The roles of different executive functioning skills in young children’s mental computation and applied mathematical problem-solving

This study investigated the relationships of four executive functioning skills (including verbal working memory, spatial working memory, inhibitory control, and cognitive flexibility) with young children’s mental computation and applied mathematical problem-solving. Two hundred and twenty-five Chinese kindergarteners were tested with a battery of general cognitive, executive functioning and mathematics skills. Results showed that when children’s age, gender, non-verbal intelligence, and listening comprehension skills were controlled, verbal working memory and cognitive flexibility were significant correlates of mental computation, whereas verbal working memory, spatial working memory, and cognitive flexibility were significant correlates of applied mathematical problem-solving. Inhibitory control was not significantly associated with the two domains of mathematics under investigation. The findings highlight the differential roles of different executive functioning skills in early mathematical skills and offer practical implication for helping young children in learning complex mathematical skills.     

BOOK REVIEWS

Book reveiw in this article
Getting Free : A Handbook for Women in Abusive Relationships, G inny N icartt , Seattle: Seal Press, 1982, xxvi + 272 pp., $7.95 (paperback). Order from the Seal Press, 312 South Washington, Seattle, WA 98104.
Wife-Battering: A Systems Theory Approach , J ean G iles -S ims , New York: Guilford Press, 1983, xiv + 193 pp., $17.50 (hardback).
The Abusive Partner: An Analysis oj Domestic Battering , M akia R oy , (Ed.) New York: Van Nostrand Reinhold, 1982, xii + 319 pp., $18.95 (hardback).
In the shadow of the past: Psychology portrays the sexes , M ikiam L ewin (Ed.), New York: Columbia University Press, 1984, 344 pp., $30.00 (hardback).
Two paychecks: Life in dual-earner families, JOAN ALDOUS (Ed.), Beverly Hills, CA: Sage, 1982, 247 pp.
Work and family. Changing roles of men and women, P atricia V oydanoff (Ed.), Palo Alto, CA: Mayfield, 1984, 383 pp.
Women at work, M ary F rank F ox and S harlene H esse -BIBER, Palo Alto, CA: Mayfield, 1984, 276 pp.     

Functional similarity and interpersonal attraction

A pair of related experiments examined the relationship of functional similarity (i.e., the degree of similarity between two interactants in assessing mutually known others on personal construct dimensions) to interpersonal attraction. In Experiment I, 10 previously unacquainted college students of both sexes participated in 10 hours of dyadic disclosure exercises over a 5-week period. As predicted, members of high functional similarity dyads evidenced greater attraction to one another than did members of low functional similarity dyads. Experiment II investigated the relationship of functional similarity to level of acquaintance (i.e., friends, nominals) and type of assessment (i.e., physical, interactional, psychological) in a 2 × 3 factorial design. As hypothesized, “friendship” pairs of male undergraduates displayed greater functional similarity than did “nominal” pairs from the same population, particularly at the deeper level of “psychological” assessment. Results are discussed in relation to classical conditioning (D. Byrne, In L. Berkowitz (Ed.), Advances in experimental social psychology, Vol. 4. New York. Academic Press, 1969), affect-reinforcement (G. L. Clore, In S. W. Duck (Ed.), Theory and practice in interpersonal attraction. New York/London: Academic Press, 1977) and information processing ( I. Ajzen, In S. Duck (Ed.), Theory and practice in interpersonal attraction, New York/London: Academic Press, 1977) models of interpersonal attraction, and are interpreted as supporting and extending (S. Duck's Theory and practice in interpersonal attraction, New York/London: Academic Press, 1977) filtering theory of friendship formation.     

The Relations Between Patterning,Executive Function,and Mathematics

Patterning, or the ability to understand patterns, is a skill commonly taught to young children as part of school mathematics curricula. It seems likely that some aspects of executive function, such as cognitive flexibility, inhibition, and working memory, may be expressed in the patterning abilities of children. The primary objective of the present study was to examine the relationship between patterning and executive functioning for first grade children. In addition, the relations between patterning, executive functioning, mathematics, and reading were examined. The results showed that patterning was significantly related to cognitive flexibility and working memory, but not to inhibition. Patterning, cognitive flexibility, and working memory were significantly related to mathematical skills. Only patterning and working memory were significantly related to reading. Regression analyses and structural equation modeling both showed that patterning had effects on both reading and mathematics measures, and that the effects of cognitive flexibility were entirely mediated by patterning. Working memory had independent effects on reading and mathematics, and also effects moderated by patterning. In sum, these findings suggest that cognitive flexibility and working memory are related to patterning and express their effects on reading and mathematics in whole or in part through patterning.     

