You’ve heard the common refrain, ‘Oh, I’m so bad at maths!’ But for up to eight per cent of us, a condition called dyscalculia means numbers are a serious struggle, with serious consequences. Scientists are now revealing its biological basis, and in Australia there’s a push for it to be seen as a legitimate and unique disability.
Natasha Mitchell: well, the full force of 2011 is with us, isn’t it, what a tumultuous start to this la Nina year for so many of us here in Australia, in Brazil, in Sri Lanka. It’s hard to comprehend the scale of it all. Natasha Mitchell on board, welcome to a year of fresh shows on the rich life of the mind. And comprehending the scale of things is in fact something we’re looking into today, but in a totally different context. How’s your head for numbers?
Numeracy skills are on the nose in Australia. a 2008 COAG report concluded that half of us, yes half, don’t have the skills needed to meet the complex demands of work and life in a modern economy. It’s a common refrain isn’t it, you’ve heard it ‘I’m crap at maths’ of course that can be for many reasons: how it’s handled in the classroom, lack of opportunity, or perhaps because our parents have transferred their own fear of maths to us. But as you’ll hear today, some of us legitimately be able to blame our brain or biology. Learning difficulties are genuine.
We’re more familiar with dyslexia, that difficulty with processing words, but it seems that up to 8% of us struggle with numbers, arithmetic and calculations because of a legitimate condition called dyscalculia, a condition that’s flown under the radar for too long. Corinne Podger is on the case.
Lucie: I do lots of French activities with my dad, create movies with my dolls, dance, I write stories with my computer all the time and would print it out and my mum takes it to work and shows a man who does lots of scripts and he says she could become a script writer. I’m not trying to brag or anything but I love writing stories, I love to read and I’m reading a really good book at the moment that my dad got me and I really enjoy reading.
Corinne Podger: Lucie is 9, she’s articulate and quick-witted and fluent in the French, English and Italian which is spoken at home. Her parents Astrid and Xavier are both school teachers. they want her to learn, and she likes school. But Lucy is receiving tuition for learning difficulties at an organisation called SPELD, Specific Learning Difficulties, Victoria and here’s why.
Can you tell the time right now?
Lucie: I can read slightly the Roman numerals: 35 (pause) 35 — no I know it’s 35 but I just can’t read because it’s something to go to, no I don’t know. I know it’s something 35.
Corinne Podger: And what time is it Xavier?
Xavier: 7.30 yes. Lucy’s maths difficulties we found that out when she was in prep and she’s been struggling since, and she’s not getting it unfortunately, and I don’t know why and how, it’s just very frustrating at times.
Astrid: Her writing was always very good; it’s the maths that has been the issue. we sometimes have the struggle at school with making people understand that it’s not because Lucy doesn’t want to do it, or can’t be bothered; it’s because she really cannot do it. She’s unable to retain a lot of the information.
Xavier: Lucie is in a way lucky that we are teachers because we are able to identify and try to remedy, but if you are an average parent and you don’t know what’s going on you know you think the kid just needs to work harder and then you put pressure on them and it’s just not working.
Corinne Podger: Lucie has difficulties with auditory processing, a mismatch between ear and brain. But that doesn’t fully explain why she can’t process numbers as well as other kids her age. She can count and she’s memorised her times tables but anything involving calculation, multiplying, dividing, telling the time, getting change at the shops, quantities and amounts is a mystery. Now she’s being tested by Professor Bob Reeve, a developmental psychologist at the mathematical cognition laboratory at the University of Melbourne. he believes Lucie is a classic dyscalculic — so what is it?
Bob Reeve: Some people refer to this as number blindness. what we actually see specific to number is that once they’ve learned a concept such as simple addition they don’t transfer or use that knowledge to study similar ideas like subtraction. whereas the person who has been poorly taught or who has poor education still has a basic idea of numeracy concepts. It really seems as if people with dyscalculia don’t see the concepts — they can learn by rote to do certain things but it appears not to transfer, or generalise to similar problems and tasks.
It is often co-morbid with other problems such as dyslexia, sometimes it’s very separate from dyslexia. I think the general agreement now is that there is a pure form that is not associated with other learning difficulties. we suspect that it is genetic, or at least a neurological problem in some respects.
Brian Butterworth: usually they’ve always been bad at maths right from the word go. Very often they will have somebody else in the family who’s bad at maths though not always. Secondly, they don’t respond to normal instruction very well. so the kid who’s missed some classes and is falling behind, that kid can be brought up to speed with the appropriate additional help. whereas a dyscalculic, he won’t be able to catch up. so the dyscalculic needs very specialised interventions in the same way that dyslexics need specialised interventions to help them to learn to read.
