数学焦虑影响儿童数学任务表现的作用机制探析

研究设计了心算加法和图形旋转/平移两类数学任务,同时采用《儿童数学焦虑问卷》、工作记忆和抑制任务,以探讨数学焦虑影响儿童数学任务表现的作用机制.213名小学五年级儿童参与研究,其中89人参与正式实验.结果发现:(1)数学焦虑与数学成绩呈显著负相关;(2)高数学焦虑组在工作记忆和两类数学任务中的得分均显著低于低数学焦虑组,而两组在抑制任务指标上差异不显著;(3)言语工作记忆和视空间工作记忆是数学焦虑影响心算加法任务的完全中介变量;视空间工作记忆是数学焦虑影响图形旋转/平移任务的完全中介变量,言语工作记忆是二者关系的调节变量.研究结果支持了加工效能理论.     

儿童执行功能与算术认知策略的关系

对35名小学2年级儿童的四种执行功能与有无工作记忆负荷两种情况下算术认知策略表现之间的关系进行了探讨.结果表明,双任务协调功能与工作记忆负荷增加时放弃策略的使用次数具有显著负相关;策略转换功能越强的儿童.算术认知策略的使用越灵活;抑制功能强的儿童在提取策略的相关表现上更好;记忆更新功能与工作记忆负荷增加时策略执行的正确率具有显著正相关.这说明,执行功能与儿童算术认知策略之间存在着特定的联系.     

数字工作记忆广度的毕生发展及其作用因素

以10~90岁的1993名自愿者为被试完成该实验研究。结果表明：（1）在最简单的心算加工负荷下,数字工作记忆广度约为6±2;（2）在10至90岁范围内,测验的最高成绩在16~19岁组（即高中生组）,回归分析表明数字工作记忆广度随年龄的对数呈抛物线变化;（3）教育因素对成年人数字工作记忆广度的随龄化过程有重要作用;（4）与我们过去的研究结果相比较,发现数字工作记忆广度受心算加工负荷的影响显著     

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。     

工作记忆对小学三年级学生解决比较问题的影响

研究工作记忆与小学生解决比较问题成绩之间的关系。实验1运用双任务作业研究一致问题和不一致问题的工作记忆负荷是否有显著差别,被试为34名小学三年级学生。实验2运用工作记忆测验研究成功解题者与不成功解题者的工作记忆容量是否有显著差别,被试为37名小学三年级学生。结果表明;(1)小学生解决比较问题的成绩受问题类型的影响,他们在一致问题上的成绩显著优于不一致问题。(2)一致问题和不一致问题的工作记忆负荷水平不同,不一致问题的工作记忆负荷大于一致问题。(3)成功解题者的工作记忆容量大于不成功解题者的工作记忆容量。本研究结果说明工作记忆对小学生解决比较问题有重要影响。     

数学困难儿童估算策略运用的中央执行负荷效应

前人研究表明中央执行影响个体的算术策略运用,但罕见考察其对数学困难儿童估算策略运用的影响。本研究运用选择/无选法范式,通过操纵不同长度数字串的排序记忆任务作为不同水平中央执行负荷,考察其对数困儿童估算策略运用的限制性作用。74名六年级儿童(数困儿童36名)参加了本研究。结果发现:(1)数困组儿童在无、低、高三种负荷条件下的策略执行正确率均显著低于正常组,反应时上只在无负荷和低负荷条件下显著差于正常组;(2)数困组儿童在三种负荷条件下的策略选择正确率和反应时上均显著差于正常组;(3)两组儿童的策略选择适应性都受到负荷的影响,负荷水平越高,两组儿童的策略选择适应性越差,且数困组儿童显著差于正常组。这表明中央执行负荷对数困儿童和正常儿童的策略运用会产生差异性影响。上述发现为深入理解中央执行功能作用于数困儿童的较差策略运用的潜在机制具有重要的理论和实践意义。     

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。     

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。     

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。     

珠心算训练儿童加法心算的ERP早成分研究

采用事件相关电位(ERP)的方法,对32名儿童进行了双位数加法心算实验,探讨了珠心算训练方式对儿童加法心算加工早期感知觉的影响。研究结果表明,与非珠心算训练儿童相比,在加法心算过程的早期阶段,珠心算训练儿童枕部P1、额中央区的N1波幅增大,而颞枕区N170以及额中央区P2波幅减小。本研究结果发现珠心算训练对儿童心算过程的早期感知有显著影响。     

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.     

The role of phonological and executive working memory resources in simple arithmetic strategies

The current study investigated the role of the central executive and the phonological loop in arithmetic strategies to solve simple addition problems (Experiment 1) and simple subtraction problems (Experiment 2). The choice/no-choice method was used to investigate strategy execution and strategy selection independently. The central executive was involved in both retrieval and procedural strategies, but played a larger role in the latter than in the former. Active phonological processes played a role in procedural strategies only. Passive phonological resources, finally, were only needed when counting was used to solve subtraction problems. No effects of working memory load on strategy selection were observed.     

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.     

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。     

不同数学焦虑成人的算术策略运用差异：ERP研究

采用事件相关电位(ERP)技术和选择/无选法范式, 在两位数加法心算和估算中, 探索高、低数学焦虑个体的算术计算策略运用及其内在机制。行为结果：数学焦虑效应在策略运用的反应时和正确率指标上的差异都不显著; 而脑电结果：高数学焦虑个体的N400波幅显著高于低数学焦虑个体; 选择条件中, 估算与心算的数学焦虑效应的N100波幅差异; 无选条件中, 高低数学焦虑个体N1-P2复合波的波幅和潜伏期差异显著。数学焦虑效应在策略编码(0~250 ms)和策略选择/执行阶段(250 ms之后)存在差异。     

Strategy use,the development of automaticity,and working memory involvement in complex multiplication

Participants practiced a set of complex multiplication problems (e.g., 3 x 18) in a pre-/postpractice design. Before, during, and after practice, the participants gave self-reports of problem-solving strategies. At prepractice, the most common strategy was a mental version of the standard multidigit algorithm, and dual tasks revealed that working memory load was high and heavier for problems solved via nonretrieval strategies. After practice, retrieval was used almost exclusively, and participant variability, automaticity level of problems (proportion of trials on which retrieval was used over the entire experiment), and error rates were significant predictors of problem-solving latencies. Practice reduced working memory involvement to minimal levels, and there was no relationship between automaticity level and working memory load. The commonalities between the present findings and findings related to automaticity development in simple arithmetic are discussed.     

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.     

The development of strategy use in elementary school children: working memory and individual differences

The current study tested the development of working memory involvement in children's arithmetic strategy selection and strategy efficiency. To this end, an experiment in which the dual-task method and the choice/no-choice method were combined was administered to 10- to 12-year-olds. Working memory was needed in retrieval, transformation, and counting strategies, but the ratio between available working memory resources and arithmetic task demands changed across development. More frequent retrieval use, more efficient memory retrieval, and more efficient counting processes reduced the working memory requirements. Strategy efficiency and strategy selection were also modified by individual differences such as processing speed, arithmetic skill, gender, and math anxiety. Short-term memory capacity, in contrast, was not related to children's strategy selection or strategy efficiency.