REVIEWS

Sex Roles and Aging: Theory and Research from a Systems Perspective , J. S inott , New York: Karger, 1986. xiv + 134pp., $24.50.
Career Guide for Women Scholars , S uzanna R ose (Ed.), New York: Springer, 1986. xx + 201pp., $16.95.
Female Psychology: A Partially Annotated Bibliography , C arole D illing and B arbara L. C laster (Eds.), New York: Coalition for Women's Mental Health, 1985, 328pp, (cost not given).     

The developmental change of young pupils’ metacognitive ability in mathematics in relation to their cognitive abilities

Metacognition is a multidimensional construct with two main dimensions: knowledge about cognition and regulation of cognition. The present study aimed to model the development of young pupils’ metacognitive abilities in mathematics in relation to processing efficiency, working memory and mathematical performance. We developed instruments measuring pupils’ metacognitive ability, mathematical ability, working memory capacity, and processing efficiency, and administered them to 126 pupils (8–11 years old) three times, with breaks of 3–4 months between them. Dynamic modeling indicated that growth in each of the abilities is affected by the state of the others, especially the state of processing efficiency. Growth modeling was used to specify the nature of change in the main aspects of mind and the possible interrelations in the patterns of change in these aspects. The initial mathematical self-image was found to depend on the corresponding processing efficiency and its advancement to rely on the development of mathematical performance and the previous working memory ability.     

工作记忆训练及对数学能力的迁移作用

工作记忆缺陷会影响个体数学能力发展。通过记忆策略、广度、刷新、转换等功能的工作记忆训练,可以改善个体认知功能。然而,工作记忆训练对个体的阅读、数学、流体智力等方面的远迁移效果并不一致。研究表明,工作记忆训练可以改善数感、视觉空间能力、推理能力等数学一般技能;也会通过改善语音工作记忆以及空间能力促进数学计算能力,或者通过改善中央执行系统,提升数学问题表征、模式识别、解题迁移、策略选择等复杂的过程,从而促进数学问题解决能力。因此,区分不同数学任务的认知过程,可以获得工作记忆训练对数学能力迁移效果的进一步证据。今后,神经影像学的证据或许也是未来工作记忆训练对数学能力提高的又一佐证。     

工作记忆训练及对数学能力的迁移作用

工作记忆缺陷会影响个体数学能力发展。通过记忆策略、广度、刷新、转换等功能的工作记忆训练,可以改善个体认知功能。然而,工作记忆训练对个体的阅读、数学、流体智力等方面的远迁移效果并不一致。研究表明,工作记忆训练可以改善数感、视觉空间能力、推理能力等数学一般技能;也会通过改善语音工作记忆以及空间能力促进数学计算能力,或者通过改善中央执行系统,提升数学问题表征、模式识别、解题迁移、策略选择等复杂的过程,从而促进数学问题解决能力。因此,区分不同数学任务的认知过程,可以获得工作记忆训练对数学能力迁移效果的进一步证据。今后,神经影像学的证据或许也是未来工作记忆训练对数学能力提高的又一佐证。     

On the law relating processing to storage in working memory

Working memory is usually defined in cognitive psychology as a system devoted to the simultaneous processing and maintenance of information. However, although many models of working memory have been put forward during the last decades, they often leave underspecified the dynamic interplay between processing and storage. Moreover, the account of their interaction proposed by the most popular A. D. Baddeley and G. Hitch's (1974) multiple-component model is contradicted by facts, leaving unresolved one of the main issues of cognitive functioning. In this article, the author derive from the time-based resource-sharing model of working memory a mathematical function relating the cognitive load involved by concurrent processing to the amount of information that can be simultaneously maintained active in working memory. A meta-analysis from several experiments testing the effects of processing on storage corroborates the parameters of the predicted function, suggesting that it properly reflects the law relating the 2 functions of working memory.     

