. Appropriate EdTech can help here. So like in our digital game, that’s a way in which EdTech might help. We need training for teachers and educational psychologists. They don’t always know about dyscalculia. In my experience, not many of them do know about dyscalculia. And recognition by policymakers and educational authorities worldwide. So thank you for listening, and I’m happy to take questions.

(audience applauding)