The tie effect in simple arithmetic: An access-based account

Simple arithmetic problems with repeated operands (i.e., ties such as 4 + 4, 6 x 6, 10 - 5, or 49 / 7) are solved more quickly and accurately than similar nontie problems (e.g., 4 + 5, 6 x 7, 10 - 6, or 48 / 6). Further, as compared with nonties, ties show small or nonexistent problem-size effects (whereby problems with smaller operands such as 2 + 3 are solved more quickly and accurately than problems with larger operands such as 8 + 9). Blankenberger (2001) proposed that the tie advantage occurred because repetition of the same physical stimulus resulted in faster encoding of tie than of nontie problems. Alternatively, ties may be easier to solve than nonties because of differences in accessibility in memory or differences in the solution processes. Adults solved addition and multiplication (Experiment 1) or subtraction and division (Experiment 2) problems in four two pure formats (e.g., 4 + 4, FOUR + FOUR) and two mixed formats (e.g., 4 + FOUR, and FOUR + 4). Tie advantages were reduced in mixed formats, as compared with pure formats, but the tie x problem-size interaction persisted across formats. These findings support the view that tie effects are strongly related to memory access and are influenced only moderately by encoding factors.     

Why is 9+7 harder than 2+3? Strength and interference as explanations of the problem-size effect

In four experiments, the problem-size effect was investigated, using an alphabet-arithmetic task in which subjects verified such problems as A + 2 = C. Problem size was manipulated by varying the magnitude of the digit addend (e.g., A + 2, A + 3, and A + 4). The frequency and similarity of problems was also manipulated to determine the contribution of strength and interference, respectively. Experiment 1 manipulated frequency at low levels of practice and found that strength could account for the problem-size effect. Experiment 2 manipulated frequency at higher levels of practice, and found that strength alone could not account for the problem-size effect at asymptote. Experiment 3 manipulated frequency and similarity and found a substantial problem-size effect at asymptote, suggesting that both strength and interference contribute to the problem-size effect. Experiment 4 manipulated similarity, keeping frequency constant, and found no problem-size effect at asymptote, suggesting that interference alone is not responsible for the problem-size effect. The results are related to findings with number arithmetic.     

Spoken numbers versus Arabic numerals: differential effects on adults' multiplication and addition.

J.-A. LeFevre, Q. Lei, B. L. Smith-Chant, and D. B. Mullins (2001) examined effects of auditory versus Arabic visual presentation formats on performance of simple multiplication. They observed a smaller problem-size effect (response time [RT] increases with numerical size) with auditory stimuli compared with Arabic stimuli. If this arises during problem encoding, as opposed to during subsequent calculation processes, the authors would expect comparable Format x Problem Size interactions for both multiplication and addition. For multiplication, the authors replicated the finding of a smaller problem-size effect for auditory stimuli than for Arabic stimuli, but found the opposite pattern for addition whereby the problem-size effect was larger with auditory stimuli than with Arabic stimuli. Decomposition of mean RT into its ex-Gaussian components, mu and tau, demonstrated that the triple interaction arose entirely in connection with tau. This suggests that the effects of auditory versus Arabic format on RT substantially reflected format-related shifts in the use of procedural strategies.     

Calculation,culture, and the repeated operand effect

A basic phenomenon of cognitive arithmetic is that problems composed of a repeated operand, so-called "ties" (e.g. 6+6, 7 x 7), typically are solved more quickly and accurately than comparable non-tie problems (e.g. 6+5, 7 x 8). In Experiment 1, we present evidence that the tie effect is due to more efficient memory for ties than for non-ties, which participants reported solving more often using calculation strategies. The memory/strategy hypothesis accounts for differences in the tie effect as a function of culture (Asian Chinese vs. non-Asian Canadian university students), operation (addition, multiplication, subtraction, and division), and problem size (numerically small vs. large problems). Nonetheless, Blankenberger (Cognition 82 (2001) B15) eliminated the tie response time (RT) advantage by presenting problems in mixed formats (e.g. 4 x four), which suggests that the tie effect with homogenous formats (4 x 4 or four x four) is due to encoding. In Experiment 2, using simple multiplication problems, we replicated elimination of the tie effect with mixed formats, but also demonstrated an interference effect for mixed-format ties that slowed RTs and increased errors relative to non-tie problems. Additionally, practicing non-tie problems in both orders (e.g. 3 x 4 and 4 x 3) each time ties were tested once (cf. Cognition 82 (2001) B15) reduced the tie effect. The format-mismatch effect on ties, combined with a reduced tie advantage because of extra practice of non-ties, eliminated the tie effect. Rather than an encoding advantage, the results indicate that memory access for ties was better than for non-ties.     