Book reviews

Art Therapy in Practice Marian Liebmann(Ed.), 1990 London, Jessica Kingsley Publishers 190 pp., £24.50

Effective Thinking Skills-Preventing and Managing Personal Problems Ricahrd Nelson-Jones, 1989 London, Cassell xii + 214 pp., £8.95 (paperback), £25 (hardback)

AIDS and the Health Care System Lawrence O. Gostin (Ed.), 1990 New Haven & London, Yale University Press 299 pp., £9.95 (paperback), £30.00 (cloth)

Disaster and Disaster Stress A. J. W. Taylor, 1989 New York, AMS Press US$32.50 (hardback)     

Alterations in Rorschach's Experience Balance under Conditions of Food and Sleep Deprivation: A Construct Validation Study

Clinard, Marshall B. (Ed.), Anomie and Deviant Behavior: A Discussion and Critique. New York, Toronto, London: Collier-Macmillan, Ltd., 1964, Free Press of Glencoe, xii, pp. 324. Reviewed by Leon J. Whitsell     

REVIEWS

Feminism and Addiction, Claudia Bepko (Ed.). New York.
Feminist Perspectives on Addictions, Nan Van Den Bergh (Ed.). New York.
Engendered Lives, Ellyn Kaschak. New York.
Seldom Seen, Rarely Heard: Women's Place in Psychology, Jams Bohan (Ed.).
Still Loved by the Sun: A Rape Survivor's Journal, Migael Scherer. New York.     

Central executive system impairment in traumatic brain injury

The aim of the present study was to identify cognitive functions affected by traumatic brain injury (TBI) and to verify the mechanism underlying cognitive impairment. More precisely, cognitive deficits following TBI can be considered as a consequence of (a) a speed processing deficit, that is a general slowing of perceptual, motor and cognitive subroutines; (b) an impairment of the Central Executive System of working memory (CES).Thirty-seven patients were submitted to a neuropsychological battery, aimed to evaluate different cognitive functions.Results showed severe deficits in speed processing, divided attention,working memory, executive functions and long term memory.Regression analyses, performed to test the two hypotheses, showed that the working memory deficit hypothesis is able to explain divided attention, executive functions and long term memory deficits more than speed processing hypothesis.     

Examining the role of working memory resources in following spoken instructions

This study investigated the involvement of working memory (WM) in following spoken instructions using concurrent tasks designed to disrupt components of the Baddeley and Hitch WM model [Baddeley, A. D., & Hitch, G. J. (1974). Working memory. In G. H. Bower (Ed.), The psychology of learning and motivation: Advances in research and theory (Vol. 8, pp. 47–89). New York, NY: Academic Press]. In each of three experiments, participants were presented with sequences of instructions to be either verbally repeated or physically performed using relevant objects. Backward counting, articulatory suppression, and eye closure during instruction encoding all disrupted recall, and also impaired recall of the linkage between movements and objects. Recall of actions was more accurate when they were physically enacted than repeated verbally, an advantage that was not affected by concurrent tasks. These findings indicate that aspects of the recall of spoken instructions including the binding of constituent movements to objects draw on multiple WM resources. The benefits of physical enactment of the instructed sequence do not appear to depend on the components of WM investigated in these studies.     

数学焦虑对工作记忆子系统及数学心算的影响分析

本研究从工作记忆容量的角度入手,探讨数学焦虑对工作记忆子系统及数学心算成绩的影响,并寻求三者之间关系的理论解释。本研究为3×2×2混合实验设计,即三组被试（高、中、低数学焦虑组）、工作记忆两个子系统（言语工作记忆和视空间工作记忆）和两种数学心算任务难度,并记录数学心算的反应时和正确率作为其成绩指标。结果表明在要求较高工作记忆容量的数学心算任务中,数学焦虑通过言语工作记忆和视空间工作记忆都会对数学心算成绩产生影响,其中视空间工作记忆是数学焦虑与复杂数学心算反应时之间的中介变量。     

