Working memory and mental arithmetic: A case for dual central executive resources

The current study was designed to examine the possible existence of two limited-capacity pools of central executive resources: one each for verbal and visuospatial processing. Ninety-one college students (M age = 19.0, SD = 2.2) were administered a verbal working memory task that involved updating numbers in 2-, 3-, and 4-load conditions. The task was administered in both single task (no-interference condition) and dual-task (verbal interference and visuospatial interference conditions) formats. Findings indicated main effects for both memory load and type of interference, as well as, a load × interference interaction. Verbal interference led to a steeper increase in errors on the primary verbal working memory task; whereas, there was a smaller increase in errors across load in both the non-verbal and no-interference conditions. The effect of verbal interference and the lack of a spatial interference effect on a primary task that utilized verbal working memory resources, suggests that the processing of verbal and spatial stimuli in a dual-task paradigm requires separate central executive resources.     

Retiring the central executive

Reasoning, problem solving, comprehension, learning and retrieval, inhibition, switching, updating, or multitasking are often referred to as higher cognition, thought to require control processes or the use of a central executive. However, the concept of an executive controller begs the question of what is controlling the controller and so on, leading to an infinite hierarchy of executives or “homunculi”. In what is now a QJEP citation classic, Baddeley [Baddeley, A. D. (1996). Exploring the central executive. Quarterly Journal of Experimental Psychology, 49A, 5–28] referred to the concept of a central executive in cognition as a “conceptual ragbag” that acted as a placeholder umbrella term for aspects of cognition that are complex, were poorly understood at the time, and most likely involve several different cognitive functions working in concert. He suggested that with systematic empirical research, advances in understanding might progress sufficiently to allow the executive concept to be “sacked”. This article offers an overview of the 1996 article and of some subsequent systematic research and argues that after two decades of research, there is sufficient advance in understanding to suggest that executive control might arise from the interaction among multiple different functions in cognition that use different, but overlapping, brain networks. The article concludes that the central executive concept might now be offered a dignified retirement.     

The roles of the central executive and visuospatial storage in mental arithmetic: A comparison across strategies

Previous research has demonstrated that working memory plays an important role in arithmetic. Different arithmetical strategies rely on working memory to different extents—for example, verbal working memory has been found to be more important for procedural strategies, such as counting and decomposition, than for retrieval strategies. Surprisingly, given the close connection between spatial and mathematical skills, the role of visuospatial working memory has received less attention and is poorly understood. This study used a dual-task methodology to investigate the impact of a dynamic spatial n-back task (Experiment 1) and tasks loading the visuospatial sketchpad and central executive (Experiment 2) on adults' use of counting, decomposition, and direct retrieval strategies for addition. While Experiment 1 suggested that visuospatial working memory plays an important role in arithmetic, especially when counting, the results of Experiment 2 suggested this was primarily due to the domain-general executive demands of the n-back task. Taken together, these results suggest that maintaining visuospatial information in mind is required when adults solve addition arithmetic problems by any strategy but the role of domain-general executive resources is much greater than that of the visuospatial sketchpad.     

When the central executive lets us down: schemas, attention, and load in a generative working memory task

Participants were asked to generate a single sequence of numbers in between two bounds. By varying the requested sequence length and way in which the question is posed, this paradigm enables assessment of the contributions to central executive functioning of schema, focus of attention, and load. With sequences of three or four numbers, a quarter of the sample failed fully to comply with the instructions. They generated an incorrect number of numbers or went outside the specified bounds. With sequences of six numbers, more than half of the sample infringed one or more of the constraints. Participants consistently generated sequences with particular generic properties. The overall frequency and patterns of infringements suggest that a substantial proportion of participants focused their conceptual attention on sequence content and often neglected the problem of how thelength and boundary constraints were going to be evaluated either before or during response delivery.     