What makes multiplication facts difficult. Problem size or neighborhood consistency?

Two current models of arithmetic fact retrieval, the network interference theory (NIT; Campbell, 1995) and the interacting neighbors (IN) model (Verguts & Fias, 2005a), predict that errors in simple multiplication should be more probable, if they include the same digit as the correct result (i.e., if they are "consistent," compared with "inconsistent" errors). In a reanalysis of error data originally reported by Campbell (1997), we provide first empirical evidence for this prediction. Furthermore, these results support the notion of different quantity representations for decades and units as proposed by Nuerk, Weger, and Willmes (2001). However, the NIT and IN-model differ in their explanations of the problem-size effect, a hallmark finding robustly observed in arithmetic fact retrieval. Only the IN-model predicts that a correct answer's neighborhood consistency can fully account for the problem-size effect, which was confirmed in our analysis.     

Canadian and Spanish youths' risk perceptions of drinking and driving, and riding with a drunk driver

The present research compared Canadian and Spanish youths' perceptions of the potential benefits and drawbacks of driving under the influence of alcohol (DUI) and riding with a drunk driver (RDD). Eighty (41 female) Canadian and 87 (71 female) Spanish undergraduates completed a survey asking about their past and forecasted engagement in DUI and RDD, and their perceptions of the benefits and drawbacks of DUI and RDD. A sizeable proportion of both samples reported DUI and RDD in the past year. Past risk takers forecasted significantly greater chances of engaging in these behaviors in the following year compared to those who had not engaged in DUI and RDD. Both samples provided significantly more drawbacks than benefits of DUI and RDD. Whereas the benefits of both behaviors tended to refer to personal effects (e.g., save money, arrive faster) that occurred before, during, or after driving, the drawbacks referred to a range of outcomes (e.g., accident, kill/injure, penal sanction) that mostly occurred during driving. Although Canada and Spain differ in important respects (e.g., potential penalty for DUI), there were similarities in the two samples' perceptions of DUI and RDD. Young people are aware of the costs of these risky behaviors but nevertheless engage in them. These findings can inform theories of the co-occurrence of risky driving behaviors, and the development of prevention programs that focus on perceived outcomes.     

Cognitive arithmetic across cultures.

Canadian university students either of Chinese origin (CC) or non-Asian origin (NAC) and Chinese university students educated in Asia (AC) solved simple-arithmetic problems in the 4 basic operations (e.g., 3 + 4, 7 - 3, 3 x 4, 12 divided by 3) and reported their solution strategies. They also completed a standardized test of more complex multistep arithmetic. For complex arithmetic, ACs outperformed both CCs and NACs. For simple arithmetic, however, ACs and CCs were equal and both performed better than NACs. The superior simple-arithmetic skills of CCs relative to NACs implies that extracurricular culture-specific factors rather than differences in formal education explain the simple-arithmetic advantage for Chinese relative to non-Asian North American adults. NAC's relatively poor simple-arithmetic performance resulted both from less efficient retrieval skills and greater use of procedural strategies. Nonetheless, all 3 groups reported using procedures for the larger simple subtraction and division problems, confirming the importance of procedural knowledge in skilled adults' performance of elementary mathematics.     

THE WILL ROGERS ILLUSION IN JUDGMENTS ABOUT SOCIAL GROUPS

Abstract— Subjects' judgments of the mean of 12 scores were influenced by the way in which the scores were dichotomized. The estimated mean was higher when the three highest scores formed one group (e.g., payments for women) and the nine lowest formed the other (e.g., payments for men) than when the nine highest were one group and the three lowest the other. We call this phenomenon the Will Rogers Illusion (WRI). The WRI occurred only when estimates of the subgroup means were made prior to the estimates of the mean of the whole group. When the latter mean was judged first, the WRI was reversed. These and other data indicate that the means of subgroups can influence judgments of group means, a finding that is relevant to research on social stereotypes.     

