Working memory as a predictor of written arithmetical skills in children: The importance of central executive functions

Background . The study was conducted in an attempt to further our understanding of how working memory contributes to written arithmetical skills in children. Aim . The aim was to pinpoint the contribution of different central executive functions and to examine the contribution of the two subcomponents of children's written arithmetical skills. Sample and method . A total of 141 third‐ and fourth‐graders were administered arithmetical tasks and measures of working memory, fluid IQ and reading. Regression analysis was used to examine the relationship between working memory and written arithmetical skills. Results . Three central executive measures (counting span, trail making and verbal fluency) and one phonological loop measure (Digit Span) were significant and predictors of arithmetical performance when the influence of reading, age and IQ was controlled for in the analysis. Conclusions . The present findings demonstrate that working memory, in general, and the central executive, in particular, contribute to children's arithmetical skills. It was hypothesized that monitoring and coordinating multiple processes, and accessing arithmetical knowledge from long‐term memory, are important central executive functions during arithmetical performance. The contribution of the phonological loop and the central executive (concurrent processing and storage of numerical information) indicates that children aged 9–10 years primarily utilize verbal coding strategies during written arithmetical performance.     

Cognitive correlates of mathematical achievement in children with cerebral palsy and typically developing children

Background . Remarkably few studies have investigated the nature and origin of learning difficulties in children with cerebral palsy (CP). Aims . To investigate math achievement in terms of word‐problem solving ability in children with CP and controls. Because of the potential importance of reading for word‐problem solving, we investigated reading as well. Sample . Children with CP attending either special (n= 41) or mainstream schools (n= 16) and a control group of typically developing children in mainstream schools (n= 16). Method . Group differences in third grade math and reading, controlled for IQ, were tested with analyses of co‐variance (ANCOVAs). Hierarchical regression was used to investigate cognitive correlates of third grade math and reading. Predictors included verbal and non‐verbal IQ measured in first grade, components of working memory (WM) and executive function (EF) measured in second grade, and arithmetic fact fluency and reading measured in third grade. Results . Children with CP in special schools performed significantly worse than their peers on word‐problem solving and reading. There was a trend towards worse performance in children with CP in mainstream schools compared to typically developing children. Conclusions . Impairments of non‐verbal IQ and WM updating predicted future difficulties in both word‐problem solving and reading. Impairments of visuospatial sketchpad and inhibition predicted future word‐problem, but not reading difficulty. Conversely, deficits of phonological loop predicted reading but not word‐problem difficulty. Concurrent arithmetic fact fluency and reading ability were both important for word‐problem solving ability. These results could potentially help to predict which children are likely to develop specific learning difficulties, facilitating early intervention.     

The contribution of working memory to children's mathematical word problem solving

The study explored the contribution of working memory to mathematical word problem solving in children. A total of 69 children in grades 2, 3 and 4 were given measures of mathematical problem solving, reading, arithmetical calculation, fluid IQ and working memory. Multiple regression analyses showed that three measures associated with the central executive and one measure associated with the phonological loop contributed unique variance to mathematical problem solving when the influence of reading, age and IQ were controlled for in the analysis. In addition, the animal dual‐task, verbal fluency and digit span task continued to contribute unique variance when the effects of arithmetical calculation in addition to reading, fluid IQ, and age were controlled for. These findings demonstrate that the phonological loop and a number of central executive functions (shifting, co‐ordination of concurrent processing and storage of information, accessing information from long‐term memory) contribute to mathematical problem solving in children. Copyright © 2006 John Wiley & Sons, Ltd.     

A comparison of working memory skills and learning in children with developmental coordination disorder and moderate learning difficulties

The present study compared 6–11 years old with developmental coordination disorder (DCD) and those with moderate learning difficulties (MLD) on measures of memory (verbal short‐term and working memory, visuo‐spatial short‐term and working memory), literacy and numeracy, and IQ. The findings indicate that children with DCD appear to be impaired in all four areas of memory function; in particular they performed at significantly lower levels than children with MLD in measures of verbal short‐term memory, visuo‐spatial short‐term and working memory. In contrast, performance of children with MLD in the memory measures was within age‐expected levels, with deficits observed only in verbal working memory tasks. There were also differential links between memory and attainment between the two groups, and these were significant even after statistically accounting for the contribution of IQ. Reasons for why working memory contributes to learning in these two developmental groups are discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

Investigating the predictive roles of working memory and IQ in academic attainment

There is growing evidence for the relationship between working memory and academic attainment. The aim of the current study was to investigate whether working memory is simply a proxy for IQ or whether there is a unique contribution to learning outcomes. The findings indicate that children’s working memory skills at 5 years of age were the best predictor of literacy and numeracy 6 years later. IQ, in contrast, accounted for a smaller portion of unique variance to these learning outcomes. The results demonstrate that working memory is not a proxy for IQ but rather represents a dissociable cognitive skill with unique links to academic attainment. Critically, we find that working memory at the start of formal education is a more powerful predictor of subsequent academic success than IQ. This result has important implications for education, particularly with respect to intervention.     

