Assessing the Approximate Number System: no relation between numerical comparison and estimation tasks

Whether our general numerical skills and the mathematical knowledge that we acquire at school are entwined is a debated issue, which many researchers are still striving to investigate. The findings reported in the literature are actually inconsistent; some studies emphasized the existence of a relationship between the acuity of the Approximate Number System (ANS) and arithmetic competence, while some others did not observe any significant correlation. One potential explanation of the discrepancy might stem from the evaluation of the ANS itself. In the present study, we correlated two measures used to index ANS acuity with arithmetic performance. These measures were the Weber fraction (w), computed from a numerical comparison task and the coefficient of variation (CV), computed from a numerical estimation task. Arithmetic performance correlated with estimation CV but not with comparison w. We further investigated the meaning of this result by taking the relationship between w and CV into account. We expected a tight relation as both these measures are believed to assess ANS acuity. Crucially, however, w and CV did not correlate with each other. Moreover, the value of w was modulated by the congruity of the relation between numerical magnitude and non-numerical visual cues, potentially accounting for the lack of correlation between the measures. Our findings thus challenge the overuse of w to assess ANS acuity and more generally put into question the relevance of correlating this measure with arithmetic without any deeper understanding of what they are really indexing.     

Beyond left and right: Automaticity and flexibility of number-space associations

Close links exist between the processing of numbers and the processing of space: relatively small numbers are preferentially associated with a left-sided response while relatively large numbers are associated with a right-sided response (the SNARC effect). Previous work demonstrated that the SNARC effect is triggered in an automatic manner and is highly flexible. Besides the left-right dimension, numbers associate with other spatial response mappings such as close/far responses, where small numbers are associated with a close response and large numbers with a far response. In two experiments we investigate the nature of this association. Associations between magnitude and close/far responses were observed using a magnitude-irrelevant task (Experiment 1: automaticity) and using a variable referent task (Experiment 2: flexibility). While drawing a strong parallel between both response mappings, the present results are also informative with regard to the question about what type of processing mechanism underlies both the SNARC effect and the association between numerical magnitude and close/far response locations.     

Look,no hands: A perceptual task shows that number magnitude induces shifts of attention

The mental representation of numbers along a line oriented left to right affects spatial cognition, facilitating responses in the ipsilateral hemispace (the spatial-numerical association of response codes [SNARC] effect). We investigated whether the number/space association is the result of an attentional shift or response selection. Previous research has often introduced covert left/right response cues by presenting targets to the left or the right. The present study avoided left/right cues by requiring forced choice upper/lower luminance discriminations to two mirror-reversed luminance gradients (the grayscale task). The grayscale stimuli were overlaid with strings of (1) low numbers, (2) high numbers, and (3) nonnumerical characters. In Experiment 1, 20 dextrals judged the number’s magnitude and then indicated whether the upper/lower grayscale was darker. Results showed leftward and rightward attentional biases for low and high numbers, respectively. Demands to process numbers along a left/right line were made less explicit in Experiment 2 (N=8 dextrals), using (1) a parity judgment and (2) arbitrary linguistic labels for top/bottom. Once again, a spatial congruency effect was observed. Because the response (up/down) was orthogonal to the dimension of interest (left/right), the effect of number cannot be attributed to late-stage response congruencies. This study required unspeeded responses to stimuli presented in free vision, whereas other experiments have used speeded responses. Understanding the time course of number-space effects may, therefore, be important to the debate associated with response selection.     

Hemispatial neglect and serial order in verbal working memory

Working memory refers to our ability to actively maintain and process a limited amount of information during a brief period of time. Often, not only the information itself but also its serial order is crucial for good task performance. It was recently proposed that serial order is grounded in spatial cognition. Here, we compared performance of a group of right hemisphere-damaged patients with hemispatial neglect to healthy controls in verbal working memory tasks. Participants memorized sequences of consonants at span level and had to judge whether a target consonant belonged to the memorized sequence (item task) or whether a pair of consonants were presented in the same order as in the memorized sequence (order task). In line with this idea that serial order is grounded in spatial cognition, we found that neglect patients made significantly more errors in the order task than in the item task compared to healthy controls. Furthermore, this deficit seemed functionally related to neglect severity and was more frequently observed following right posterior brain damage. Interestingly, this specific impairment for serial order in verbal working memory was not lateralized. We advance the hypotheses of a potential contribution to the deficit of serial order in neglect patients of either or both (1) reduced spatial working memory capacity that enables to keep track of the spatial codes that provide memorized items with a positional context, (2) a spatial compression of these codes in the intact representational space.     