Stimulus-independent thought depends on central executive resources

Stimulus-independent thoughts (SITs) are streams of thoughts and images unrelated to immediate sensory input. Four experiments examined the contribution of aspects of working memory to production of SITs. In Experiments 1 and 2, interventions that were targeted on, respectively, phonological and visuospatial components of working memory both interfered with production of SITs, but there was evidence that these tasks also made demands on central executive resources. Experiments 3 and 4 specifically examined the hypothesis that production of SITs and control of nonproceduralized tasks both depend on central executive resources, and so should show mutual interference. In Experiment 3, prior practice on pursuit rotor and memory tasks reduced the interference with SITs from concurrent task performance. In Experiment 4, randomness within a task involving random-number generation was less when SITs were being produced concurrently than it was when they were not. The results suggest that production of SITs depends on central executive resources.     

The effect of working memory load on semantic illusions: What the phonological loop and central executive have to contribute

When asked how many animals of each kind Moses took on the Ark, most people respond with “two” despite the substituted name (Moses for Noah) in the question. Possible explanations for semantic illusions appear to be related to processing limitations such as those of working memory. Indeed, individual working memory capacity has an impact upon how sentences containing substitutions are processed. This experiment examined further the role of working memory in the occurrence of semantic illusions using a dual-task working memory load approach. Participants verified statements while engaging in either articulatory suppression or random number generation. Secondary task type had a significant effect on semantic illusion rate, but only when comparing the control condition to the two dual-task conditions. Furthermore, secondary task performance in the random number generation condition declined, suggesting a tradeoff between tasks. Response time analyses also showed a different pattern of processing across the conditions. The findings suggest that the phonological loop plays a role in representing semantic illusion sentences coherently and in monitoring for details, while the role of the central executive is to assist gist-processing of sentences. This usually efficient strategy leads to error in the case of semantic illusions.     

The role of executive control in tool use

Comparing cognitive functions between humans and nonhuman primates is helpful for understanding human tool use. We comment on the latest insights from comparative research on executive control functions. Based on our own work, we discuss how even a mental function in which non-human primates outperform humans might have played a key role in the development of tool use.     

Mental models in propositional reasoning and working memory's central executive

We examine the role of working memory's central executive in the mental model explanation of propositional reasoning by using two working memory measures: the classical “reading span” test by Daneman and Carpenter (1980 Daneman, M. and Carpenter, P. A. 1980. Individual differences in working memory and reading. Journal of Verbal Learning and Verbal Behavior, 19: 450–466. [Crossref] , [Google Scholar]) and a new measure. This new “reasoning span” measure requires individuals to solve very simple anaphora problems, and store and remember the word solution in a growing series of inferential problems. We present one experiment in which we check the involvement of the central executive in conditional and disjunctive inference tasks and compare predictions of the new reasoning span test with those of the classical reading span test. The results of the experiment confirm that reasoning responses, which according to mental model theory require high cognitive work, are predicted by working memory measures. Results also show that some reasoning responses are probably obtained by means of superficial biases or strategies that do not load working memory. The reasoning span test, which involves the central executive to a greater degree, predicts reasoning performance better than the reading span test. The significance and possibilities of the new measure in studying reasoning are discussed.     

The development of analogy making in children: Cognitive load and executive functions

The aim of the current study was to investigate the performance of 6-, 8-, and 14-year-olds on an analogy-making task involving analogies in which there are competing perceptual and relational matches. We hypothesized that the selection of the common relational structure requires the inhibition of other salient features, in particular, perceptual matches. Using an A:B::C:D paradigm, we showed that children’s performance in analogy-making tasks depends crucially on the nature of the distractors. Children chose more perceptual distractors having a common feature with C compared with A or B (Experiment 1). In addition, they were also influenced by unstructured random textures. When measuring reaction times instead of accurate responses, only the 8-year-olds’ reaction times were significantly influenced by perceptual distractors. The 6-year-olds seemed to select the first match they noticed, and the 14-year-olds were not influenced (or much less influenced) by featural distractors. These results are compatible with an analogy-making account based on varying limitations in executive functioning at different ages.     

