Frequency of finger looking during finger counting is related to children's working memory capacities

Finger counting can be useful in solving arithmetic problems, noticeably because it reduces the working memory demand of mental calculations. However, proprioceptive information might not be sufficient to keep track of the number of fingers raised during problem solving, and visual input may play an important role in this process. The present study was designed to address this question and shows that 8-year-old children look at their fingers in 60% of the trials during finger counting when solving additive problems. Moreover, our results reveal that the frequency of finger looking is negatively correlated with working memory capacities and is higher for more difficult problems. These findings suggest that finger looking is recruited in managing the cognitive demand of the arithmetic task, probably by providing additional external cues to monitor the number of steps that have to be incremented during finger counting.     

工作记忆子成分在听觉障碍儿童心算过程中的作用

采用2×2×3的混合实验设计,比较听力正常儿童和听觉障碍儿童在心算作业上的差异,考察了工作记忆子成分在听觉障碍儿童心算过程中的作用。结果表明,与听力正常儿童相比,听觉障碍儿童在高存储负载水平下的心算成绩显著降低,说明语音回路负责心算过程中的存储成分;而且听觉障碍儿童在对中央执行能力有高需求的实验条件下的作业水平并不比正常听力儿童差,说明他们的中央执行能力并没有受到损失。     

心算困难儿童的语音复述

心算中语音复述和计算加工交替进行,其中任何一方面落后都会导致心算困难。使用视觉心算成绩和听觉心算成绩相减的范式,研究计算能力正常但心算水平落后的儿童的语音复述水平。结果发现,不同年级心算困难儿童呈现不同的困难模式,2、4年级心算困难儿童语音复述水平正常,但由于语音工作记忆容量的落后,导致缺少足够的注意资源进行计算加工。3年级心算困难儿童在语音工作记忆容量和语音复述上都存在落后,导致心算困难,呈现出双重困难模式。     

心算活动机制的研究

心算是一种重要的思维活动,是认知心理学的研究主题之一,心算活动具有明显的问题大小效应,其加工过程与工作记忆和长时记忆存在密切关第。此外,对心算的加工机制进行跨学科的综合研究,是今后心算研究的主要方向。     

工作记忆广度对儿童算术认知策略的影响

选取113名小学二年级儿童为被试,探讨了工作记忆广度对儿童算术认知策略的影响。结果表明:不同工作记忆广度儿童在出声、手动、心里数数、竖式、分解、凑整、猜测和放弃策略的选择频次上具有显著差异,在算术认知策略的执行上,差异明显;随着工作记忆广度的增加,出声策略表现出了波动型的变化曲线,手动、心里数数、凑整和猜测策略具有门槛型的变化趋势,竖式、分解和放弃策略呈现出阶梯状的变化特点。这些结果说明,儿童算术认知策略表现受到其工作记忆容量明显的限制性作用。     

西方数学学习困难研究的综述

近十年来,西方心理学界对数学学习困难(MD)的研究不断地增加。本文阐述了MD研究的几个主要的方面：MD界定与鉴别的复杂性、工作记忆各个成分对MD的影响、MD数概念与计数知识的发展、MD算术策略的特征及发展。并在此基础上提出几点对MD研究的思考。     

心算活动机制的研究

心算是一种重要的思维活动,是认知心理学的研究主题之一。心算活动具有明显的问题大小效应,其加工过程与工作记忆和长时记忆存在密切关系。此外,对心算的加工机制进行跨学科（认知心理学、神经科学等）的综合研究,是今后心算研究的主要方向。     

Visuospatial and verbal memory in mental arithmetic

Working memory allows complex information to be remembered and manipulated over short periods of time. Correlations between working memory and mathematics achievement have been shown across the lifespan. However, only a few studies have examined the potentially distinct contributions of domain-specific visuospatial and verbal working memory resources in mental arithmetic computation. Here we aimed to fill this gap in a series of six experiments pairing addition and subtraction tasks with verbal and visuospatial working memory and interference tasks. In general, we found higher levels of interference between mental arithmetic and visuospatial working memory tasks than between mental arithmetic and verbal working memory tasks. Additionally, we found that interference that matched the working memory domain of the task (e.g., verbal task with verbal interference) lowered working memory performance more than mismatched interference (verbal task with visuospatial interference). Findings suggest that mental arithmetic relies on domain-specific working memory resources.     

工作记忆中央执行对儿童算术认知策略的影响

运用“双重任务”范式,以113名小学二年级儿童为被试,考察了儿童工作记忆的中央执行对算术认知策略表现的影响。结果表明:中央执行对儿童算术认知策略的选择产生了针对性的影响,集中表现在外部策略、支持性策略和猜测放弃策略上。中央执行干扰使策略执行的正确率下降、反应时增加。在简单加法任务上,中央执行影响了外部策略和支持性策略的选择频次;在复杂任务中,这种影响体现在外部策略和放弃策略上。无论是简单任务还是复杂任务,中央执行的干扰都造成了策略整体执行效果的下降。     

工作记忆成分与儿童算术认知

根据Baddeley和Hitch(1974)提出的工作记忆多成分模型,研究者对工作记忆的各个成分与儿童算术认知之间的关系进行了广泛的探索。同语音环和视空间模板相比,中央执行在儿童算术认知加工中的作用显得更为关键。目前,探讨各种中央执行功能与儿童算术认知的关系,以及由此来解释算术学习困难儿童的认知成因是这个领域研究者最为关注的焦点。     

Math Anxiety: Personal, Educational, and Cognitive Consequences

Highly math-anxious individuals are characterized by a strong tendency to avoid math, which ultimately undercuts their math competence and forecloses important career paths. But timed, on-line tests reveal math-anxiety effects on whole-number arithmetic problems (e.g., 46 + 27), whereas achievement tests show no competence differences. Math anxiety disrupts cognitive processing by compromising ongoing activity in working memory. Although the causes of math anxiety are undetermined, some teaching styles are implicated as risk factors. We need research on the origins of math anxiety and on its "signature" in brain activity, to examine both its emotional and its cognitive components.     