象似性和手语学习经验对中国手语-汉语跨模态语义启动效应的影响

采用启动条件下的词汇判断任务,考察熟练手语使用者和无手语经验成年听人的跨模态语义启动效应。结果发现：1)在象似词条件下,两组被试判断汉语语义相关词的反应时均快于语义无关词,说明手语象似词和汉语词之间存在跨模态语义启动效应。2)在非象似词条件下,仅手语熟练被试判断汉语语义相关词的反应时快于语义无关词,无手语经验被试判断汉语语义相关词和无关词的速度没有差异。这是由于前者心理词库中的手语词和口语词共享语义表征,而后者主要依赖手语象似词的视觉模拟性。整个研究表明,中国手语和汉语间存在跨模态语义启动效应,但该效应受到手语词象似性和手语学习经历的调节。     

Dissociated backward priming effects in lexical decision and pronunciation tasks

Backward priming was examined at 150- and 500-msec prime-target stimulus onset asynchronies (SOAs) using visually presented primes and targets in lexical decision and pronunciation tasks. Two kinds of backward relations were used: compound items for which targets and primes formed a word in the backward direction (e.g., prime: HOP; target: bell), and noncompound items for which targets and primes did not form a word but were associatively related in the backward but not the forward direction (e.g., prime: BABY; target: stork). Results showed that backward priming effects were equivalent for compounds and noncompounds. However, for lexical decisions, backward priming occurred at both SOAs, whereas for pronunciation, it occurred only at the 150-msec SOA. We discuss how this SOA-dissociated backward priming effect in lexical decision and pronunciation tasks poses a serious challenge for all theories of semantic priming.     

Bidirectional associations in multiplication memory: conditions of negative and positive transfer

A variety of experimental evidence indicates that the memory representation for multiplication facts (e.g., 6 x 9 = 54) incorporates bidirectional links with a forward association from factors to product and a reverse association from product to factors. Surprisingly, the authors did not find evidence in Experiment 1 of facilitative transfer-of-practice from multiplication (6 x 9 = ?) to factoring (54 = ? x ?); in fact, multiplication practice produced item-specific interference with factoring. Similarly, the authors found no evidence in Experiment 2 that repetition of specific factoring problems (54 = ? x ?) facilitated performance of corresponding multiplication problems (6 x 9 = ?). In Experiment 3, participants practiced both multiplication and factoring and presented facilitative transfer in both directions. Thus, bidirectional facilitation occurred if both operations were practiced, but interference occurred when only one operation was practiced. We propose that this seemingly paradoxical behavior occurs because it is adaptive for the bidirectional retrieval structure to retain operational flexibility in the context of practicing both operations, whereas it is adaptive to specialize the memory representation for the practiced operation (i.e., factoring or multiplication) when only one operation is practiced.     

Retrieval-induced forgetting of arithmetic facts across cultures

Retrieving a single-digit multiplication fact (3×4 =12) can slow response time (RT) for the corresponding addition fact (3+4=7). The present experiment investigated effects of problem type (i.e., tie addition problems such as 3+3 vs. non-ties such as 3+4) and cultural background on this retrieval-induced forgetting (RIF) phenomenon in young adults. Canadians answering in English (n=36), Chinese adults answering in English (n=36), and Chinese answering in Chinese (n=36) received four blocks of multiplication practice and then two blocks of the addition counterparts and control additions. Tie addition problems presented a robust RIF effect that did not differ between groups, but only the Canadian group showed RIF for non-ties and only for small non-ties with sum≤10 (3+4). The Chinese groups' RIF effect for addition ties, but not small non-ties, converges with recent evidence that ties are solved by direct memory retrieval whereas small non-ties may be solved by highly efficient procedural processes in skilled performers.     

加减法问题大小效应的加工机制

有关问题大小效应的加工机制存在两类不同的解释。初期的提取理论认为,问题大小效应是由算术知识的储存表征的各种特征所决定的。后期研究开始关注如计数、分解这样的非提取策略在问题大小效应形成中的作用,认为大问题任务中更低的提取效率和非提取加工效率以及更多采用非提取策略都会造成算术任务的问题大小效应。由于加法和减法中使用的各种加工策略的比重不同,所以表现为不同形式的问题大小效应。今后研究应该考虑采用不同的研究手段,并统一划分大问题和小问题的标准     

An evaluation of sex and cultural differences in arithmetic retrieval-induced forgetting

Retrieval practice of arithmetic facts (e.g. 2?×?3) can interfere with retrieval of other, closely related arithmetic facts (e.g. 2?+?3), increasing response time (RT) and errors for these problems. Here we examined potential sex and culture-related differences in arithmetic retrieval-induced forgetting (RIF). This was motivated by re-analyses of several published arithmetic RIF data sets that appeared to show that the effect occurred for women but not men. Experiment 1 (n?=?72) tested for possible sex differences in a diverse but predominantly Canadian university sample. Experiment 2 (n?=?48) examined potential sex differences in native Chinese participants, which previous research indicated may not be susceptible to the RIF effect for a particular subset of small addition problems (sum?≤?10). In Experiment 1, we found no evidence that the addition RIF effect differed between male and female adults. In Experiment 2, the Chinese adults showed RIF for tie problems (e.g. 2?+?2, 3?+?3, etc.) regardless of sex, but neither sex presented RIF for small non-tie addition problems. The results indicated that the RIF effect is not gender specific, and there might not be strong memory retrieval competition between addition and multiplication facts for non-tie problems in Chinese adults.     