Corinne Podger: One of the world’s great maths evangelists, cognitive neuroscientist Professor Brian Butterworth from University College London, author of books like The Mathematical Brain. He’s collaborated with Bob Reeve and is a leading light in dyscalculia research.
Brian Butterworth: there are two things that we know about and we don’t know an awful lot at this stage. One is there’s an abnormality in the parietal lobes, and the parietal lobes are the critical areas representing numerical magnitude in the brain. so knowing that five-ness is bigger that four-ness, that’s a parietal lobe function, and we know there’s abnormality in the critical little bit of the parietal lobe that represents number magnitude. Elizabeth Isaacs at the Institute of Child Health and her colleagues have found that there’s less grey matter in that little bit of brain in her dyscalculics than there were in her control group.
Another group in Stanford, led by Vinod Menon, have found that the connections between this part of the parietal lobe and other parts of the brain are different in dyscalculics. The other thing that’s now known is that the activity in these areas is different in dyscalculics than in matched controls. so we think that both structure and functioning are different in dyscalculics. And of course there is a problem about causal relationships here. so if you don’t do much maths because you’re dyscalculic does that reduce the grey matter density in the relevant bit of brain? does it change the way in which connectivity is set up? does it change the pattern of activation, or is it the other way around, that you start off with different grey matter density and this leads to dyscalculia? These are things that we’re only now beginning to investigate because only now have we got information about brain abnormalities in these dyscalculate learners.
Corinne Podger: The first person with dyscalculia that you came across, a woman called Kathy. how did she process numbers?
Brian Butterworth: well she processed them really badly so if you asked her what 9 + 6 was she would have great difficulty doing that, and yet she was able to program computers, she was able to run a small software business. But for her it was really, really difficult. And we asked her to describe her mental picture of numbers and that was really, really strange, because what she would do was she would say well I have this mental picture and I’ll draw it out for you of what the numbers look like. And she would go 1, 2, 3, 4, 5 and then I put the next lot of numbers which are 5, 6, 7, 8, 9 and 10 and then I put the next lot of numbers which are 10, 11, 12 and so on up to 20. so she was representing 5 twice in her mental picture and she was representing 10 twice and 20 twice so that when she tried to count through in the way that, say, an early learner would count through she got things wrong. so she had a very, very abnormal mental representation.
Corinne Podger: what do we know about the causes of dyscalculia, is it inherited?
Brian Butterworth: we think it’s inherited in a lot of cases, we don’t know if it’s inherited in all cases. we know it’s inherited from twin studies, so if one identical twin has it the other identical twin is very likely to have it. we also know that it persists into adulthood. there was a study done by Ruth Shalev in Tel Aviv which showed that of the dyscalculics that she tested at age 11, most of them were dyscalculic at the age of 17, and almost all of them were still very poor at arithmetic. so it’s something you’re most likely born with though it may not be heritable in some of those cases, and it persists. And we’ve been doing studies of lots of what we call high functioning dyscalculics who are dyscalculate even though they are very successful in their work, and they are very intelligent and they’ve had all the advantages.
Corinne Podger: Someone who’s had all of the advantages is Professor Paul Moorcraft, with a distinguished career in the military and international affairs. he now heads up the Centre for Foreign Policy Analysis in London and we spoke on a crummy phone line as he headed off to oversee Sudan’s independence referendum. Paul was diagnosed dyscalculic by Professor Butterworth a few years ago.
Paul Moorcraft: It’s partly if somebody dictates a number to me over the phone, for example, I can’t remember for more than two or three numbers. And when I physically write them down I will inadvertently transpose them. I have trouble reading train timetables. to actually explain what it is it’s difficult to do, I just cannot understand maths. It’s not a phobia, it’s not a psychological thing, it is a physical inability even no matter how hard I try, and even though I’m a professor, I cannot write down numbers and I have a spatial awareness problem when it comes to numbers. if you talk to me about dimensions of something. I have trouble visualising that.
I worked in the Ministry of Defence and I had a safe, and there were documents, and then you weren’t supposed to write the numbers down for security reasons. And I used to add up with my fingers which is a bit embarrassing if you’re in senior meetings in Whitehall in London. so I hid it for many, many years.
Corinne Podger: And there would be a lot of people listening to this thinking ah, that sounds like me, I’m dyscalculic. But you found that it’s not very common.
