The role of working memory

When children engage with numerical calculation, the tasks are often supported by aspects of working memory. Working memory is “the ability we have to hold and manipulate information in the mind over short periods of time” (Gathercole and Alloway, 2008). Poor working memory is often associated with low attainment in mathematics (Geary, 2011). Using the work of Baddeley, Hitch and others, Pickering and Gathercole (2001) suggest that working memory consists of three components.

These components include two “slave systems”, the Phonological Loop (PL) and the Visuo-spatial Sketchpad (VSSP) and the Central Executive (CE).

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The PL holds information that is related to sound and, therefore is associated with spoken and written language and pictures, where these act as triggers for particular patterns of sounds. Information is held in the PL for approximately two seconds, unless it is consciously rehearsed. The VSSP stores non-verbal information which is either visual (such as colour or shape) or spatial (such as movement or position).

These slave systems can be thought of as short term memory capacities.

The term “working memory” suggests that there is more going on than just remembering things in short term memory. It is the CE that is responsible for the more complex aspects of working memory. The CE is responsible for activities such as organisation of the flow of information, planning and, when necessary, retrieving information from long term memory. For example, when you want to work out the sale price of an item that is reduced by 10%, you might use the fact that you already know that 10% is equivalent to ¹/10 and that there is a quick way to calculate ¹/10 of an amount of money. This knowledge is stored in long term memory, but the CE can call upon it, so that you can then calculate the new price. However, while you are retrieving the knowledge from your long term memory, you also need to hold on to the original price (in your PL) and once you know how to calculate the new price, you need to be able to manipulate this “in your head” in order to work out the desired new price. Put like this, it does not sound so easy!

In a study of children 6 and 7 year olds in the UK, a correlation was found between children’s working memory and their attainment in mathematics (Gathercole and Alloway, 2008). Most children are expected to score between 85 and 115. Anything below 85 is considered a poor score. In the study, the average score for working memory, for children scoring below average in mathematics, was below 85, but the average score for their short term verbal memory was above 100 and was actually higher than the average for the middle attaining group of children. Unfortunately, this factor was not discussed. It may be that the children had developed this ability in order to compensate for weaknesses in other areas, such as visuo-spatial memory.

Another study of children at age 14 years, found again that the children with the lowest attainment had average working memory assessment scores below 85, but, unfortunately for this group, no score for short term memory was shown (Gathercole and Alloway, 2008).

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Children with poor working memory, are likely to have particular difficulty with arithmetic:

There are several reasons for this. First, working memory overload in the individual activities designed to develop numeracy skills will result in frequent errors and task failures, impairing the

incremental process of acquiring basic number skills and

knowledge, and slowing down the child’s rate of learning. Second, mental arithmetic is heavily dependent on working memory….it requires not only the storage of arbitrary numerical information, but also the retrieval and application of number rules that may not yet have been securely learned.

(Gathercole and Alloway, 2008, p.54)

In young children, this kind of difficulty might be observed in counting recall tasks.

Cowan (1987) suggested that when children are engaging with counting recall tasks, they try to remember the numerosity of the collections, but once they start to count a second, or subsequent, collection, they forget how many were in the earlier

collections. Hitch, Towse and Hutton (2001) investigated speed and performance in counting recall tasks. They argued that children who process information more quickly are less likely to forget. This suggests that a child who processes information quickly will not need to “hold” the information for as long as a child who processes information more slowly. This is not as straight forward as it may at first appear though, as there are individual differences amongst children which make this a non-trivial relationship. Hitch, Towse and Hutton also highlight the relationship between the rate at which children forget individual items or sets and the effect of

experiencing this forgetting. It might also be the case, though, that children who are at an early stage of learning about number and counting find that they expend a significant amount of effort in counting the dots and keeping track of each count.

In general, if children have poor working memory, they score poorly in all areas of mathematics (Gathercole and Alloway, 2008), but this is not always the case. For example, children with motor coordination difficulties tend to be more successful with tests of verbal working memory than visuo-spatial working memory, whereas

children with language impairments tend to be more successful with tasks of

visuo-37

spatial working memory than tasks involving verbal working memory (Gathercole and Alloway (2008). Cowan, Donlan, Newton and Lloyd (2005), however, when working with a group of 7 to 9 year old children, found that children with specific language impairments (SLI) also had poor visuo-spatial skills as demonstrated by their low scores in the Corsi span task (where children with specific language impairments are defined as those who have been assessed as being significantly delayed in receptive and expressive language while achieving age-appropriate scores on tests of non-verbal skills).

It seems, then, that the relationship between working memory and performance in mathematical tasks is not straightforward (Raghubar, Barnes and Hecht, 2010; Hitch, Towse and Hutton, 2001). The main reason for this is that performance in

mathematical tasks depends on a wide range factors in addition to that of working memory. These include:

….age, skill level, language of instruction, the way in which mathematical problems are presented, the type of mathematical skill under consideration and whether that skill is in the process of being acquired, consolidated, or mastered.

(Raghubar, Barnes and Hecht, 2010, p.119)