The association between children's numerical magnitude processing and mental multi-digit subtraction

Children apply various strategies to mentally solve multi-digit subtraction problems and the efficient use of some of them may depend more or less on numerical magnitude processing. For example, the indirect addition strategy (solving 72–67 as “how much do I have to add up to 67 to get 72?”), which is particularly efficient when the two given numbers are close to each other, requires to determine the proximity of these two numbers, a process that may depend on numerical magnitude processing. In the present study, children completed a numerical magnitude comparison task and a number line estimation task, both in a symbolic and nonsymbolic format, to measure their numerical magnitude processing. We administered a multi-digit subtraction task, in which half of the items were specifically designed to elicit indirect addition. Partial correlational analyses, controlling for intellectual ability and motor speed, revealed significant associations between numerical magnitude processing and mental multi-digit subtraction. Additional analyses indicated that numerical magnitude processing was particularly important for those items for which the use of indirect addition is expected to be most efficient. Although this association was observed for both symbolic and nonsymbolic tasks, the strongest associations were found for the symbolic format, and they seemed to be more prominent on numerical magnitude comparison than on number line estimation.     

Time estimation in Alzheimer's disease and the role of the central executive

The aim of this study was to evaluate the role of short-term memory and attention in time estimation. For this purpose we studied prospective time verbal estimation in 21 patients with Alzheimer's disease (AD), and compared their performance with that of 21 matched normal controls in two different conditions: during a digit span task and during an attentional task. Results showed that the performance of AD patients was significantly worse than that of the controls; the interaction between group and condition was significant. We suggest a role of attentional-executive functions in prospective time estimation.     

Processing overlap-dependent distractor dilution rather than perceptual target load determines attentional selectivity

The perceptual load theory of attentional selection argues that the degree to which distractors interfere with target processing is determined by the “perceptual load” (or discrimination difficulty) of target processing: when perceptual load is low, distractors interfere to a greater extent than when it is high. A well-known exception is load-independent interference effects from face distractors during processing of name targets. This finding was reconciled with load theory by proposing distinct processing resources for faces versus names. In the present study, we revisit this effect to test (a) whether increasing the processing overlap (perceptual, lexical, conceptual) between potential targets and distractors would reinstate the classic load effect, and (b) whether this data pattern could be better explained by load theory or by a rival account that argues that distractor dilution rather than target load determines the degree of distractor interference. Over four experiments, we first replicate the original finding and then show that load effects grow with increasing processing overlap between potential targets and distractors. However, by adding dilution conditions, we also show that these processing overlap dependent modulations of distractor interference can be explained by the distractor dilution perspective but not by perceptual load theory. Thus, our findings support a processing overlap dilution account of attentional selection.     

Separate roles for executive and phonological components of working memory in mental arithmetic

A dual-task methodology was used to investigate the roles played by executive and phonological aspects of working memory in mental arithmetic. Experiment 1 showed that suppression of articulation impaired the ability to add a pair of briefly presented three-digit numbers. Suppression had no effect when the need to store temporarily was minimized by making the numbers visible throughout calculation. Experiment 2 showed that disrupting executive processes by requiring concurrent performance of a Trails task impaired the ability to add numbers that remained permanently visible. Performance on the Trails task deteriorated as the number of carry operations in the addition increased. Experiment 3 showed that this decline in Trails performance was not simply due to the extra time taken by carrying. These and other features of the results suggest that the carrying component of mental arithmetic places substantial demands on executive processes, whereas the need to retain problem information is met by the phonological loop. The results are consistent with an interpretation of executive processes according to which there is a limit on the capacity to inhibit strongly primed routine operations.     