Brian Butterworth: It’s about as common as dyslexia. so it’s somewhere between 3% and 6% those are the best prevalence estimates that we have at the moment. so that means 1 child in each class is probably going to be dyscalculic on average. And if you look, for example, at the economic consequences of this, they are actually rather serious. if you could just get the bottom 10% of arithmetic learners up to the minimum OECD level, which isn’t very high then you would increase GDP growth by quite a lot. so for example in England if we could get the 10% half of those would be dyscalculic up to the minimum level that would increase our GDP growth by .44%. Now that doesn’t sound very much but if you know that GDP growth in the UK is say 2% and that additional .44% is actually a 25% increase in GDP growth.
So I think one of the things that’s really important going forward is to find effective ways of getting dyscalculics up to at least a reasonable level of competence at arithmetic, and that’s one of the things that we’re currently trying to do.
Corinne Podger: You’ve designed a test for dyscalculia which I understand is used in schools in Britain — now how does it work?
Brian Butterworth: we wanted a test which as far as possible didn’t depend upon your educational experiences. so if you have a standard arithmetic test then if you’ve been to a good school you’re going to be better at it on the whole than if you’ve been to a bad school. so we wanted something that was very simple and something which targeted these simple functions in the parietal lobe. so the critical tests in our screener for dyscalculia is how quickly and accurately you could innumerate objects in a display, how quickly you could say that are 5 objects there. And how quickly and how accurately you can compare two numbers, how quickly you can say that 5 is bigger than 3.
And we find this is highly predictive of your ability to do arithmetic, it distinguishes between kids who are bad at arithmetic because they’re dyscalculic and therefore would be bad on these innumeration and comparisons tests from kids who are bad at arithmetic but are not bad on those two tests. And what we say in the screener notes is that if you’re bad at arithmetic but good a innumeration and comparison, then you not dyscalculic, there’s another reason for why you’re bad at arithmetic and the teacher or the educational psychologist then as to try and find out what it is that’s gone wrong in your particular education.
Corinne Podger: Dyslexic kids are being picked up earlier and earlier but what about dyscalculia? well you can’t screen for it before age 6 but Bob Reeve and colleagues are working on spotting infants, even babies, who can’t process numeric information years before they encounter maths.
Bob Reeve: We’ve started to go back pretty much to infancy to look at the precursors of number. And they’re not going to look like what you think of as number, as in counting. so we see them as quantity, the recognition of very small sets of number. The most obvious one that people look at is approximate number, whether children can discriminate between sort of two sets of numbers, or infants can discriminate between two sets of numbers.
Corinne Podger: two sets of things.
Bob Reeve: two sets of things, two sets of objects, two sets of dots, two sets of lines. The idea is that the closer the two sets are together the more difficult it is to discriminate between them and so the ability to discriminate between similar sets is termed ‘approximate number’ and in some sense it’s seen as a precursor for the development of ‘symbolic number’ or of what we might think of as Arabic number. And the idea is that these very basic forms of quantity discrimination support or scaffold the later forms of number. if those early bases are not there then it is very difficult to scaffold or associate these later forms with what we might think of as the cultural development of number — addition, subtraction and counting and so on.
Corinne Podger: These sound like abstract difficulties but research worldwide indicates that they point to dyscalculia. so are there interventions and can they work? well it’s early days.
Bob Reeve: we don’t have an intervention science at this particular point in time and we don’t know if it can be remedied and certain people argue, and it’s a very negative argument, that because it is likely that pure dyscalculia is a brain difficulty, you may not be able to teach it in the same way as you teach other things for that particular group of people.
Brian Butterworth: we know it’s lifelong for some people; we don’t know if they would have still been dyscalculic if they’d had the appropriate intervention. we think that the way to help them is to strengthen what we call basic number concepts. so getting them to do plenty of practice with innumeration, with counting, with comparing numbers and doing very simple addition and subtraction, so they have a feel for numbers which the rest of us take for granted but which they find very difficult to achieve.
Corinne Podger: Difficult but not impossible, as you’re about to hear here on All in the Mind on ABC Radio National going global on Radio Australia and on podcast, I’m Corinne Podger.
Mary Delahunty: most people have automaticity with a lot of these things but people with dyscalculia have to learn the steps, they just don’t have it automatically. they often resort to very primitive methods of calculating or adding or subtracting or whatever they do. because they haven’t developed any strategies for moving on from just doing a one-by-one count.
Corinne Podger: Mary Delahunty is a special education mathematics teacher in Melbourne. Her approach is to fix number concepts in her students’ minds firmly enough so they are not always struggling with the basics. She also helps them to find work-arounds so they can survive in our numeric world.
