The role of working memory in the carry operation of mental arithmetic: Number and value of the carry

Two experiments were conducted to investigate the role of phonological and executive working-memory components in the carry operation in mental arithmetic. We manipulated the number of carry operations, as previous research had done, but also the value that had to be carried. Results of these experiments show that in addition to the number of carry operations, the value of the carry is also an important variable determining the difficulty of arithmetical sums. Furthermore, both variables (number and value) interacted with each other in such a way that the combination of multiple carries and values of carries larger than one resulted in more difficult problems irrespective of the presence of a working-memory load. The findings with respect to working-memory load suggest that mainly the central executive is important in handling the number of carry operations as well as the value that has to be carried. The implications of the present findings for our views on mental arithmetic and its reliance on working memory are discussed.     

The role of working memory in carrying and borrowing

The present study analyzed the role of phonological and executive components of working memory in the borrow operation in complex subtractions (Experiments 1 and 2) and in the carry operation in complex multiplications (Experiments 3 and 4). The number of carry and borrow operations as well as the value of the carry were manipulated. Results indicated that both the number of carry/borrow operations and the value of the carry increased problem difficulty, resulting in higher reliance on phonological and executive working-memory components. Present results are compared with those obtained for the carry operation in complex addition and are further discussed in the broader framework of working-memory functions.     

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 role of working memory in analogical mapping

The impact of a working-memory load on analogical mapping was examined in two experiments, using a dual-task paradigm. In Experiment 1, we used a phonological working-memory load; in Experiment 2, we used a phonological working-memory load and an executive working-memory load. The subjects were required to identify correspondences between visual scenes, either for single objects or for three objects simultaneously. The results indicated that the imposition of either a phonological or an executive working-memory load decreased the frequency with which the subjects identified correspondences between scenes based on relations and increased the frequency with which they identified correspondences based on object attributes. The frequency with which subjects made relational mappings was increased by the instruction to find correspondences for multiple objects in a scene simultaneously, rather than for just one. These results indicate that mapping on the basis of relations places greater demands on both modality-specific buffers and executive components of working memory than does mapping on the basis of object attributes.     

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,strategy execution,and strategy selection in mental arithmetic

A total of 72 participants estimated products of complex multiplications of two-digit operands (e.g., 63 × 78), using two strategies that differed in complexity. The simple strategy involved rounding both operands down to the closest decades (e.g., 60 × 70), whereas the complex strategy required rounding both operands up to the closest decades (e.g., 70 × 80). Participants accomplished this estimation task in two conditions: a no-load condition and a working-memory load condition in which executive components of working memory were taxed. The choice/no-choice method was used to obtain unbiased strategy execution and strategy selection data. Results showed that loading working-memory resources led participants to poorer strategy execution. Additionally, participants selected the simple strategy more often under working-memory load. We discuss the implications of the results to further our understanding of variations in strategy selection and execution, as well as our understanding of the impact of working-memory load on arithmetic performance and other cognitive domains.     

Working memory, strategy execution, and strategy selection in mental arithmetic

A total of 72 participants estimated products of complex multiplications of two-digit operands (e.g., 63 × 78), using two strategies that differed in complexity. The simple strategy involved rounding both operands down to the closest decades (e.g., 60 × 70), whereas the complex strategy required rounding both operands up to the closest decades (e.g., 70 × 80). Participants accomplished this estimation task in two conditions: a no-load condition and a working-memory load condition in which executive components of working memory were taxed. The choice/no-choice method was used to obtain unbiased strategy execution and strategy selection data. Results showed that loading working-memory resources led participants to poorer strategy execution. Additionally, participants selected the simple strategy more often under working-memory load. We discuss the implications of the results to further our understanding of variations in strategy selection and execution, as well as our understanding of the impact of working-memory load on arithmetic performance and other cognitive domains.     

Book reviews

Results from past studies show that the central executive, as conceptualised in the working memory model of Baddeley and Hitch (), plays an important role in simple mental arithmetic. According to this model the central executive is viewed as a unitary system. Recent research, however, suggests that the “central executive” can be fractionated in more autonomous executive functions, such as inhibition, response selection, planning, and input monitoring. In four experiments we studied the role of two possible executive functions (input monitoring and response selection) in solving simple sums. Subjects solved one‐digit sums (e.g., 5 + 7) in a single‐task condition as well as in dual‐task conditions. The results show that secondary tasks, which require a choice, impair the calculation of simple sums. On the other hand, an increased degree of input monitoring in the secondary tasks does not seem to impair the calculation of the sums. These findings show that response selection is strongly involved in simple arithmetic and may be one of the core executive processes in mental arithmetic.     

