Neuropsychology and maths
The neuropsychology of maths
The neuropsychology of maths development is starting to be understood. One of the key issues in understanding how maths develops is the concept of numerosities, which means automatically recognising the number of objects in a set. This seems to be an inbuilt ability present from very early in infancy. In experiments babies as young as one week old have been shown to react differently to different numbers of objects.
A proportion of children seem to find maths inherently difficult and it is believed that many of these children may have a difficulty in recognising numerosites (Butterworth 2008). There is some evidence that difficulty with maths is associated with the anterior intraparietal sulcus in the brain (Butterworth 2008). It is important that children struggling with maths understand numerosities and the Neurogames are formulated to teach and reinforce this.
Developmental stages in learning maths
The first developmental task in maths is to learn to count. This includes learning number words, that these words follow a set order, that each number is only linked with one object (i.e. one to one correspondence) and that a child can announce the number of objects using the last number word (cardinal principal) (Gelman & Gallistel 1978). The Tomato Tumble game teaches and reinforces all these stages. This stage normally starts to develop between the ages of 2-3 years although a significant number of older children fail to fully understand maths at this level.
After learning to count and understand number, the next stage of development is learning to add or count on. This typically develops between the ages of 3-5 years. The Nutty Numbers game teaches addition firstly using objects and then teaches automatic memory for number bonds. This mirrors the natural process of development. Automatic memory for maths typically develops around the ages of 6-7 although a significant number of children continue to count using their fingers until much later. This tends to make further mathematical development harder. The Nutty Numbers game teaches automatic memory for numbers.
Multiplication and division typically develop later although some of the concepts are present earlier. In the UK national curriculum children are introduced to multiplication and division concepts in year 2 (age 6-7). The Nutty Numbers game starts to introduce the concepts of multiplying and dividing numbers in a simple way.
Difficulty learning maths – Dyscalculia
Children in practice seem to find maths difficult for a number of reasons. A significant group of children (about 6-7%) seem to have difficulty in understanding basic numerosities (Butterworth 2008). Some children seem to have difficulty in automatically recognising number and quantity and then have difficulty moving onto more advanced concepts. The Tomato Tumble game addresses these problems. A number of children have difficulty holding information in mind (working memory). This makes mental arithmetic very difficult. A lot of children also fail to learn number facts automatically. This results in difficulty with calculations involving higher numbers. The Nutty Numbers game addresses this problem by teaching children to automatically remember number facts.
One of the leading experts in this field is Professor Brian Butterworth. A good summary of mathematical development can be found in his paper ‘The development of mathematical abilities‘ from the Journal of Child Psychology and Psychiatry (2005) 46:1 93-18.
Butterworth, B. (2008) Developmental Dyscalculia in our edited book: J. Reed & J. Warner-Rogers (2008) Child Neuropsychology: Concepts, Theory, and Practice. Oxford: Wiley-Blackwell.
Butterworth, B. (1999). The Mathematical Brain. London: Macmillan.
Gelman, R., & Gallistel, C.R. (1978). The Child’s Understanding of Number (1986 edn). Cambridge, MA: Harvard University Pre