The Role of Executive Function in Arithmetic Problem-Solving Processes: A Study of Third Graders

This study investigated the roles of different executive function (EF) components (inhibition, shifting, and working memory) in 2-step arithmetic word problem solving. A sample of 139 children aged 8 years old and regularly attending the 3rd grade of primary school were tested on 6 EF tasks measuring different EF components, a reading task and a reading comprehension task, an arithmetic facts task evaluating basic knowledge of calculation, and three 2-step arithmetic word problems. Multiple hierarchical regression analyses were conducted to investigate the roles of the different EF components in the various phases of the problem-solving process. The results showed that EF affects the various phases of problem solving differently over and above calculation knowledge and reading abilities. The implications of these findings are discussed in relation to further understanding the role of cognitive skills in mathematical problem solving and in relation to instructional approaches that may increase children’s performance on 2-step arithmetic word problems.     

Representation and working memory in early arithmetic

Working memory has been implicated in the early acquisition of arithmetic skill, but the relations among different components of working memory, performance on different types of arithmetic problems, and development have not been explored. Preschool and Grade 1 children completed measures of phonological, visual-spatial, and central executive working memory, as well as nonverbal and verbal arithmetic problems, some of which included irrelevant information. For preschool children, accuracy was higher on nonverbal problems than on verbal problems, and the best and only unique predictor of performance on the standard nonverbal problems was visual-spatial working memory. This finding is consistent with the view that most preschoolers use a mental model for arithmetic that requires visual-spatial working memory. For Grade 1 children, performance was equivalent on nonverbal and verbal problems, and phonological working memory was the best predictor of performance on standard verbal problems. For both age groups, problems with added irrelevant information were substantially more difficult than standard problems, and in some cases measures of the central executive predicted performance. Assessing performance on different components of working memory in conjunction with different types of arithmetic problems provided new insights into the developing relations between working memory and how children do arithmetic.     

Executive Function and Processing Resources as Predictors of Adult Age Differences in the Implementation of Encoding Strategies

This research examined adult age differences in recall of word lists under different encoding conditions: association (story generation), rehearsal, and a control condition. Executive function and cognitive processing resources (speed and working memory) were investigated as mediators of these age differences. Younger (aged 17-48 years) and older (aged 65-88 years) adults completed a battery of tests of executive function, speed of information processing, working memory, and recall. Age differences in recall were evident for those who used the complex association encoding strategy only. For those using the association strategy, an examination of encoding strategy protocols revealed age differences in the integration of words, which were also related to subsequent recall performance. The association between integration and recall was accounted for by executive function and working memory, but not by speed of processing. Speed accounted for age differences in recall but its contribution to recall was largely independent from that of the impact of integration during encoding.     

Working memory impairments in children with specific arithmetic learning difficulties.

Working memory impairments in children with difficulties in arithmetic have previously been investigated using questionable selection techniques and control groups, leading to problems concluding where deficits may occur. The present study attempted to overcome these criticisms by assessing 9-year-old children with difficulties specific to arithmetic, as indicated by normal reading, and comparing them with both age-matched and ability-matched controls. A battery of 10 tasks was used to assess different aspects of working memory, including subtypes of executive function. Relative to age-matched controls, children with poor arithmetic had normal phonological working memory but were impaired on spatial working memory and some aspects of executive processing. Compared to ability-matched controls, they were impaired only on one task designed to assess executive processes for holding and manipulating information in long-term memory. These deficits in executive and spatial aspects of working memory seem likely to be important factors in poor arithmetical attainment.     