Working Memory Deficits in Boys with Attention-deficit/Hyperactivity Disorder (ADHD): The Contribution of Central Executive and Subsystem Processes

The current study investigated contradictory findings from recent experimental and meta-analytic studies concerning working memory deficits in ADHD. Working memory refers to the cognitive ability to temporarily store and mentally manipulate limited amounts of information for use in guiding behavior. Phonological (verbal) and visuospatial (nonverbal) working memory were assessed across four memory load conditions in 23 boys (12 ADHD, 11 typically developing) using tasks based on Baddeley's (Working memory, thought, and action, Oxford University Press, New York, 2007) working memory model. The model posits separate phonological and visuospatial storage and rehearsal components that are controlled by a single attentional controller (CE: central executive). A latent variable approach was used to partial task performance related to three variables of interest: phonological buffer/rehearsal loop, visuospatial buffer/rehearsal loop, and the CE attentional controller. ADHD-related working memory deficits were apparent across all three cognitive systems--with the largest magnitude of deficits apparent in the CE--even after controlling for reading speed, nonverbal visual encoding, age, IQ, and SES.     

Manipulation of responsibility in non-clinical subjects: does expectation of failure exacerbate obsessive-compulsive behaviors?

An exaggerated sense of responsibility is currently considered as the ground for the obsessive-compulsive disorder. Obsessive-like behaviors, such as hesitations and checks, may be induced in non-clinical subjects by increasing perceived responsibility (i.e., perceived personal influence on negative outcomes). In line with Salkovskis' proposal [The cognitive approach to anxiety: threat beliefs, safety-seeking behavior, and the special case of health anxiety and obsessions, in: P.M. Salkovskis (Ed.), Frontiers of Cognitive Therapy, Guilford, New York], we tested the hypothesis that reduced coping abilities (i.e., an exaggerated expectation of failure) are another effectual factor contributing to obsessive-like behaviors. We examined 47 normal volunteers in a visuo-spatial memory task, and manipulated their perceived personal influence and expectation of failure by giving differential instructions and feedback about their performance. Increase of perceived personal influence induced slowness, hesitations and checks without enhancing performance. Expectation of failure exacerbated obsessive-like behaviors, again without affecting performance. These results confirm the role of responsibility in obsessive-like behavior and indicate that reduced coping abilities may contribute to worsen dysfunctional strategies.     

The role of planning in different mathematical skills

Despite the fact that planning has been found to be a significant predictor of reading (particularly of reading comprehension), much less is known about its contribution to mathematics. The purpose of this study was to examine the role of two levels of planning (operation planning and action planning) in three mathematical skills (calculation fluency, math problem-solving, and math reasoning). Eighty Grade 2 children from Shanghai, China were assessed on measures of nonverbal cognitive ability (nonverbal matrices), working memory (digit span backwards and N-back), operation planning (matching numbers, planned codes, and planned search), action planning (crack the code), and mathematics (calculation fluency, math problem-solving, and math reasoning). The results of regression analyses showed that both levels of planning accounted for unique variance in mathematics over and above the effects of nonverbal cognitive ability and working memory. The effects of action planning were particularly strong in math problem-solving. These findings suggest that measures of planning could be used along with measures of working memory to detect children at-risk for mathematics disabilities and that intervention programmes targeting planning could be developed to boost children's mathematics performance.     

Differences in mathematical reasoning between typically achieving and gifted children

Mathematical giftedness refers to mastery in a specific mathematical domain at an earlier than expected age. The present study examined which cognitive processes accounted for differences in mathematical reasoning between gifted children (MRG) and their typically achieving peers (TA). Naming speed, phonological awareness, short-term memory, executive functioning, and working memory were examined in 51 children aged approximately 7 years. A series of stepwise regression models, using a contrast variable to capture differences in mathematical reasoning between MRG and TA children, were created to examine which cognitive domains accounted for differences in mathematical reasoning. Short-term memory (r²?=?.08) and visual-spatial working memory (r²?=?.39) emerged as the only cognitive predictors within a model that included gender, age, and fluid intelligence. This model captured all of the variance distinguishing mathematics reasoning between MRG and TA children, explaining an overall contribution of 70% of the variance in mathematical reasoning.