## Why study the development of mathematics in children with SLI?

It is important to think about how we make sense of numbers. We are surrounded by numbers in everyday life; are all numbers processed in the same way? To illustrate this point, think about a trip to the supermarket. There are many ways in which the supermarket presents numerical information in order to tempt us to part with our money. How do we decide if the 'good deal' we are presented with is in fact the bargain it purports to be? When we see goods nearing the end of their sell by date, they are often presented with a brightly colour sticker sating usual price and 'now price'. In this instance the computation is fairly automatic - we can look at the difference between the two values and determine if the saving is a worthwhile one. An alternative method of presenting 'special offer goods' is to offer a saving if two of a product is bought at the same time. In the example illustrated below, the shopper is informed that to buy 240 tea bags represents the best value for money, however there is an additional offer available with a saving if two of the smaller size packs are bought. This leads to a decision having to be made about which is the best bargain. This type of mathematical computation is not automatic; it requires a decision to be made to regarding how the calculation will be made.

53.2p per100g

59.8p per 100g

## 2 FOR £4.48

These examples raise interesting questions. Are there (at least) two systems for processing number; one a fast approximation based on a 'mental number line', another slower, but more precise, which may be based on language systems. There is also the question of conceptual understanding; how would different number processing systems interrelate with conceptual knowledge? This leads to the issue of SLI. How do children with SLI process number? Do they have the same number systems? Can they build a mental number line? To what extent are their arithmetic skills in deficit? How does their language deficit impact on their conceptual understanding? Do they understand the language of mathematical instruction? With these issues in mind the NumberTalk project aimed to study the development of mathematical skills in children with SLI.

## The selection of our sample

In the NumberTalk study we had 180 children, 60 of these were year 3 children with specific language impairment (SLI). These individuals experience significant difficulties with communication despite having non-verbal skills (and learning potential) in the average or above average range. The children in our sample showed language deficits as measured by The Reception of Grammar Test (TROG) and/or a test of non-word repetition (CNRep) when compared with non-verbal ability, as measured by Raven Coloured Progressive Matrices (RCPM). We had two control groups: 60 age-matched controls (AC) who were matched for age, gender and non-verbal ability; and 60 language-matched controls (LC) who were matched on the TROG test, but also matched for gender and non-verbal ability; these children were typically from Year 1, although some did come from reception classes. Table 1. below shows a summary of these measures.

 Mean age (years) Raven raw TROG raw CNRep raw AC meanN = 60 8.2 25.0 16.0 27.4 LC meanN = 60 6.0 18.4* 11.6 22.1 SLI meanN = 60 8.2 24.3 11.7 22.1

* The three groups were matched on their age equivalent percentiles.

The data for the project have been collected and analysed. You can read a report of some of the findings here. If you have any comments or queries regarding the project please feel free to contact us, either directly to one of the email addresses above, or through this link; contact us.