Strategies in subtraction problem solving in children

The aim of this study was to investigate the strategies used by third graders in solving the 81 elementary subtractions that are the inverses of the one-digit additions with addends from 1 to 9 recently studied by Barrouillet and Lépine. Although the pattern of relationship between individual differences in working memory, on the one hand, and strategy choices and response times, on the other, was the same in both operations, subtraction and addition differed in two important ways. First, the strategy of direct retrieval was less frequent in subtraction than in addition and was even less frequent in subtraction solving than the recourse to the corresponding additive fact. Second, contrary to addition, the retrieval of subtractive answers is confined to some peculiar problems involving 1 as the subtrahend or the remainder. The implications of these findings for developmental theories of mental arithmetic are discussed.     

The relationship between mental rotation and arithmetic: do number line estimation,working memory,or place-value concept matter?

Mental rotation is positively related to arithmetic ability; however, the mechanism underlying this relationship remains unclear. The possible roles of working memory, place-value concept, and number line estimation in the correlation between mental rotation and whole-number computation were investigated. One hundred and fifty-five first-grade students were tested to determine their mental rotation ability, arithmetic ability, and non-verbal intelligence. One year later, their working memory, place-value concept, number line estimation, and overall arithmetic ability were assessed. After controlling for age, gender, and prior arithmetic ability, we found that mental rotation uniquely predicted arithmetic ability after one year. Further mediation analyses demonstrated that number line estimation significantly mediated the relationship between mental rotation and arithmetic ability. In contrast, neither working memory nor place-value concept significantly mediated the relationship between mental rotation and arithmetic ability. This study highlights that mental number line estimation is the most important element explaining the influence of a dynamic spatial skill, that is, mental rotation, on arithmetic ability among young Chinese children.     

Instruction and load effects on high-skill and low-skill individuals: A study in the domain of mental arithmetic

What happens when people are asked to respond as quickly or as accurately as possible? This study tested the effects of speed/accuracy instructions and working-memory load on people's strategy efficiency and strategy selection. Adult participants solved simple addition problems (Experiment 1) and simple multiplication problems (Experiment 2) under load and no-load conditions and provided trial-by-trial strategy reports. High-skill participants were more efficient than low-skill participants, but the underlying causes of these skill-related effects differed across experiments. In the addition experiment, high-skill participants responded adaptively to the changing situations by changing their strategy choices, which resulted in smaller effects on their actual performance. Low-skill participants in contrast, did not change their strategy choices as adaptively, which resulted in less efficient performance—and especially so under load conditions. In the multiplication experiment, high-skill and low-skill participants differed in strategy efficiencies rather than in strategy choices. In the discussion, the results are further interpreted and future adaptations for the adaptive strategy choice model (ASCM; Siegler & Jenkins, 1989) are suggested.     

Identifying the nature of impairments in executive functioning and working memory of children with severe difficulties in arithmetic

An age-matched achievement-matched design was used to examine whether the executive functioning and working memory impairments exhibited by children with severe difficulties in arithmetic (SDA) are better viewed as developmental lags or as cognitive deficits. Three groups of children were included: 20 SDA children, 20 typically achieving children (CM) matched in chronological age with the SDA children, and 20 younger typically achieving children (AM) matched in achievement with the SDA group. While children with SDA did not exhibit impairments in color-word inhibition and verbal working memory, they did demonstrate impairments in shifting, quantity-digits inhibition, and visuospatial working memory. As children with SDA did not perform more poorly than their AM counterparts on any of these tasks, impairments in specific areas of executive functioning and working memory appear to reflect developmental lags rather than cognitive deficits.     

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.     

Working memory and children's use of retrieval to solve addition problems

This study tested the hypothesis that children with high working memory capacities solve single-digit additions by direct retrieval of the answers from long-term memory more often than do children with low working memory capacities. Counting and reading letter span tasks were administered to groups of third-grade (mean age=107 months) and fourth-grade (mean age=118 months) children who were also asked to solve 40 single-digit additions. High working memory capacity was associated with more frequent use of retrieval and faster responses in solving additions. The effect of span on the use of retrieval increased with the size of the minimum addend. The relation between working memory measures and use and speed of retrieval did not depend on the numerical or verbal nature of the working memory task. Implications for developmental theories of cognitive arithmetic and theories of working memory are discussed.     

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.     

心算形式对不同近似数量系统敏锐度儿童心算表现的影响

选取112名二年级小学生,以点阵比较任务测量近似数量系统敏锐度,同时以工作记忆测验成绩为协变量,探究了不同心算形式（视算、读算）对不同近似数量系统敏锐度儿童心算表现的潜在影响。结果显示：（1）心算形式显著影响心算的正确率,读算形式下儿童的心算表现最好;（2）控制工作记忆影响后,心算形式与近似数量系统敏锐分组均对心算正确率影响显著。总体来讲,读算可能是提高小学儿童简单心算表现的有效形式,并能提高低近似数量系统敏锐度儿童的心算表现。