工作记忆成分的年龄相关差异对算术策略运用的预测效应

采用选择/无选范式,借助工作记忆成套测验,在两位数乘法估算问题中探讨了工作记忆系统各成分对不同年龄段个体算术策略运用的预测效应。结果显示:(1)工作记忆的不同成分与年龄之间存在明显的相关。表现为,除视空模板成分外,其他各成分得分随着年龄增长而呈现上升趋势;(2)估算策略运用中,年龄与策略选择显著相关,表现为随着年龄增长,策略选择表现明显提高;(3)估算策略运用中,不同年龄个体的工作记忆不同成分和策略选择表现出不同的联系,中央执行均显示出显著的预测效应,语音环路和视空模板的预测效应均不显著。不同年龄个体的工作记忆不同成分对策略执行的预测效应均不显著。上述发现对于深刻理解工作记忆系统在算术认知策略运用中的作用机制具有重要理论含义。     

How older adults use cognition in sentence-final word recognition

This study examined the effects of executive control and working memory on older adults’ sentence-final word recognition. The question we addressed was the importance of executive functions to this process and how it is modulated by the predictability of the speech material. To this end, we tested 173 neurologically intact adult native English speakers aged 55–84 years. Participants were given a sentence-final word recognition test in which sentential context was manipulated and sentences were presented in different levels of babble, and multiple tests of executive functioning assessing inhibition, shifting, and efficient access to long-term memory, as well as working memory. Using a generalized linear mixed model, we found that better inhibition was associated with higher accuracy in word recognition, while increased age and greater hearing loss were associated with poorer performance. Findings are discussed in the framework of semantic control and are interpreted as supporting a theoretical view of executive control which emphasizes functional diversity among executive components.     

Working memory, reading, and mathematical skills in children with developmental coordination disorder

The aim of the present study was investigate the relationship between working memory and reading and mathematical skills in 55 children diagnosed with developmental coordination disorder (DCD). The findings indicate a pervasive memory deficit in all memory measures. In particular, deficits observed in visuospatial short-term and working memory tasks were significantly worse than in the verbal short-term memory ones. On the basis of these deficits, the sample was divided into high and low visuospatial memory ability groups. The low visuospatial memory group performed significantly worse on the attainment measures compared to the high visuospatial memory group, even when the contribution of IQ was taken into account. When the sample was divided into high and low verbal working memory ability groups, verbal working memory skills made a unique contribution to attainment only when verbal IQ was taken into account, but not when performance IQ was statistically controlled. It is possible that the processing demands of the working memory tasks together with the active motor component reflected in the visuospatial memory tasks and performance IQ subtest both play a crucial role in learning in children with DCD.     

Susceptibility of spatial and verbal working memory to demands of the central executive

We used a dual-task paradigm to examine the degree to which domain-specific spatial and verbal subsystems depend on the domain-general central executive. Forty participants were asked to retain spatial or verbal information while performing a concurrent secondary task related to simple arithmetic. The secondary tasks consisted of three cognitive processes: single-digit addition, a digit-carrying operation, and digit reading. The single-digit addition and carry operation include central executive functioning, while digit reading relies solely on the phonological loop. The single-digit addition caused a performance decrement on the spatial working memory task, while the digit reading impaired performance on the verbal working memory task. The carry operation interfered with recall accuracy on both working memory tasks. The spatial working memory task was significantly correlated with the verbal working memory task only when the secondary task was more demanding on the central executive. Our results suggest that spatial working memory rather than verbal working memory is susceptible to failure of central executive functioning and that the central executive plays an important role in regulating the cognitive demands of different domains.     

Working memory and phonological processing as predictors of children’s mathematical problem solving at different ages

The study explored the contribution of working memory (WM) to mathematical problem solving in younger (8-year-old) and older (11-year-old) children. The results showed that (1) significant age-related differences in WM performance were maintained when measures of phonological processing (i.e., digit naming speed, short-term memory, phonological deletion) were partialed from the analysis; (2) WM predicted solution accuracy of word problems independently of measures of problem representation, knowledge of operations and algorithms, phonological processing, fluid intelligence, reading, and math skill; and (3) a second-order WM factor was correlated with problem solving, suggesting that a general or executive system underlies age-related performance. The results were interpreted as support for the notion that the executive system was an important predictor of age-related changes in problem solving beyond the contribution of math and reading skills, and this system operates independently of the phonological system and domain-specific knowledge in predicting solution accuracy.     

Do young and older adults rely on different processes in source memory tasks? A neuropsychological study

Source memory has consistently been associated with prefrontal function in both normal and clinical populations. Nevertheless, the exact contribution of this brain region to source memory remains uncertain, and evidence suggests that processes used by young and older adults may differ. The authors explored the extent to which scores on composite measures of neuropsychological tests of frontal and medial temporal function differentially predicted the performance of young and older adults on source memory tasks. Results indicated that a frontal composite measure, consistently associated with source memory performance in older adults, was unrelated to source memory in young adults, although it was sensitive to a demanding working memory task. The memory composite score, however, predicted performance in the young group. In addition, item and source memory were correlated in young but not older people. Findings are discussed in terms of age-related differences in working memory and executive functions, and differential binding processes necessary for item and source memory. The requirement to integrate item and source information at encoding appears to place greater demands on executive or working memory processes in older adults than in younger adults.     