中央执行负荷对成人估算策略运用的影响

随机选取128名大学生为被试, 运用选择/无选法研究范式, 考察了不同中央执行负荷对估算策略运用的影响。结果发现：(1)中央执行负荷不影响策略分布; (2)策略运用条件、中央执行负荷影响策略执行。主次一致任务, 负荷对策略执行反应时的影响随负荷强度增大而增大, 对策略执行精确度影响不大; 而对主次不一致任务, 低负荷对策略执行反应时及精确度影响都不明显; (3)策略运用条件、中央执行负荷影响策略选择。负荷强度对策略选择反应时起重要作用, 只有当次级任务负荷高时, 干扰作用才明显; (4)成人的策略选择适应性受负荷强度的影响。无负荷条件下个体策略适应性更好。     

How automatic is “automatic vigilance”? The role of working memory in attentional interference of negative information

Whereas attentional interference of negative information has previously been assumed to be automatic, the present research hypothesised that this effect depends on the availability of working-memory resources. In two experiments, participants judged the gender of angry versus happy faces. Working-memory load was manipulated by the presence or absence of a math task (Study 1) or mental rehearsal of a one- versus 8-digit number (Study 2). The results showed that angry faces interfered more with gender naming than happy faces, but only when working-memory load was low. As such, attentional interference of negative stimulus features can be modulated by top-down attentional control processes.     

Understanding the role of executive control in the Implicit Association Test: Why flexible people have small IAT effects

The goal of the present research was to investigate the role of three central-executive functions—switching of mental sets, inhibition of prepotent responses, and simultaneous storage and processing (i.e., working-memory capacity)—in accounting for method variance in the Implicit Association Test (IAT). In two studies, several IATs with unrelated contents were administered along with a battery of central-executive tasks, with multiple tasks tapping each of the above executive functions. Method variance was found to be related to the switching factor, but not to the inhibition factor. There was also evidence for a small independent contribution of the working-memory capacity factor. The findings constrain process accounts of the IAT, lending support to an account in terms of task-set switching, and they have consequences for applications.     

How cognitive load affects duration judgments: A meta-analytic review

A meta-analysis of 117 experiments evaluated the effects of cognitive load on duration judgments. Cognitive load refers to information-processing (attentional or working-memory) demands. Six types of cognitive load were analyzed to resolve ongoing controversies and to test current duration judgment theories. Duration judgments depend on whether or not participants are informed in advance that they are needed: prospective paradigm (informed) versus retrospective paradigm (not informed). With higher cognitive load, the prospective duration judgment ratio (subjective duration to objective duration) decreases but the retrospective ratio increases. Thus, the duration judgment ratio differs depending on the paradigm and the specific type of cognitive load. As assessed by the coefficient of variation, relative variability of prospective, but not retrospective, judgments increases with cognitive load. The prospective findings support models emphasizing attentional resources, especially executive control. The retrospective findings support models emphasizing memory changes. Alternative theories do not fit with the meta-analytic findings and are rejected.     

运算动量效应的理论解释及其发展性预测因素

了解运算偏差的形成与发展对探索算数运算系统的内在机制具有重要意义,早期的算数运算能力是儿童理解和进行复杂数学运算的基础。运算动量偏差是指个体在进行基本数学运算时倾向于高估加法运算结果而低估减法运算结果的一种运算偏差,主要包括三种理论解释,即注意转移假说、启发式解释和压缩解释。鉴于运算动量效应在成年群体中相对稳定却在不同发展阶段儿童中存在不一致的证据,数学能力的提高与空间注意的成熟可结合不同的理论解释来阐明儿童发展过程中运算动量效应的变化趋势。未来可以进一步整合多种研究任务以揭示运算动量效应的发展轨迹,考察数量表征系统与运算动量效应间的关联,探究运算动量效应在不同运算符号中的稳定性,探讨不同因素共同作用对运算动量效应的影响,并设计有关数学能力的干预措施以减少运算动量效应这一运算偏差。     

The role of response selection and input monitoring in solving simple arithmetical products

Several studies have already shown that the central executive, as conceptualized in the working memory model of Baddeley and Hitch (1974), is important in simple mental arithmetic. Recently, attempts have been made to define more basic processes that underlie the "central executive." In this vein, monitoring, response selection, updating, mental shifting, and inhibition have been proposed as processes capturing executive control. Previous research has shown that secondary tasks that require a choice decision impair the calculation of simple sums, whereas input monitoring has not been found to be a sufficient condition to impair the calculation of sums (Deschuyteneer & Vandierendonck, 2005). In the present article, we report data on the role of input monitoring and response selection in solving simple arithmetical products. In four experiments, participants solved one-digit products (e.g., 5 x 7) in a single-task, as well as in a dual-task, condition. Just as for solving simple sums, the results show a strong involvement of response selection in the calculating of simple products, whereas input monitoring does not seem to impair the calculation of such products. These findings give additional evidence that response selection may be one of the processes needed for solving simple mental arithmetic problems.     

