心算的策略选择

从策略选择的角度来研究心算是当前心算研究的一个重要领域。有关心算活动中问题大小效应、距离效应、奇偶效应等的行为与认知神经科学研究揭示了心算活动中不同的策略选择, 进一步加深了我们对心算加工特点的了解。未来研究在注重具体问题解决的同时, 还应注重实验设计的严密性、研究的深入性与综合性相兼顾等问题。     

无意识元认知调控下的策略转换

通过两位数乘法算式答案判别任务研究无意识元认知调控下策略转换的的认知加工特征。整个算式答案判别任务分为两种策略使用情境：一种为只可以使用尾数策略的任务情境;另一种为既可以使用尾数策略,又可以使用奇偶策略的任务情境。实验结果表明：1）无意识元认知具有高选择性、高效性和高潜力,能在策略使用情境转变之后,快速察觉并选择使用更为简单、高效的奇偶策略;2）尾数策略使用的强大思维定势阻止奇偶策略的意识化,致使绝大多数被试未能发现任务情境的变化而在内隐状态下使用了奇偶策略;3）策略在内隐或外显状态下使用具有同等效力,策略内隐使用具有高效性和高潜力。     

网络语言的创造性加工过程:新颖N400与LPC

采用事件相关电位(ERP)技术比较在语义违反范式下网络语言和标准汉语的语义加工差异。结果发现:(1)不管是网络语言还是标准汉语,相对于语义一致条件,语义不一致条件在400 ms诱发了一个更负的负成分,但网络语言的经典N400差异波具有更晚的潜伏期和更长的持续时间;(2)溯源结果发现,网络语言和标准汉语的经典N400差异波的早期和晚期的定位均分别定位于丘脑和前扣带回,表明N400延迟效应是由个体对网络语言相对低的流利度所致,反映了认知冲突的延续;(3)在语义一致性条件下,网络语言比标准汉语诱发了一个更负的新颖N400和一个更正的晚期正成分(LPC),分别定位于前扣带回和海马,二者分别反映了新颖网络含义的识别以及新颖语义信息的整合与新颖语义联结的形成。ERP结果支持了网络语言加工属于创造性思维过程。     

环性传递结构的启动优势及脑电证据

采用三词对材料构成两种结构的社会情境：环性传递结构和线性传递结构,通过合理情境判断任务和脑电技术,探讨社会结构的加工机制。结果发现,与线性结构相比,环性结构引发显著的启动优势效应,诱发额区和中央区更小P200波幅、更大N400波幅和更小P600波幅。这表明,被试对环性社会结构具有自动化的整体加工优势。可能的解释指向中华文化的环性结构图式偏好,支持社会结构认知的文化建构性观点。     

内隐学习策略的存在及其外显转化

该研究采用＂乘法算式答案正误判断的实验室任务＂,以＂奇偶检查策略＂为具体策略研究对象,探查内隐奇偶检查策略的存在及其自动性特征。实验结果表明：（1）奇偶检查策略可以以内隐方式存在,但经过不断练习可最终上升到意识层面;（2）奇偶检查策略的外显和内隐使用表现出各自独立的优势效应。外显学习策略的优势效应主要表现在正确算式判断任务中,而内隐学习策略则在错误算式判断任务中表现出＂内隐优势效应＂的趋势;（3）内隐奇偶检查策略的人为外显化并不能促使个体增加使用该策略的频率,也不能有效提高策略的执行效率。     

空间推理的脑机制：一项ERP研究

记录14名正常成人完成四种空间推理及一种基线任务（记忆任务）时的事件相关电位,对空间推理的脑电活动情况进行考察。研究结果表明,在200ms-900ms窗口,推理任务比基线任务诱发更大的正成分。对不同推理任务的比较表明,具体与抽象材料的单模型推理诱发相似的波形;单模型与有效的双模型任务诱发的ERP成分明显不同,在300ms-600ms窗口,后者比前者诱发更大的正波;在200-600ms时间窗口,存在有效结论与无有效结论的双模型问题也诱发明显不同的ERP波形。研究的结果表明,推理与记忆涉及不同的加工要求,推理需要整合前提的信息,而记忆只需要储存前提信息。在解决双模型推理问题时,从200ms开始,被试就对刺激材料进行初步的加工与判断,随后对双模型问题采用有注解的单模型加工策略。另外,不同材料的空间推理任务之间的波形较为一致,表明视觉表象并未明显影响空间推理过程。     