The use of procedural knowledge in simple addition and subtraction problems

In a first experiment, adults were asked to solve one-digit additions, subtractions and multiplications. When the sign appeared 150 ms before the operands, addition and subtraction were solved faster than when the sign and the operands appeared simultaneously on screen. This priming effect was not observed for multiplication problems. A second experiment replicates these results on addition and multiplication and, moreover, shows that the priming effect in addition is observed for all problems, including very small ones such as 4+3. In fact, the only problems that were not primed by the addition sign were tie problems, which confirms that they have a special status in memory. Taken together, these results suggest that abstract procedures are pre-activated by the addition and subtraction signs and that these procedures are consequently used by adults to solve the problems. No such procedures would be pre-activated for multiplication, which are then most probably solved by retrieval of the result from memory. Moreover, while obviously two different strategies were used by individuals in order to solve addition and multiplication, solution times were similar when the problems were presented in their whole. These results, which question most of the conclusions of the current literature, support Anderson's model (1982) and Baroody's assumptions (1983) on the existence of compacted procedures that could be as fast as retrievals.     

A rehabilitative program for central executive deficits after traumatic brain injury

Deficits affecting Central Executive System (CES) of working memory (WM) are the main neuropsychological outcome after traumatic brain injury (TBI) and can also explain deficits in other domains, like divided attention, executive functions and long-term memory. For this reason we developed a rehabilitative program based on CES functions and we expected to find an improvement in WM as well as in those cognitive functions controlled by the CES.The experimental group was composed by 9 TBIs, selected for WM deficits, whereas the control group was composed by 6 TBIs, without WM deficits, but with speed processing deficits. All patients performed a cognitive training, based on PASAT (Gronwall & Wrightson, 1981)and two new versions of this task.The results showed in the experimental group an improvement in WM and in the cognitive functions controlled by the CES, whereas control patients did not show any improvement after the cognitive training.     

Use of indirect addition in adults' mental subtraction in the number domain up to 1,000

This study examined adults' use of indirect addition and direct subtraction strategies on multi-digit subtractions in the number domain up to 1,000. Seventy students who differed in their level of arithmetic ability solved multi-digit subtractions in one choice and two no-choice conditions. Against the background of recent findings in elementary subtraction, we manipulated the size of the subtrahend compared to the difference and only selected items with large distances between these two integers. Results revealed that adults frequently and efficiently apply indirect addition on multi-digit subtractions, yet adults with higher arithmetic ability performed more efficiently than those with lower arithmetic ability. In both groups, indirect addition was more efficient than direct subtraction both on subtractions with a subtrahend much larger than the difference (e.g., 713 - 695) and on subtractions with a subtrahend much smaller than the difference (e.g., 613 - 67). Unexpectedly, only adults with lower arithmetic ability fitted their strategy choices to their individual strategy performance skills. Results are interpreted in terms of mathematical and cognitive perspectives on strategy efficiency and adaptiveness.     

Age of onset of marijuana use and executive function

[Correction Notice: An Erratum for this article was reported in Vol 26(3) of Psychology of Addictive Behaviors (see record 2011-29227-001). Figure 1 should have been presented in color. All versions of this article have been corrected.] Marijuana (MJ) remains the most widely abused illicit substance in the United States, and in recent years, a decline in perceived risk of MJ use has been accompanied by a simultaneous increase in rates of use among adolescents. In this study, the authors hypothesized that chronic MJ smokers would perform cognitive tasks, specifically those that require executive function, more poorly than control subjects and that individuals who started smoking MJ regularly prior to age 16 (early onset) would have more difficulty than those who started after age 16 (late onset). Thirty-four chronic, heavy MJ smokers separated into early and late onset groups, and 28 non-MJ smoking controls completed a battery of neurocognitive measures. As hypothesized, MJ smokers performed more poorly than controls on several measures of executive function. Age of onset analyses revealed that these between-group differences were largely attributed to the early onset group, who were also shown to smoke twice as often and nearly 3 times as much MJ per week relative to the late onset smokers. Age of onset, frequency, and magnitude of MJ use were all shown to impact cognitive performance. Findings suggest that earlier MJ onset is related to poorer cognitive function and increased frequency and magnitude of MJ use relative to later MJ onset. Exposure to MJ during a period of neurodevelopmental vulnerability, such as adolescence, may result in altered brain development and enduring neuropsychological changes. (PsycINFO Database Record (c) 2012 APA, all rights reserved).