Making sense of maths problems and undertaking maths calculations in one’s head can put an enormous strain on the “working memory” - the short term memory that also allows us to remember the start of a sentence while we are talking through the end of the sentence.
Most, if not all, people who suffer from dyscalculia have problems with their working memory, although working memory problems are not necessarily an indicator of dyscalculia.
Many researchers have observed that the failure of children to keep abreast of maths lessons and learn at the level that might be expected for their age and intelligence is associated with difficulties in processing data in this “short term” or “working” memory. This is because in our everyday lives we tend to undertake quite a range of mental arithmetic activities related to everything from remembering our phone number to deciding if one has enough money left to buy something.
Thus children who find maths difficult often do so because they struggle to get past the mental arithmetic stage. They may learn part of their “times tables” and be able to recite the table one day, but then forget it completely the next day.
For the dyscalculic child the cause of this problem is the dyscalculia itself which always brings with it a difficulty in handling numbers. For the non-dyscalculic child the problem can be an overload of the short term memory and lack of practice at using this memory other than in a classroom situation where other children may be more adept at handling numbers.
Obviously since maths knowledge is always cumulative (that is to say, for example, one can’t really learn division without understanding subtraction) children with short term memory problems can fall behind very early on in their studies.
So it is helpful if children who suffer from short term memory problems which result in poor performance in mental maths can undertake one of more of these four activities which encourage the development of this memory.
1: Take it slowly
For times tables never progress to the next table until the first one is learned, as this only adds to the confusion. One way to help the children who are having difficulty is to give them a few cards with the multiplication written on one side (eg “2 x 4”) and the answer on the other side.
The child says the multiplication and then says the answer while turning over the card. If the answer is not known the child can see it, read it and say it, and so does not spend time guessing at the wrong answer.
If the child is struggling with a table do not progress to the introduction of further cards and don’t move onto another table. The point is for the individual to be answering correctly and have the knowledge secure in his/her brain. By all means stop after a few steps within the table. Thus one might only get to 5 x 4 before the knowledge breaks down, and thus the pupil or student only has five cards. When those five can be said correctly then a sixth card can be added, but again there is no further progress until the six cards can be read and the answer said without pause.
Eventually the repetition of the table can move the table into the long term memory so that in future the individual with working memory problems no longer has to recite the whole table to find the answer to a multiplication question.
This has a double benefit since it means that with a multiplication question there is less dependence on the working memory, leaving it free for other work, while in some situations the child will not have to say the whole table but simply find the answer in the long term memory as an established fact (along with the child’s name, the child’s age, address and other key facts).
2: An alternative to cards
Working with cards is helpful because cards are easy to transport, but if this causes difficulty for the pupil or student, then moving counters of the type used in games like snakes and ladders and ludo can be used. The individual says “once three is three” and moves three counters from the central pool to one side, putting them in a line.
Then the individual quickly selects another three and says “two three’s are six” and adds these three counters o the initial group of three.
3: Giving numbers meaning.
It is obviously helpful if the pupil or student can remember the phone number of a parent, but phone numbers can be difficult to remember because they are long and generally meaningless.
Therefore if the phone number to be remembered can be broken into meaningful sections the number itself is easier to remember.
For example if the individual’s age, or the number of the dyscalculic person’s house, or a number on the parent’s car or any other number that the pupil or student has an association with turns up in the number of the phone, that can be easier to read.
Certainly the number has to broken down into sections to make this work, and it can take a while to learn all ten numbers after the zero, but it can be worth the effort, since the whole activity can strengthen the meaning of the number to the individual. The year of the person’s birth, the number of a nearby main road travelled each day on the way to school, the age of a relative, a number that turns up in a song - we are looking in all cases for anything that has a meaning to the child. This can even work by always saying a particular two digit number in a singularly odd voice!
Remember the individual numbers should be meaningful and the sequence to be remembered should have some meaning as well.
4. Practise focussing on numbers.
Here one might show the pupil or student four cards each with a number on. The cards are turned over and immediately the individual is asked, “what is the number on the third card?” Most people start by reading the numbers left to right and then reciting the answer. Practising doing this again and also gradually reducing the time the pupil or student is given to see the numbers helps strengthen the ability of the memory to focus on numbers .