正性情绪诱导下的自我参照加工：来自ERPs的证据

采用事件相关电位考察正性情绪对自我参照加工程度效应的影响。实验采用图片启动范式, 先呈现情绪图片, 然后再呈现自我参照刺激。实验发现, 在P2上, 中性情绪条件比正性情绪条件激发了更大的波幅, 高自我相关的刺激比其它刺激诱发了更短的P2潜伏期; 在N2上, 高自我相关名字比中等自我相关名字和非自我相关名字诱发了更小的N2的波幅和更长潜伏期; 在P3上, 高自我相关名字比中等自我相关名字和非自我相关名字诱发了更大的P3波幅, 中等自我相关名字比非自我相关名字诱发了更大的P3波幅。实验结果表明, 人类大脑对正性情绪刺激的加工可能是不敏感的。无论在正性情绪启动还是中性启动的影响下, 自我参照加工都能展现出稳定的特征, 而且高自我相关的刺激会得到更为深入和精细的加工, 表现出自我参照加工的程度效应。     

工作记忆和感觉运动速度在心算加工年老化过程中的作用

对心算加工年老化研究有助于阐明认知老化规律,然而有关心算老化的少量研究结果仍存在不一致甚至矛盾之处。导致这种不一致的原因十分复杂,表面上看,不同认知老化研究所采用的统计方法不尽相同导致了结果的歧异。例如,在心算的年老化研究中,有的研究结论基于群体的数据分析,如层级回归分析(hierarchical regres-sion analyses)或方差分析,如Sahhouse和Coon(1994);另有一些研究先对每一个体数据作线性回归分析,如此得到斜率和截距(分别表示心算的中枢加工时间和外周感觉运动时间),然后再行层级回归分析或方差分析,如Al-len等(1992,1997)。这两类统计分析所得的结果很不一致。从理论上看,只要所采用的统计方法是合理的,统计方法的不尽相同应不会导致矛盾。但在实际情况下,统计分析误差增加了结论不一致的可能性,从而增大了揭示心算老化复杂性规律的难度。事实上,心算活动的年龄差异可能来自于记忆、加工速度等不同认知资源的老化差异。为了深入探讨这一问题,我们进一步研究了工作记忆和感觉运动速度在心算加工年老化过程中的作用。被试共161人,20—79岁,身体健康,受教育年限12年以上,以10岁段划分为6个年龄组,组间文化程度基本匹配。被试任务包括：(1)连续减法心算,分别为1000—3、1000—7、1000—13及1000—17等4种,在排除了被试看屏幕和按键的感觉运动时间后得到心算所需的时间;(2)数字计算工作记忆,根据工作记忆对信息同时进行加工和储存的特点,要求被试计算完题后再回忆答案,以获得工作记忆广度指标;(3)“数字复制”(digit copying),以获得感觉运动速度指标。实验在386微机上进行。对所得数据分别进行了上述群体数据与个体数据分析。两种数据分析方法得到了相同的结果,一致表明,在控制工作记忆与感觉运动速度的年龄差异后,心算活动的年龄差异显著降低。而且,控制感觉运动速度的年龄差异后心算活动年龄差异的降低程度要大于控制工作记忆的年龄差异后心算活动年龄差异的降低程度。这说明,感觉运动速度在心算加工年老化过程中发挥了更大作用。但是,工作记忆与感觉运动速度二者的年龄差异并不能完全解释心算活动的年龄差异,表明心算加工的年老化存在其特殊性过程,不支持认知老化的普遍减慢假说(genenalized slowing hypotllesis)。     