Mary Delahunty: Just to give you an example of one little boy that I’ve worked with for over 12 months. he was about 9 or 10 at the time and his parents contacted me quite distraught, they had two reports from psychologists that he would never get anywhere with his mathematics and there was no point worrying about it. he was able to count but just, counting by 1s and then he’d go back and when he needed to calculate he would go back and then he’d count the first bit, then he’d count the second bit and then he’d count the whole lot.
Corinne Podger: so perhaps at the age of 9 his development in mathematics was of a much younger child?
Mary Delahunty: I would say he was probably operating as a preschool student, that we would expect to be able to sort and sequence at that time. I used a multi-sensory approach so that every time they touched something they could sort of feel this was a multiple of something, this was another bit to add on. we used buttons to work our additions, and he could go back and check, so after a while he got the idea that he could hold that number, that quantity, in his mind. That led him to be able to actually use his memory rather than overload it to hold a concept in his mind of what a number looked like and what the quantity was.
Corinne Podger: Mary’s put together a goodie box of beads, beans, blocks and seeds to give numbers shape, substance and, hopefully, meaning.
Mary Delahunty: It turns on the senses, it helps to print the image in your mind. When you feel something you can often transfer that into the image of what it looks like, what it feels like. we have icy pole sticks, I have magnetic marbles so we can make groups of things so you can chain and unchain them. we made bean sticks to count by tens… And so…sometimes they’re on that same continuum as all the other students but they need that many more exposures to something before they actually can take it in and hold it in their memory.
Our working memory is really important, because what we’ve implanted in our mind we don’t have to go back and redo, we’re not using our memory to overload what we do so we can move on. so it’s very important that we actually can form those images.
Corinne Podger: There’s also problems sometimes with understanding time, which comes down to numbers but it includes concepts like after and before.
Mary Delahunty: Dealing with time, what I get the children or the students to do first of all stick gum nuts, stick anything on around the clock so that when they go past the 12 they can shut their eyes, touch it. most of our counting around the clock is by 5s or by 10s, or going halfway up the hill and halfway down the hill. so what I get them to do is I actually get them to make a continuous length. so we make our clock with a tape and then we spread it out along the ground, you can double it and make a hill out of it so we are going up the hill and down the hill. Once we’ve learned to count by 5s we can do it with a clock, we roll it back up and put it back into the circular shape so they can see it.
Corinne Podger: Is there a level beyond which people with dyscalculia can’t progress in the sense that somebody who’s blind isn’t going to be able to see?
Mary Delahunty: we can’t cure some of these things. we can improve how they do it but we can also give them shortcuts. we know that we can use talking calculators to help support students, so that when problems are presented they can listen to it being stated first, that helps them to process it in their mind and to get the information correct. or remember a pattern for something that helps short circuit what you need to do to be able to calculate.
Corinne Podger: Mary Delahunty’s gum nut arsenal — it sounds like it’s working wonders. Professor Brian Butterworth wants to know the extent to which dyscalculia might be overcome. He’s designed online classes so that dyscalculic children can do basic maths tasks over and over again. He’s found it does improve arithmetic ability and wants to find out if it also boosts brain function.
Brian Butterworth: It’s been done for dyslexia, and we know that with the right kinds of intervention patterns of activation in the relevant parts of the reading brain change. And one of the interesting things in the dyslexia literature is that the changes are towards making brain activity more normal. Now it wasn’t obvious that that was going to be the outcome. One possibility is that the dyslexic reading brain would find a different way of doing effective reading from the rest of us. But what in fact they found was that the dyslexic brain became more like the normal brain after the intervention.
So one of the things that we’re interested in with dyscalculia is whether intervention makes the dyscalculic brain more normal, or whether the intervention just helps the dyscalculic learner find a different way of doing the same task.
Corinne Podger: There’s been quite a vigorous debate about whether dyscalculia, the neurological difficulty with numbers and maths, is entirely distinct from dyslexia, a difficulty with words and language. has that debate been settled?
Brian Butterworth: I think it has but other people don’t agree with me about this. The problem is that kids who have dyslexia often have dyscalculia, and kids who have dyscalculia often have dyslexia. But not all of them do. so you find kids who are just dyscalculic and kids who are just dyslexic. And if you look at the parts of the brain that are involved in reading, they scarcely overlap at all with the parts of the brain that are involved in arithmetic. That’s one reason for thinking that they are distinct. we are beginning to understand better the kinds of genes that are involved in dyslexia, and they don’t seem to be genes that are involved in dyscalculia. so again, at the genetic level, there seems to be a difference.