基于易感人格的药物成瘾者工作记忆对执行控制功能的调节作用

为了解工作记忆在易感性人格对药物成瘾者执行控制功能和抑制性影响过程中的调节作用,采用BIS和SSS量袁以及连续操作测验（CPT）、2-back任务、威斯康星卡片分类任务（WCST）对150名药物成瘾者和100名年龄、性别及智商相匹配的非药物成瘾者实施冲动性人格、认知控制功能测试。结果发现在2-back任务正确率（工作记忆）高低不同的情况下,注意冲动性人格特质得分对执行控制功能会产生不同的影响。这说明工作记忆在冲动性人格对抑制性的影响中具有调节作用。     

The influence of working memory on reading growth in subgroups of children with reading disabilities

This 3-year longitudinal study determined whether (a) subgroups of children with reading disabilities (RD) (children with RD only, children with both reading and arithmetic deficits, and low verbal IQ readers) and skilled readers varied in working memory (WM) and short-term memory (STM) growth and (b) whether growth in an executive system and/or a phonological storage system mediated growth in reading performance. A battery of memory and reading measures was administered to 84 children (11-17 years of age) across three testing waves spaced 1 year apart. The results showed that skilled readers yielded higher WM growth estimates than did the RD groups. No significant differentiation among subgroups of children with RD on growth measures emerged. Hierarchical linear modeling showed that WM (controlled attention), rather than STM (phonological loop), was related to growth in reading comprehension and reading fluency. The results support the notion that deficient growth in the executive component of WM underlies RD.     

Working memory and error detection in texts: what are the roles of the central executive and the phonological loop?

Subjects performed a text error detection task, either alone or in conjunction with a secondary task aimed at specifically hindering the functioning of either the central executive in working memory or of the phonological loop. We focused on the decline in detection performance as a function of the type of error to be detected (typographical, orthographic, or semantic/syntactic) and the processing span required for detection (one word, several words within the same clause, or several clauses). The results showed that the central executive in working memory is involved in detecting semantic/syntactic errors and in detecting orthographic ones, but not in detecting typographical errors. Moreover, the degree of involvement increases with the processing span. The phonological loop is involved in detection whenever processing above the word level is required. As observed in many studies, these results suggest that the difficulty subjects have detecting semantic errors as compared to other types of errors is due to the heavier working memory load: maintenance of the phonological representation and greater involvement of the central executive. © 1998 John Wiley & Sons, Ltd.     

High-performers use the phonological loop less to process mental arithmetic during working memory tasks

This study investigated the effects of three working memory components—the central executive, phonological loop, and visuospatial sketchpad—on performance differences in complex mental arithmetic between individuals. Using the dual-task method, we examined how performance during two-digit addition was affected by load on the central executive (random tapping condition), phonological loop (articulatory suppression condition), and visuospatial sketchpad (spatial tapping condition) compared to that under no load (control condition) in high- and low-performers of complex mental arithmetic in Experiment 1. Low-performers showed an increase in errors under the random tapping and articulatory suppression conditions, whereas high-performers showed an increase of errors only under the random tapping condition. In Experiment 2, we conducted similar experiments on only the high-performers but used a shorter presentation time of each number. We found the same pattern for performing complex mental arithmetic as seen in Experiment 1. These results indicate that high-performers might reduce their dependence on the phonological loop, because the central executive enables them to choose a strategy in which they use less working memory capacity.     

Towers of Hanoi and London: contribution of working memory and inhibition to performance

The Tower of Hanoi and Tower of London have become well-established executive function tasks that presumably tap cognitive skills mediated by the frontal cortex. It has been assumed that the two tower tasks are more or less interchangeable and that both measure working memory and inhibition processes. These assumptions were tested in a study involving 37 normal college volunteers (M age = 20 years). Participants were administered the Tower of Hanoi (TOH), Tower of London-Revised (TOL-R), two working memory tests, and two tests of inhibition. The two tower tasks correlated significantly (r = .39), but only moderately. The working memory and inhibition variables explained over one-half of the variance in TOL-R performance; however, there was a relatively weaker contribution of inhibition to TOH performance.