How do different components of working memory affect our ability to perform mental addition?

Logie, R. H., Gilhooly, K. J., & Wynn, V. (1994). Counting on working memory in arithmetic problem solving. Memory and Cognition, 22, 395–410.

It's difficult to find  studies that focus on the influence of cognitive abilities on specific arithmetic functioning.  This study is about 20 years old, but it is focused on the question of working memory's influence on the ability to perform mental addition of two digit numbers.

Why is that important?

When the child we work with has a difficulty in a specific arithmetic function, for example mental addition, we want to know which cognitive abilities lie at the base of this difficulty.  Then we can assess those cognitive abilities and see if indeed they are significantly low.  If so, we have a suggested explanation for the child's arithmetic difficulties and can recommend proper treatmemt.

Logie and his colleagues isolated each of the components of working memory (according to Baddeley's model) and looked into its separate influence on mental addition.

Working memory, according to Baddeley's model, consists of a phonological loop (Temporary storage of linguistic information maintained through vocal or sub-vocal rehearsal), a visuospatial sketchpad (Temporary storage of visual/spatial information) and a central executive (attentional control of action.   The central executive focuses the attention and divides attention between 2 goals or 2 stimuli streams ). 

The episodic buffer is not mentioned in this study.  It may have been added to the model after this paper was published.

Why did the authors use mental addition with two digit numbers  and not single digit numbers?

We retrieve many addition (or multiplication) facts in single digit numbers automatically from long term memory, without calculation.  That's why adding one digit numbers, even sequentially, does not measure the influence of working memory on the ability to execute mental calculations.

The participant's task was to add a series of two digit numbers (e.g.    13+ 18(31)+ 13(44)+21(65)+ 13(78)+25(103)) that was presented auditorily or visually.  After hearing or reading the first two addends, the other addends were read or heared one by one.  The participants were asked to keep the subtotals in their memory, and to say the total sum after the whole series has been read or listened to.  The presentation of the whole series took 20 seconds.

In some of the trials, the participants performed the same task (of course with different numbers) while concurrently performing another task.  The other task was planned to load one component of working memory (the phonological loop, the visuospatial sketchpad or the central executive).  It was hypothesized  that if a specific component (for example the phonological loop) is required for mental addition,  concurrent performance of another task that activates this component will disrupt mental addition

How is the phonological loop related to mental addition?  When we do mental addition, it is hypothesized that we subvocally rehearse the numerals.  We  presumably use subvocal rehearsal in the the addition process itself. 

Ellis and HennelIey showed that the arithmetic performance and verbal memory span of Welsh speaking children are poorer than when the same children perform the same tasks in English!  Apparently, when the number words are longer (as is probably the case in Welsh) it takes longer not only to articulate them but also to rehearse them subvocally.  Long words place a load on short term memory span, which has a limited capacity anyway.  Since we need memory span for mental calculation, mental calculation is disrupted too.  Similar differences in performance in tasks of digit span, counting and calculation due to the length on number words   were found in Chinese, English, Arabic, Hebrew, Spanish and Italian.  The length of number words in a language affects the ability of speakers of that language to perform mental calculation.,

How is the visuospatial sketchpad  related to mental addition?  It is hypothesized that people create visual images of the number line and perform the addition procedure on it.

How is the central executive related to mental addition? The central executive is supposed to coordinate the activities of the phonological loop and the visuospatial sketchpad, and maybe to perform the addition procedure itself.

How did the researchers create a load on the three components of working memory?  The task that placed a load on the phonological loop required the participants to repeat the word "the" once a second (concurrently with  the mental addition task).  The task that loaded the visuospatial sketchpad required the participants to watch irrelevant pictures or to press buttons while performing the mental addition task.

 The task that loaded the central executive required the participants to generate a letter once a second, as randomly as they can.  They were asked to imagine that they draw a note with the letter out of a hat, say the letter and return the note to the hat (and thus they can use the same letter again).  They performed this task while doing mental addition.

Generating random letters requires participants to follow what they have already said so as not to repeat the same letter too many times, and to inhibit familiar sequences like "abcd".  These processes of inhibition, monitoring, planning and control are executive functions.    It's known that generating random letters disrupts the ability to solve syllogisms and other complex tasks.

What were the results?

When the addition problems were presented auditorily, disrupting the central executive (through the generation of random letters) caused a significant rise in errors in mental addition.  Disrupting the phonological loop (through repeatedly saying "the") caused a more modest rise in calculation mistakes.  The disruption was bidirectional: mental addition disrupted saying "the" and generating random letters.

Disrupting the visuospatial sketchpad (through watching irrelevant pictures or pressing buttons) did not affect mental addition.

Even when the addition problem was presented visually (the participant read the problem off a screen), disrupting the phonological loop caused a rise in the number of mistakes in mental addition.  But the amount of disturbance was lower than when the addition problem was presented auditorily.  It's clear that subvocal rehearsal is involved in the performance of mental addition, whether the problem is presented auditorily or visually.

Disrupting the central executive, when mental addition was presented visually, caused a rise in the number of mistakes in mental addition, similar to the effect that was seen when the presentation was auditory. 

Disrupting the visuospatial sketchpad when mental addition was presented visually, caused a small rise in errors in mental addition.  This may mean that participants used visual imagery (maybe of the number line) while performing mental addition (but only when the task was presented visually).

Generally, participants made fewer mistakes when mental addition was presented visually than auditorily.  This happened also when there was no concurrent task (when participants performed only mental addition).

What are the conclusions?

·         When the child we work with has difficulty with mental addition we should look for a problem with working memory, especially the phonological loop (measured by tasks like digit span) and the central executive (measured by tasks that measure executive functions, like WCST).

·         It's better to presents addition problems visually, not auditorily, even to children with no arithmetic difficulties.  This gives them a better chance to solve them correctly, with fewer mistakes.

·         It's interesting whether these findings apply also to subtraction, multiplication and division.