But it might be that there’s some common cause for both dyslexia and dyscalculia, we don’t know that yet and that seems entirely possible. what I think to me is clear but to many people in the dyslexia business is not clear, is that dyslexia doesn’t cause dyscalculia. so the fact that you’re not very good at reading of course is going to handicap you in lessons, but in itself it doesn’t actually affect your ability to represent numbers in the brain.
Corinne Podger: Dyscalculia can be a lifelong disability but, like dyslexia, it’s not recognised as such by Australia’s Disability Discrimination Act which is deliberately broad in an attempt to be inclusive. But it leaves schools with no clear guide on who to prioritise for extra help. last year the National Dyslexia Working Party urged the federal government to create a new disability category, that of specific learning difficulties. The recommendation was made with dyslexia in mind but working party member Dr Nola Firth from the Murdoch Children’s Research Institute says it could also cover dyscalculia, echoing moves abroad.
Nola Firth: In say America and Canada and the UK the words ‘specific learning disabilities’ are actually in the disability discrimination legislation. But here they’re not. because we haven’t got it specifically stated in law as specific learning disabilities, it’s not so well understood here. perhaps if I can talk a little bit about the history — there was an inquiry in the 70s in the Senate as to whether the ‘specific learning difficulties’ it was called at that stage existed. And, in our country unfortunately, we decided that it was due to bad teaching. It didn’t exist. whereas at a similar time in America, Canada and the United Kingdom, they came to a different conclusion. And they were in fact right and we were wrong.
It was done with the best of intentions but I think as a result of that we’ve lagged behind here. In all those countries all teachers have a mandatory requirement of education in dyslexia and dyscalculia — it’s specific learning disabilities so it covers both. It’s important so that people who have had an informed diagnosis know that they are entitled to reasonable adjustments, which are the words that are used. right throughout their lives. It starts in kindergarten, primary school, secondary school, tertiary education and then workplace, so that they can reach their true potential which in fact might be very high. People can be gifted and have either of these conditions.
Bob Reeve: there is still a strong belief that you can teach all children anything but if you have a subgroup of atypical children, as in dyscalculia, who may need special exposure to teaching practice, we should know about that, we should actually do something about it. we now have to convince policymakers and educators of the value of this.
Brian Butterworth: There’s a circular problem with recognition. In order to get it recognised by education authorities including government you need to be able to have a way of reliably identifying it and I think we’ve got that. you also need to have a way of reliably helping the kids who have that problem, and I think we’re on the way to that. But until we’ve got those two elements in place, parents are not going to say I want my child to be identified as having this particular problem and to get this kind of help for that problem. And without the parents getting active about it governments aren’t going to get active about it. And if you look at the history of dyslexia it’s because the parents of dyslexic individuals were very vocal that governments recognised it..
So what we need is for the current government, in the UK and presumably in Australia as well, to recognise that this is a problem where you can identify the individuals, you can help the individuals and that actually it makes economic sense to put in place programs to identify and help dyscalculic learners.
Astrid: we don’t expect for her to become a scientist or to work in that field but we feel it’s important for her to have enough maths to get her through school and to get her through life. you know just the everyday maths of working out your interest rate, counting back change, all the basic things that we use in everyday life.
Lucie: my teachers, it might help them know that I don’t know, like it’s not that I don’t want to listen, like she’s explaining on the board and I say I don’t understand and then they say you’re not listening. It will help them know well OK she really does not understand.
Natasha Mitchell: Lucie with her mum Astrid and before them, Professor Brian Butterworth, Associate Professor Bob Reeve and Dr Nola Firth, speaking to producer Corinne Podger. Details and oodles of extra resources about dyscalculia on our website as ever, abc.net.au/rn/allinthemind. And on my blog extra audio including an extended interview with Brian — if there’s a man that makes numbers sexy he’s the one.
And more on efforts to have dyscalculia recognised in the next edition of the DSM or Diagnostic and Statistical Manual for Mental Disorders by the American Psychiatric Association — we’ll have to see how that goes.
So I want to hear about your experiences as a parent, or as a person challenged by numbers, or not, perhaps you’re a maths whizz. Love your stories, particularly on our Audioboo pilot channel, look for ‘speak your mind’ on the website and follow the instructions. or there’s the comments board on this week’s page too.
Thanks to studio engineer Carey Dell, I’m Natasha Mitchell, more heady talk next week. Bye for now.
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