There is substantial research about the lasting influence of early experiences in learning about number and arithmetic and the two key skills of classification (closely linked to generalising) and seriation (putting things in order of size and/or value). The two skills are critical to the foundations of maths. They develop the abilities to see patterns and organise information and data.
Brian Butterworth, the UK's leading expert on dyscalculia, emphasises the importance of 'subitising'. This is the ability to see a small quantity of randomly organised dots and simply know how many are there and of 'numerical Stroop'. This is the ability to identify the digit symbol that represents the bigger numerical quantity whilst ignoring the font size, for example, to identify 6 as representing the bigger quantity when shown a pair of digits such as, 6 4.
The ability to count forwards is a sequencing (seriation) task as is the, frequently, more challenging task of counting backwards. Young children are expected to rote learn number facts, such as 5 + 8 or 2 x 6 and quickly retrieve them from long term memory. These are not easy tasks for many children and can be a source of frustration for all involved, children, parents and teachers.
A key issue in learning is that first learning is dominant. So, if a child learns that 6 + 8 is 15, it will be difficult to 'unlearn' that and replace it with 6 + 8 = 14. The child has to be able to inhibit that incorrect first learning. These problems will be exacerbated by the demand to answer quickly. My, by now, extensive informal survey of teachers at my lectures around the world tells me that many children are giving up on maths around the age of 7 years old.
We need to get the correct information in there first time and we need to constantly revisit to check that it is still there.
The input at home needs to generate success and be low stress and purposeful. So, for very young children work on subitising, that is, identifying consistently and accurately small quantities, linking these to the symbols/digits. Try sequencing objects in size. use seriation and classification games. Counting forwards and backwards, in ones when young and later in twos and tens is a key skill and sets the foundations for addition and subtraction. Demonstrate the counting with objects such as chunky counters and link quantities to the symbols. Use lots of appropriate vocabulary such as, 'add one more, take away one' and the key question, 'Is it bigger or smaller?'
Be careful about demanding that children do these tasks quickly. A key problem is speed of processing. remember that failure rarely motivates, so ensure that children are challenged appropriately.
Try to find the maths in everyday life, so that it is seen as a normal activity and skill. 'How long does it take to walk/drive to school?' 'How many chocolates in a packet/box?' 'How many steps to climb?' 'How many leaves on a tree?'
Try to include estimating as well as precise answers to encourage that important skill. Estimating is a less judgemental activity in that answers are 'close, bigger, smaller, not that close' as compared to 'right' and 'wrong'.
On the individual (socially/ emotionally/ behaviourally) and in education (on learning / Attainment / behaviour) Good teachers and parents watch and notice, they pick up the non-verbal information that makes communication empathetic. To para-phrase a remarkable pioneer, 'You teach the maths as it is to the child as he is.'
Maths seems to be a subject that generates anxiety in more people than any other subject in school and life. Some people become maths phobic, which may or may not be a consequence of dyscalculia, but a consequence of too much experience of failure. That is a personal judgement for the individual. The avoidance of maths is very common. Low achievers in schools avoid being wrong in maths by avoiding maths. This avoidance can be total, or maybe restricted to certain topics, for example, 'I don't do fractions'. A child will withdraw from involvement in maths if he or she does not experience success at a level that is both meaningful and encouraging for them as an individual. Teachers and parents have to provide opportunities for the child to experience meaningful successes. Complementary to this is that intervention should not solely be asking a child to do what he or she can't do.
Not every teacher in primary school is confident when teaching maths. Their memories of their own school experiences may contribute to that. Early experiences are a dominant influence unless counter-balanced by more positive experiences. Anxieties and attitudes to maths can be passed through families and classrooms.
In the early years (and, I would argue later, too) meaningful manipulatives and visual images will help learning attitudes. More on this in the next section. Also of help to children who are unable to organise their work on paper, for example, to line up columns of numbers, is the use of squared paper where the squares are sized to suit the individual.
Strategies to help learning start with a pro-active recognition of the potential barriers to learning. Children may have very weak short term memories so they do remember instructions or sequences of information. Information should be presented in chunks that are manageable for the child … and repeated. Short term memory does not store information. When it is lost not amount of concentration will bring it back.
One of the counter-productive beliefs of maths is that computations should be done quickly. This is especially so for mental arithmetic tasks. One of the often-found characteristics of maths learning difficulties and dyscalculia is a slow speed of processing information. It takes a little longer for some children. The expectation of quick responses can be very demotivating. Give more time, but do this discretely and creatively so that the child doesn't feel singled out as 'slow'.
Wipe-clean boards are a useful tool for reducing the impact of negative evaluations on motivation. It is easy to make wrong answers vanish. Encourage sub-vocalising, repeating information almost silently to help in holding that information for enough time to do what it asks. Research I did back in the 1980s with Colin Lane confirmed the efficacy, for many, but not all children as is ever the case, of using self-voice for rote learning.
Having a good working memory is strongly related to being good at maths. For young children this is especially apposite for mental arithmetic. A weak working memory will dramatically reduce a child's ability to perform mental arithmetic. There will be children with weak working memories, so they cannot hold information for long enough to perform the steps in a calculation. Teachers and parents should know the stm and WM capacity of their children. Long term memory stores facts and procedures. A child's long-term memory capacity may be poor for maths facts whilst being good for, say, spelling. This is part of the specificity of the specific learning difficulty of dyscalculia. An approach that will help with facts and also have the benefit of strengthening an understanding of maths is to encourage and teach the connections between facts, to develop strategies that use what you know to work out what you can't remember. It is an approach that encourages meta-cognition, that is, thinking about how you are thinking.
Examples are working out 6 + 7 from 6 + 6, which in turn is related to 5 + 5. This starts with visual and/or manipulatives, alongside symbols and is progressed to just the symbols.
..or working out 7 lots of 6 (7 x 6) from adding 5 lots of 6 (5 x 6) and 2 lots of 6 (2 x 6), that is 30 + 12 = 42 (which infers that the child has been shown that multiplication is adding together 'lots of' the same number.
For many children the secure facts are for 1, 2, 5, 10 and later for 20, 50, 100 and so on. Build on these. Build on strengths. A key concept to understand is place value. It is a sophisticated concept and is absolutely critical to understanding maths. (Note: Many more of these methods are available as video tutorials on my website: www.mathsexplained.co.uk)