By Kate Papageorgiou
This is a relatively new term in special education (DFeS 2001 Bird, R. website) and as such it is not widely known about. Even many maths teachers do not know it exists and when they do may mistake this for; just a term for those who are not good at maths. It may appear like an excuse for why the child cannot do maths. However, in my opinion and my experience as a specialist tutor, this is not the case.
A person with dyscalculia may be able to understand some quite complex maths but they may be unable to understand the concepts of how big a number is. They may have no notion of what place value actually means and if you show them they may be suddenly amazed.
For example, I have one student who knows a lot about symmetry and shape and is also quite good at solving logic problems, whereas, when he first started working with me, it became apparent that despite these abilities, he could not successfully count up to twenty, let alone count back down again. I have another student who, at 13 is working towards an F at GCSE Maths, whilst working towards a B in History. This student can discuss some interesting things about circles and tessellation, she can tell you a lot about shapes and their properties, she came to me knowing all this but not able to explain what you are actually doing when you multiply nor able to do subtraction successfully when it is necessary to decompose one ten into ten units (this may be called carrying or borrowing by some of you but is actually an exchange, which can be modelled quite nicely using a teashop analogy as laid out below).
As a tutor of those with learning difficulties and with a background in science, I often get chosen by parents who are looking for help with maths despite my desire to do more literacy. I had studied the books on how to teach literacy and even practised the process on a number of students but now am having to develop on the job a similar method for children with maths difficulties.
I go back to the basic building blocks, just like a dyslexia program starts with the letters and vowels and consonants, I go back to the basic digits and look at how they match the quantity in the same way you match letters to sounds. I then look at categories of number, starting with odd and even. I look at place value using Dienes blocks to show how big a ten is compared to a one and a hundred and then a thousand. This can be a massive revelation to children who may appear to be learning the numbers well and may even be able to count.
I may have to spend time with my students looking at bigger and smaller in terms of number. They can tell you if they are not getting a fair share but have failed to generalise this to; this number is bigger than that number. I may have to look at this in particular when we add another digit to the number, e.g. go from working in tens and units to hundreds, tens and units.
Many of my students then have to be taught the meaning of the zero as a place holder. This can be quite a revelation for even their parents, that at the advanced age of 12, the child has not registered that you have to put a zero in the middle of a number like one hundred and two.
Many of my students cannot learn multiplication tables, though some can. However, when they can they often do not know the meaning of the tables, what they are representing nor how they can be applied. In some cases it can be detrimental to their learning if they do know the tables off by heart as it can be then very difficult to get them to go back and learn what the two times table actually mean. It is then essential to teach them how to calculate a more difficult times table and show them what they mean this way. Without the understanding, many of the children who can learn their tables by rote but have an underlying maths disability, will not know them a few years later. If they
understand them they can eventually learn them over the repeated need to calculate them.
While I am not advocating going back to not teaching the tables, it is far more important that children be expected to show that they understand how to derive them than just repeat a chant and as such I would suggest that a child with a difficulty learning the tables should not be coached until they can chant them, but instead they should be encouraged to use an abacus, counters, jelly beans and other useful items to help them calculate the multiplication facts and the division facts in as many different ways and in answer to as many different problems as possible.
It is always good to be able to eat the grand total at the end, so how about working with a basic 1 to 2 biscuit mix? This can be multiplied up to find out how much you need to put in the mixture to make the right number of cookies for a party or for a week for the family.
By doing problems in the real world you are showing the child that the maths has an application. This means it is important to play games. There are many domino games and dice rolling games you can add in at the end of a session. I always start with a place value or number concept game, follow with a memory game involving numbers, quickly move to a logic puzzle or two. I then do some new material, some of the new material I do with the children can actually make them quite upset when they realise that no one ever bothered to explain this simple thing to them before.
As a result of my work I have been developing concept cards for the older children to take away with them. These explain the definitions we use in maths and numeracy. Many of them appear to be quite simple but I can reassure you there are many students, even quite old ones, who cannot explain what an odd number is nor tell me what to multiply actually means. These same people cannot tell me how many beads I have put on the desk and revealed to them for about 2 or 3 seconds without counting one at a time and as such they fail at 4 beads or 5. My superbly numerate husband can do 11. After 5 minutes training I was able to do 9 or 10. I have found that after a number of weeks working with basic number concepts and learning the intrinsic feel for a quantity, many of my students will be up to this capacity.
Recovery of basic number ability appears to be easier than recovery of basic literacy and yet there are so many maths teachers around who are happy to tell us that; ‘it is possible to just not be able to do maths and there is nothing you can do about it.’ I would contest that this is not the case.
The tea shop; This is a little local tea shop run by volunteers, one of the daily teams doesn’t leave much change in the till for the float for the next day, so there are lots of ten pound notes but hardly any pound coins. For ease of calculation all items cost multiples of a pound. Lots of the volunteers have now taken to ensuring they arrive at the shop with 10 pound coins in the morning. I am guessing that most of you can now see where I am going with this. With the use of some monopoly money to represent the notes and coins in the till we can now sell and give change, showing the need to break open a ten in to ones. This is done by exchanging a ten with ten coins out of a volunteer’s purse.
You will notice that unlike many other SpLDs there is no national organisation to raise the profile and no one to co-ordinate lobbying the Education Department to ensure that sufferers get a fair deal.
I hope that I have given you an insight into this difficulty and perhaps some ways to help those around you. I am sure that if you are interested you will need to read more so may I suggest the following:
See http://www.ronitbird.com/dyscalculia/ for more information
http://www.crossboweducation.com/ for various resources
Kate Papageorgiou is a specialist tutor working with students with dyslexia, dyspraxia and dyscalculia. Kate will be co-speaker in the experiential slot at our summer conference http://www.oups.org.uk/events/annual-conference
This article originally appeared in News & Views Summer 2015.