工作记忆负荷和自动化提取对小学生加法心算策略执行效果的影响

本研究选取43名小学四年级学生(18名男生和25名女生)为实验被试,探究了工作记忆负荷和自动化提取对复杂加法心算策略效果的影响.结果显示:(1)工作记忆负荷对复杂加法心算策略的影响显著,即一项加法心算策略所需的工作记忆负荷越小,该策略的执行效果越好;(2)自动化提取对加法心算策略的影响显著,即一项加法心算策略所需自动化提取的程度越高,该策略的执行效果越好;(3)工作记忆负荷和自动化提取对加法心算策略效果的交互作用显著,表现为在自动化提取水平较高的情况下,工作记忆负荷的大小对心算策略执行效果的影响差异不显著;而在自动化提取水平较低的情况下,工作记忆负荷小的心算策略的执行效果显著优于工作记忆负荷大的心算策略的执行效果.     

奇偶检查策略的内隐性质与使用特点

选取36名被试完成乘法算式答案正误判断的实验任务,结果发现:其中有31名被试在无意识情况下使用了"奇偶检查策略",在对奇偶非匹配错误答案算式和奇偶匹配错误答案算式进行判断时,在反应时和错误率两个变量上均存在显著的奇偶效应;其中在双偶数乘数算式上判断上"奇偶效应"作用显著,说明"内隐奇偶检查策略"具有明显的使用偏好和固着使用特点。     

Influence of the large–small split effect on strategy choice in complex subtraction

Two main theories have been used to explain the arithmetic split effect: decision‐making process theory and strategy choice theory. Using the inequality paradigm, previous studies have confirmed that individuals tend to adopt a plausibility‐checking strategy and a whole‐calculation strategy to solve large and small split problems in complex addition arithmetic, respectively. This supports strategy choice theory, but it is unknown whether this theory also explains performance in solving different split problems in complex subtraction arithmetic. This study used small, intermediate and large split sizes, with each split condition being further divided into problems requiring and not requiring borrowing. The reaction times (RTs) for large and intermediate splits were significantly shorter than those for small splits, while accuracy was significantly higher for large and middle splits than for small splits, reflecting no speed–accuracy trade‐off. Further, RTs and accuracy differed significantly between the borrow and no‐borrow conditions only for small splits. This study indicates that strategy choice theory is suitable to explain the split effect in complex subtraction arithmetic. That is, individuals tend to choose the plausibility‐checking strategy or the whole‐calculation strategy according to the split size.     

The odd-even effect in addition: an analysis per problem type

The odd-even effect is a well documented finding in the literature on mental arithmetic, at least for multiplication. It implies that false answers with the same parity as the correct answer are rejected more slowly than false answers with a different parity. For addition, this effect is not so well documented. The study by Krueger and Hallford (1984) is the only one that investigated odd-even effects for addition. However, they did not investigate odd-even effects per problem, even though there are indications that problem type can modulate odd-even effects for multiplication (Lemaire & Reder, 1999). Therefore, we wanted to get more insight into odd-even effects for addition by investigating odd-even effects per problem type. Our results extended the findings of Krueger and Hallford. First of all, we found an interaction between split and problem type. The most important and new result of present study, however, was a strong parity effect for E + E problems. We discuss our results in terms of two alternative explanations for odd-even effects, namely use of a parity rule on the one hand and familiarity with even outcomes on the other.     

Menatal addition: A test of three verification models

Three explanations of adults’ mental addition performance, a counting-based model, a direct-access model with a backup counting procedure, and a network retrieval model, were tested. Whereas important predictions of the two counting models were not upheld, reaction times (RTs) to simple addition problems were consistent with the network retrieval model. RT both increased with problem size and was progressively attenuated to false stimuli as the split (numerical difference between the false and correct sums increased. For large problems, the extreme level of split (13) yielded an RT advantage for false over true problems, suggestive of a global evaluation process operating in parallel with retrieval. RTs to the more complex addition problems in Experiment 2 exhibited a similar pattern of significance and, in regression analyses, demonstrated that complex addition (e.g., 14+12=26) involves retrieval of the simple addition components (4+2=6). The network retrieval/decision model is discussed in terms of its fit to the present data, and predictions concerning priming facilitation and inhibition are specified. The similarities between mental arithmetic results and the areas of semantic memory and mental comparisons indicate both the usefulness of the network approach to mental arithmetic and the usefulness of mental arithmetic to cognitive psychology.     

