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.

Cognitive training can improve fluid ability

 

 

Fluid ability is the ability to tackle new unfamiliar problems, that require making inferences, generalizations, abstract thinking, planning, monitoring and flexible thinking.

 

Who wouldn't like to improve his fluid ability?

 

It might be possible – through practice in n-back tasks.

 

What is an n-back task?

 

It's an apparently simple task:  one is presented with a series of items (pictures, numbers etc.) that are presented sequentially.  The person responds (by pushing a button or verbally) every time that the item presented is identical with the item presented n items ago.  For example, in a 2- back task, the person responds every time the item presented is identical with the item presented 2 items ago.  In a 3- back task, the person responds every time the item presented is identical with the item presented 3 items ago.

This might sound simple, but it's not easy at all (said from a personal experience).  You should try it!   In this site the task is presented as a nice looking game:

http://cognitivefun.net/test/4

As you'll see, practice improves performance in this "game".  You can progress to higher levels: 3-back, 4-back and further.

This task also has a dual version (I would call it an "extreme" version).  In this version, a person has to follow 2 different series of items (one visual and the other auditory) simultaneously, and to respond (by pressing a button) when in each of the series the item presented is identical with the item presented n times ago.

In this research,

The relationship between n-back performance and matrix reasoning — implications for training and transfer

 Susanne M. Jaeggi  , Barbara Studer-Luethi  , Martin Buschkuehl ,Yi-Fen Su John Jonides , Walter J. Perrig  Intelligence (2010)

http://www.psy.unibe.ch/unibe/philhuman/psy/apn/content/e5616/e5621/e7504/e7774/files7775/Download_ger.pdf

the researchers tried to find out whether practice in an n-back task affects university student's fluid ability and working memory. Fluid ability was measured by matrices tests, and working memory was assessed by a test that required participants to recall a sequence of stimuli in the correct order in addition to completing a distracting processing task.

Some of the students practiced with an n-back task for a month.  They practiced in their maximal ability level (3-back, 4-back and so on), to make the practice effective.  They practiced 20 minutes per day for four weeks.  Following practice, they all improved on the n-back task.  Some students reached a 7-back level (I think I can only dream about reaching this level)!

Fluid ability and working memory were re-measured following practice.  Performance in the matrices tests improved following n-back practice!  Performance in working memory tests did not improve.

What does the n-back task train?

It might be training memory span.  Memory span is a narrow ability within "short term memory".  Memory span is the ability to maintain items in immediate awareness and to produce them immediately.  "Forward digit span" is a good example of a memory span test.

The n – back, like other memory span tasks, requires maintaining the order of the heard or seen items in immediate awareness. While the item list in other memory tasks is "static", here one has to keep track of information that keeps flowing in throughout task performance, and concurrently keep track of the number of items presented after each item.  This makes the task more complex than other memory span tasks.

This task requires a different kind of manipulation than other working memory tasks (like "backward digit span"). This explains it's relatively low correlation with working memory measures.

What explains the n-back task's influence on fluid ability? It might be the fact that one has to deal quickly with "online" information, compare it with existing information while updating this existing information.  This makes it a task that is related with fluid ability.

What do sentence recall tests measure?

In sentence recall tests, the child listens to one sentence and tries to repeat it as precisely as he can.  Usually, the sentence's length and complexity grow as the test progresses.

This test is usually thought of as measuring memory span.  Memory span, in CHC theory, is a narrow ability within short term memory.  Memory span is "the ability to encode information, keep it in immediate awareness and produce it immediately in the order in which it was presented."  Or, put another way: "the ability to attend to and immediately recall temporally ordered elements in the correct order after a single presentation."  (Flanagan et al.,2007, Schneider and McGrew, 2012 ). 

Sentence recall is also an efficient marker of SLI – Specific Language Impairment and of dyslexia.  Performance in sentence recall tests is also related to reading comprehension.

A few researchers, including Baddeley, suggest that the sentence recall task involves short term memory as well as long term memory.  Sentence recall requires using general information, semantic knowledge (that help us understand what the sentence is about - the 'gist' of the sentence), and grammatical and syntactic knowledge.  Utilizing these knowledge types requires the involvement of long term memory.   The sentence recall task also requires keeping track of the structural aspects of the sentence ("keeping" the word order in the phonological loop, for example).  This involves short term memory.