Well-Being,Personal Success and Business Performance Among Entrepreneurs: A Two-Wave Study

This two-wave longitudinal study among 121 entrepreneurs in The Netherlands investigated bi-directional relationships between entrepreneurs’ well-being and performance. Results of Smart PLS analyses showed positive well-being at Time 1 (work engagement; life satisfaction; and job satisfaction) predicted subjective entrepreneurial success 2 years later, both as indicated by entrepreneurs’ reports of achieved financial success (including personal income security and wealth, business turn-over, sales and profit growth), as well as perceptions of achieved personal success (personal fulfilment, community impact and employee relations). No relations were found with objective indicators of business performance (profit; turnover; and number of employees) over time. The expected recursive relationship between performance and well-being was only found in the short term; a better objective financial situation immediately preceding the second measurement moment, predicted better well-being at T2. These results are both in line with a well-being–performance (gain) cycle, and the happiness set-point thesis that predicts resilience in the face of events. This paper contributes to the literature by emphasizing the importance of entrepreneurs’ well-being as a key factor in long-term subjective financial and personal entrepreneurial success. The practical implication is that entrepreneurs should maintain and improve their own well-being to achieve positive long term business outcomes.     

Sex roles and fertility in college women

A study was conducted to examine the relationship of sex-role acceptance to actual and desired fertility. Two samples of women (105 undergraduates and 40 members of a women's organization) were administered the Bem Sex-Role Inventory and a questionnaire which assessed the women's behavioral acceptance of traditional female sex roles. The behavioral measures were sex-typed college major for the undergraduates and employment status for the women's organization sample. In addition, vocational interests were measured and related to fertility for the women's organization sample. Multiple regression analyses indicated that behavioral measures of sex-role acceptance accounted for more variance in predicting desired and actual fertility than did the Bem Sex-Role Inventory.     

Divergent effects of detachment from work: a day-level study on employee creativity

Detachment from work during non-work time is generally related to a decrease in work-related strain. However, it might also hamper employees’ generation of new and useful ideas about work by completely shutting off work-related thoughts and/or feelings outside of work. In this day-level study, we used a within-person design to investigate the role of cognitive and emotional detachment from work during non-work time in relation to equivalent types of job demands and job resources, in the prediction of employee creativity. Cognitive detachment from work refers to mentally disconnecting from work and no longer thinking about job-related issues, whereas emotional detachment from work refers to affectively disconnecting from work and no longer experiencing job-related emotions. Survey data were gathered over the course of eight consecutive days from 151 health care employees. Multi-level analyses revealed that: (1) cognitive detachment was positively related to creativity, irrespective of the level of cognitive job demands and resources; (2) high emotional job demands in combination with either low levels of emotional detachment or high levels of emotional job resources were positively related to creativity. This day-level study provides insight into the relation between detachment from work and creativity from a process perspective, by showing specific conditions under which different types of detachment from work benefit employee creativity.     

Roman digit naming: evidence for a semantic route

Earlier research with monolinguals and bilinguals showed that numbers may be named through both a semantic and a phonological route, depending on the number's language and format (Arabic or verbal), task demands, and naming language. The present study investigated the importance of the semantic route for the processing of a third representation of magnitude, namely Roman digits. Using an interference paradigm, we showed that the processing of Roman target digits is influenced by Arabic digit distractors, both in a naming task and a parity judgment task. Roman digits were processed faster if the target and distractor were of the same magnitude. If this was not the case, processing speed slowed down as the numerical distance between target and distractor increased. This strongly suggests that semantic access is mandatory when naming Roman digits. Implications are discussed for the number processing domain and for models of translation in bilinguals.     

The SNARC effect does not imply a mental number line

In this study, we directly contrast two approaches that have been proposed to explain the SNARC effect. The traditional direct mapping account suggests that a direct association exists between the position of a number on the mental number line and the location of the response. On the other hand, accounts are considered that propose an intermediate step in which numbers are categorized as either small or large between the number magnitude and the response representations. In a magnitude comparison task, we departed from the usual bimanual left/right response dimension and instead introduced the unimanual close/far dimension. A spatial-numerical association was observed: small numbers were associated with a close response, while large numbers were associated with a far response, regardless of the movement direction (left/right). We discuss why these results cannot be explained by assuming a direct mapping from the representation of numbers on a mental number line to response locations and discuss how the results can be explained by the alternative accounts.     

Child care under pressure: the quality of Dutch centers in 1995 and in 2001

In 2001, the authors assessed the quality of care provided to children in 51 care groups from 39 child-care centers in The Netherlands using the Infant/Toddler Environment Rating Scale (T. Harms, D. Cryer, & R. M. Clifford, 1990) and compared the results with the quality of child care assessed in 1995 (M. H. van IJzendoorn, L. W. C. Tavecchio, G. J. Stams, M. J. E. Verhoeven, & E. J. Reiling, 1998). The overall quality and scale scores for language and learning activities were significantly lower in 2001 than in 1995. Child-care centers founded within the past 6 years (all nonsubsidized centers) scored considerably lower than did older, mostly subsidized, centers. The results are discussed from the perspective of changes in the socioeconomic and political context of child care.