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。     

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。     

Number comparison and number ordering as predictors of arithmetic performance in adults: Exploring the link between the two skills,and investigating the question of domain-specificity

Recent evidence has highlighted the important role that number-ordering skills play in arithmetic abilities, both in children and adults. In the current study, we demonstrated that number comparison and ordering skills were both significantly related to arithmetic performance in adults, and the effect size was greater in the case of ordering skills. Additionally, we found that the effect of number comparison skills on arithmetic performance was mediated by number-ordering skills. Moreover, performance on comparison and ordering tasks involving the months of the year was also strongly correlated with arithmetic skills, and participants displayed similar (canonical or reverse) distance effects on the comparison and ordering tasks involving months as when the tasks included numbers. This suggests that the processes responsible for the link between comparison and ordering skills and arithmetic performance are not specific to the domain of numbers. Finally, a factor analysis indicated that performance on comparison and ordering tasks loaded on a factor that included performance on a number line task and self-reported spatial thinking styles. These results substantially extend previous research on the role of order processing abilities in mental arithmetic.     

Implicit temporal tuning of working memory strategy during cognitive skill acquisition

Complex cognitive tasks such as multiple-step arithmetic entail strategies for coordinating mental processes such as calculation with processes for managing working memory (WM). Such strategies must be sensitive to factors such as the time needed for calculation. In 2 experiments we tested whether people can learn the timing constraints on WM demands when those constraints are implicitly imposed. We varied the retention period for intermediate results using the well-known digit size effect: The larger the operands, the longer it takes to perform addition. During learning participants practiced multiple-step arithmetic routines combined with large or small digits. At transfer, they performed both practiced and novel combinations. Practice performance was affected by digit size and WM demands. However, the transfer performance was not fully explained by the digit size effect or the practice effect. We argue that participants acquired temporal tuning of the WM strategy to the implicit retention interval imposed by the digit size and kept using the tuning mode to unpracticed data set.     

A model of exact small-number representation

To account for the size effect in numerical comparison, three assumptions about the internal structure of the mental number line (e.g., Dehaene, 1992) have been proposed. These are magnitude coding (e.g., Zorzi & Butterworth, 1999), compressed scaling (e.g., Dehaene, 1992), and increasing variability (e.g., Gallistel & Gelman, 1992). However, there are other tasks besides numerical comparison for which there is clear evidence that the mental number line is accessed, and no size effect has been observed in these tasks. This is contrary to the predictions of these three assumptions. Moreover, all three assumptions have difficulties explaining certain symmetries in priming studies of number naming and parity judgment. We propose a neural network model that avoids these three assumptions but, instead, uses place coding, linear scaling, and constant variability on the mental number line. We train the model on naming, parity judgment, and comparison and show that the size effect appears in comparison, but not in naming or parity judgment. Moreover, no asymmetries appear in primed naming or primed parity judgment with this model, in line with empirical data. Implications of our findings are discussed. This work was supported by Grant P5/04 from the Interuniversity Attraction Poles Program—Belgian Science Policy and by a GOA grant from the Ghent University Research Council to W.F.     

Mental addition in third,fourth, and sixth graders

Research on mental arithmetic has suggested that young children use a counting algorithm for simple mental addition, but that adults use memory retrieval from an organized representation of addition facts. To determine the age at which performance shifts from counting to retrieval, children in grades 3, 4, and 6 were tested in a true/false verification task. Reaction time patterns suggested that third grade is a transitional age with respect to memory structure for addition—half of these children seemed to be counting and half retrieving from memory. Results from fourth and sixth graders implicated retrieval quite strongly, as their results resembled adult RTs very closely. Fourth graders' processing, however, was easily disrupted when false problems were presented. The third graders' difficulties are not due to an inability to form mental representations of number; all three grades demonstrated a strong split effect, indicative of a simpler mental representation of numerical information than is necessary for addition. The results were discussed in the context of memory retrieval versus counting models of mental arithmetic, and the increase across age in automaticity of retrieval processes.