Gathercole found in 2005, that people with high phonological memory are able to retain the word order in sentences much better than people with low phonological memory.  People with low phonological memory have more errors of omissions  and insertions  (they add and/or delete words from the sentence).  Sentence recall tests are correlated with nonword repetition tests, which are influenced by memory span.

Marshall and Nation found in 2003, that children with normal levels of reading accuracy and speed but low reading comprehension, also have low sentence recall.  These children have no difficulties in memory span tests.  The researchers suggest that the low performance in sentence recall tests is related to long term memory's involvement in sentence recall tasks.

In this study:

The role of sentence recall in reading and language skills of children with learning difficulties.  Alloway, T.P. and Gathercole, S.E.  learning and Individual differences, 15 (2005) 271-282

http://www.academia.edu/2651151/The_role_of_sentence_recall_in_reading_and_language_skills_of_children_with_learning_difficulties

participated children in elementary school with learning difficulties.  They were tested with reading, language, working memory, expressive vocabulary and sentence recall tests and the Wechsler test.  The hardest items in the sentence recall test were not longer sentences but were more complex sentences.  The goal was to see whether the sentence recall test is related to reading or to language skills.

A correlation of 0.6 was found between sentence recall and memory span.  But, when the unique contribution of each factor to the prediction of reading and language skills was examined, it was found that sentence recall explained a significant amount of the variance in reading and language skills above the contribution of age, IQ, expressive vocabulary, memory span and working memory.

So, sentence recall test measures much more than memory span.  Gathercole and Alloway suggest that sentence recall predicted performance in reading and   language tests because    sentence recall tests requires the use of both short term memory and linguistic and conceptual knowledge found in long term memory. 

Intelligence and cognitive abilities part 4: Short Term Memory

Intelligence and cognitive abilities part 4:  Short Term Memory

This is a complicated subject, mainly because different papers define the same concepts differently.

I chose to define the concepts within CHC framework. 

Is working memory training effective? Only within modest limits.

   

While working on part 4 of my series of presentations (which will 

be about short term memory), I found this paper:

Melby – Lervag, M. and Hulme, C.  Is working memory training effective? A meta analytic review.  Developmental Psychology 2013, vol 49 no. 2, 270-291.

https://www.apa.org/pubs/journals/releases/dev-49-2-

 270.pdf

This meta-analysis reviewed several research based

computerized working memory training methods.

Before shortly reviewing it, I'll define short term memory, memory span and working memory within the CHC 

framework.  These definitions are from this excellent chapter:

Schneider, W. J.,& McGrew, K. (2012).  The Cattell-

Horn-Carroll model of intelligence. In, D. Flanagan & P. Harrison (Eds.), Contemporary Intellectual Assessment: Theories, Tests, and Issues (3rd ed.) (p. 99-144). New York: Guilford.

http://www.iapsych.com/articles/schneider2012.pdf

Within CHC framework, short term memory is the ability to encode, maintain and manipulate information in one's immediate awareness.  There are 2 narrow abilities within 

short term memory:

1.  memory span – the ability to encode information, maintain it in immediate awareness and immediately reproduce it in the sequence in which it was represented.

2.  working memory capacity: the ability to direct the focus of attention to perform relatively simple manipulations of information within immediate awareness while avoiding distracting stimuli and engaging in controlled searches for information in long term memory.

Back to the  Melby – Lervag  and Hulme paper:

A.  Interesting facts from this paper:

Working memory reflects a domain –general cognitive capacity and not modality specific systems (verbal vs. visual).

Working memory capacity places a general limitation on attentional capacity.  The unique variance measured by working memory tasks that is not shared with memory span is executive attention.  That's why working memory (but not memory span) correlates very highly with fluid ability and executive attention.  Some say that working memory is identical to fluid ability and executive control.  This leads to the hypothesis that people with high working memory capacity will perform better on tasks requiring the inhibition of distracting information.

B.  Results of the meta - analysis

The meta – analysis included 23 studies of training methods which had randomized controlled trials and at least 2 week interventions.  Participants were mostly healthy and typically developing children and adults.

 It turned out that the training programs yield short term improvements on working memory tasks (tasks close to those trained).  These improvements are not sustained after 9 months for verbal working memory, and might be modestly sustained after 5 months for visuospatial working memory.

 There was no evidence that working memory training roduces generalized gains to other skills like verbal ability, word decoding or arithmetic, even right after training.

To conclude, the findings cast strong doubts on claims 

that working memory training is effective in improving 

cognitive ability and scholastic achievement.