Executive-process interactive control: A unified computational theory for answering 20 questions (and more) about cognitive ageing

Although the effects of ageing on human information processing and performance have been studied extensively, many fundamental questions about cognitive ageing remain to be answered definitively. For example, what are the sources of age-related slowing? How much is working-memory capacity reduced in older adults? Is time-sharing ability lost with age? Answering such questions requires a unified computational theory that characterises the interactive operations of many component mental processes and integrates diverse data on cognitive ageing. Toward fulfilling this requirement, an executive-process interactive control (EPIC) architecture has been extended to model performance of both young and older adults. EPIC models yield accurate accounts of ageing effects on reaction times and accuracy in basic dual-task and working-memory paradigms. From these accounts, it appears that time-sharing ability and working-memory capacity decrease relatively little until after 70 years of age. Before age 70, at least some apparent performance decrements may be attributable to conservative executive processes and inefficient task procedures rather than decreased "hardware" functionality. By clarifying and deepening such insights, unified computational theories like EPIC will help answer many questions about cognitive ageing.     

Acquisition and use of mental operators: the influence of natural order of events

The present article reports two experiments investigating the influence of natural order of events on the acquisition and use of knowledge about operations, in short mental operators. The principle of use specificity states that task performance depends directly on the similarity between acquisition context and the present situation. In contrast, the principle of natural order proposes that knowledge about operations can always be applied easier (faster) if reasoning follows the natural order of events. In Experiment 1, participants had to apply alphabet-arithmetic operators and LISP functions in a prognosis task (A + 2 = ?) or a retrognosis task (? - 2 = A). In alphabet-arithmetic, an advantage for the first kind of task at the beginning of training decreased with increasing practice. In LISP, however, a preference for this task (corresponding with a prospective knowledge use) emerged with increasing practice. In Experiment 2, arithmetic relations between digit pairs had to be induced. In a causal context condition, relations were described as input and output of electric circuits, in a neutral context the relations were described as arithmetic dependencies. A preference for the prognosis task was found for the causal context condition (corresponding with a prospective knowledge use) but not for the neutral one. The findings suggest that the natural order of events moderates the acquisition and use of mental operators. Further research is required to clarify the bases for this moderation.     

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。     

Scheduling Processes in Working Memory: Instructions Control the Order of Memory Search and Mental Arithmetic

Humans must often use working memory to execute processes one at a time because of its limited capacity. Two experiments tested where limits in access to working memory occur. Subjects searched a short-term memory set for one stimulus digit and performed mental arithmetic with another stimulus digit. In one experiment, they were told to carry out the mental arithmetic before the memory search and to make the arithmetic response first. In the other, they were instructed to perform the tasks in the opposite order. The overt responses were executed in the prescribed order. Moreover, the covert working memory processes were executed in the prescribed order, as revealed by a critical path network analysis of reaction times. Results are explained in terms of a double-bottleneck model in which central processes and responses are constrained to be carried out for one task at a time.     

Do multiplication and division strategies rely on executive and phonological working memory resources?

The role of executive and phonological working memory resources in simple arithmetic was investigated in two experiments. Participants had to solve simple multiplication problems (e.g., 4 x 8; Experiment 1) or simple division problems (e.g., 42 / 7; Experiment 2) under no-load, phonological-load, and executive-load conditions. The choice/no-choice method was used to investigate strategy execution and strategy selection independently. Results for strategy execution showed that executive working memory resources were involved in direct memory retrieval of both multiplication and division facts. Executive working memory resources were also involved in the use of nonretrieval strategies. Phonological working memory resources, on the other hand, tended to be involved in nonretrieval strategies only. Results for strategy selection showed no effects of working memory load. Finally, correlation analyses showed that both strategy execution and strategy selection correlated with individual-difference variables, such as gender, math anxiety, associative strength, calculator use, arithmetic skill, and math experience.     

Relationships between executive function,working memory,and decision-making on the Iowa Gambling Task: Evidence from ventromedial patients,dorsolateral patients,and normal subjects

The results of previous studies are inconsistent in regard to the relationship between the Iowa Gambling Task (IGT), working-memory (WM), and executive tasks, and whether these cognitive processes could be considered as mechanisms underlying a decision-making deficit. Moreover, the relationship between the IGT and executive measures is examined based on a limited number of executive tasks, within different populations showing diffuse damage. In addition, there are fewer studies carried out within control participants, with those studies also being inconclusive. It is also suggested that the association of the IGT performance with executive tasks depends on whether the IGT was running under ambiguity or under risk. In this work, all of these issues are studied. Results showed that both patients with ventromedial (VMPFC, N = 10) and dorsolateral (DLPFC, N = 10) prefrontal cortex lesions are significantly impaired on almost all executive tasks, WM tasks, and the IGT. Furthermore, when the IGT is run under risk, there are significant correlations between executive measures and the IGT for the DLPFC patients and the control participants (N = 34) but not the VMPFC patients. No correlation was found between WM tasks and the IGT for both frontal subgroups and control participants. These findings suggested that the mechanisms underlying the IGT deficit differ according to the lesion locations.