The effect of culture on perspective taking

People consider the mental states of other people to understand their actions. We evaluated whether such perspective taking is culture dependent. People in collectivistic cultures (e.g., China) are said to have interdependent selves, whereas people in individualistic cultures (e.g., the United States) are said to have independent selves. To evaluate the effect of culture, we asked Chinese and American pairs to play a communication game that required perspective taking. Eye-gaze measures demonstrated that the Chinese participants were more tuned into their partner's perspective than were the American participants. Moreover, Americans often completely failed to take the perspective of their partner, whereas Chinese almost never did. We conclude that cultural patterns of interdependence focus attention on the other, causing Chinese to be better perspective takers than Americans. Although members of both cultures are able to distinguish between their perspective and another person's perspective, cultural patterns afford Chinese the effective use of this ability to interpret other people's actions.     

心理学视野下的社会变迁研究：研究设计与分析方法

近年来,社会变迁导致的文化、心理与行为变化及其相互建构已经成为心理学的研究热点。社会变迁研究通常涉及和变迁相关的时间效应、时代效应以及和变迁无关的年龄效应。在考察变迁趋势及其影响因素时,常用的研究设计有跨时间比较、跨代际比较、跨地区比较(历史重构)等方法;常用的分析方法有传统的相关和回归分析和现代的时间序列分析(比如交叉滞后相关和格兰杰因果检验)等。由于每一种设计都有其优点和不足,在具体研究中,研究者要根据研究的问题和可操作性选择合适的方法;如果可能,最好同时采用多种方法,以寻求基于不同方法的聚合证据。     

Sequential modulations of logical-recoding operations in the Simon task

The Simon effect consists of faster responses to the color (or another nonspatial feature) of spatially corresponding stimuli than to spatially noncorresponding stimuli. Recently, several studies observed the Simon effect after corresponding predecessor trials, but not after noncorresponding predecessor trials. To explain these sequential modulations, Stürmer et al. (2002) proposed a mechanism modulating the ability of stimulus position to automatically activate a response. The present study investigated which events are effectively triggering this mechanism in a variant of the Simon task, in which both stimuli and responses varied in color (participants wore colored gloves) as well as in horizontal position. In the same-color task (e.g., green stimulus-green response), a normal Simon effect showed up after corresponding trials, but no effect occurred after noncorresponding trials. In the alternate-color task (e.g., green stimulus-red hand), no effect occurred after spatially corresponding trials, whereas an inverted Simon effect was found after noncorresponding trials. Additional analyses showed that repetition (or alternation) effects did not affect the results. The results are discussed in terms of a conflict-monitoring account (Stürmer et al., 2002), and in terms of a feature-integration account (Hommel et al., 2002).     

Culture and state boredom: A comparison between European Canadians and Chinese

The primary goal of the present research was to examine cross-cultural validity of the Multidimensional State Boredom Scale (MSBS) by comparing a European Canadian sample and a Chinese sample. The secondary goal was to explore cross-cultural differences in the actual experience of boredom between European Canadian and Chinese participants when they completed a psychological survey. After establishing cross-cultural validity of the MSBS by eliminating items that functioned differentially across the two cultural groups, we found that European Canadians scored higher on the MSBS than did Chinese. Results are consistent with the literature on cultural differences in ideal affect, such that European North Americans (vs. East Asians) tend to value high-arousal positive affects (e.g., excitement) more, and low-arousal positive affect less (Tsai, Knutson, & Fung, 2006).     

A Framework for Explaining Aggression Involving Groups

Aggression involving groups (versus individuals) can be particularly severe (e.g., hazings). Although an impressive amount of experimental research on the aggression of individuals exists, relatively less experimental research on aggression involving groups exists. We use existing theories of aggression and the available research to present a framework of aggression when groups are involved. We propose a provisional model that suggests that the extent of aggression to be committed depends on the composition of both source (i.e., perpetrators – group or individual) and target (i.e., victims – group or individual) entities. Evidence suggests that groups commit and receive more aggression than individuals. We propose that accessible hostile thoughts and the experience of negative affect contribute to the target effect (i.e., more aggression committed toward groups versus individuals), whereas disinhibition processes and arousal contribute to the source effect (i.e., more aggression committed by groups versus individuals). Our framework can guide future theory and research on aggression involving groups.