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.     

Observation of Depictive Versus Tracing Gestures Selectively Aids Verbal Versus Visual–Spatial Learning in Primary School Children

Previous research has established that gesture observation aids learning in children. The current study examined whether observation of gestures (i.e. depictive and tracing gestures) differentially affected verbal and visual–spatial retention when learning a route and its street names. Specifically, we explored whether children (n = 97) with lower visual and verbal working‐memory capacity benefited more from observing gestures as compared with children who score higher on these traits. To this end, 11‐ to 13‐year‐old children were presented with an instructional video of a route containing no gestures, depictive gestures, tracing gestures or both depictive and tracing gestures. Results indicated that the type of observed gesture affected performance: Observing tracing gestures or both tracing and depictive gestures increased performance on route retention, while observing depictive gestures or both depictive and tracing gestures increased performance on street name retention. These effects were not differentially affected by working‐memory capacity. Copyright © 2016 John Wiley & Sons, Ltd.     

Using aptitude measurements for the optimal assignment of subjects to treatments with and without mastery scores

For assigning subjects to treatments the point of intersection of within-group regression lines is ordinarily used as the critical point. This decision rule is critized and, for several utility functions and any number of treatments, replaced by optimal monotone, nonrandomized (Bayes) rules. Both treatments with and without mastery scores are considered. Moreover, the effect of unreliable criterion scores on the optimal decision rule is examined, and it is illustrated how qualitative information can be combined with aptitude measurements to improve treatment assignment decisions. Although the models in this paper are presented with special reference to the aptitude-treatment interaction problem in education, it is indicated that they apply to a variety of situations in which subjects are assigned to treatments on the basis of some predictor score, as long as there are no allocation quota considerations.     

An efficient algorithm for PARAFAC of three-way data with large numbers of observation units

The CANDECOMP algorithm for the PARAFAC analysis ofn×m×p three-way arrays is adapted to handle arrays in whichn>mp more efficiently. For such arrays, the adapted algorithm needs less memory space to store the data during the iterations, and uses less computation time than the original CANDECOMP algorithm. The size of the arrays that can be handled by the new algorithm is in no way limited by the number of observation units (n) in the data.The authors are obliged to Jos ten Berge for his comments on an earlier version of this paper. The research of Henk A. L. Kiers has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.     

Similarity of attitudes and instrumentality as determinants of aggression by policemen

The influences of two determinants of aggression were investigated by means of a two by two factorial design. Aggression was operationally defined in terms of the amount and intensity of obnoxious sounds which the subject delivered to the confederate while the latter was trying to perform a task involving estimation of distances. In order to manipulate the first independent variable one half of the group of subjects were led to believe that the victim was someone who had many attitudes similar to their own. The other subjects thought they had to cope with a partner whose attitudes were dissimilar. The second independent variable was manipulated by suggesting to one half of the group of subjects that they would be able to earn increasing sums of money (up to a fixed maximum) depending on the loudness of sounds they were prepared to deliver to their partner. In the non-reward condition money was not mentioned. The subjects were young policemen. The data showed a strong effect of the similarity variable, with significantly more aggression being shown to a dissimilar partner. However, external reward did not lead to a clear increase of aggression. In the discussion attention is given to the relevance of these data to the problem of control of violence in our society.     

Compathy or Physical Empathy: Implications for the Caregiver Relationship

In this article a case is made for the importance of a previously overlooked phenomenon, physical empathy orcompathy,defined as the physical manifestation of caregiver distress that occurs in the presence of a patient in physical pain or distress. According to the similarity of a caregiver's response to the original symptoms, there can be four types of compathetic response: identical, initiated, transferred, and converted. Controlling for the compathetic response may involve narrowing one's focus and/or changing caregiver attitudes. Finally, we argue that while the compathetic response may be beneficial to the caregiving relationship, enabling the provision of appropriate and adequate humane treatment and care, the caregiver must at times shield against the compathetic response in order to provide care.     

Co‐thought gestures in children's mental problem solving: Prevalence and effects on subsequent performance

Co‐thought gestures are understudied as compared to co‐speech gestures yet, may provide insight into cognitive functions of gestures that are independent of speech processes. A recent study with adults showed that co‐thought gesticulation occurred spontaneously during mental preparation of problem solving. Moreover, co‐thought gesturing (either spontaneous or instructed) during mental preparation was effective for subsequent solving of the Tower of Hanoi under conditions of high cognitive load (i.e., when visual working memory capacity was limited and when the task was more difficult). In this preregistered study ( https://osf.io/dreks/ ), we investigated whether co‐thought gestures would also spontaneously occur and would aid problem‐solving processes in children (N = 74; 8–12 years old) under high load conditions. Although children also spontaneously used co‐thought gestures during mental problem solving, this did not aid their subsequent performance when physically solving the problem. If these null results are on track, co‐thought gesture effects may be different in adults and children.     

Are Arabic numerals processed as pictures in a Stroop interference task?

In a picture-word interference task, picture naming is interfered by an incongruent word, but word naming is hardly hindered by the presence of an incongruent picture. In this study, we investigated whether Arabic digits are processed more like pictures or like words. We report two experiments in which Arabic digits and verbal numerals were confronted in a Stroop task. Arabic digit naming is interfered by the presence of an incongruent verbal numeral, while naming the verbal numeral is not influenced by the presence of an incongruent Arabic digit. In a second experiment, we excluded the hypothesis that the results are due to ignoring the Arabic digits: interferences from an incongruent distracter were similar for both notations in a semantic classification task. It seems that an asemantic conversion for Arabic digits is too slow to influence naming times, and that Arabic digit naming, like picture naming, is semantically mediated.     

Multidimensional Adaptive Testing with Optimal Design Criteria for Item Selection

Several criteria from the optimal design literature are examined for use with item selection in multidimensional adaptive testing. In particular, it is examined what criteria are appropriate for adaptive testing in which all abilities are intentional, some should be considered as a nuisance, or the interest is in the testing of a composite of the abilities. Both the theoretical analyses and the studies of simulated data in this paper suggest that the criteria of A-optimality and D-optimality lead to the most accurate estimates when all abilities are intentional, with the former slightly outperforming the latter. The criterion of E-optimality showed occasional erratic behavior for this case of adaptive testing, and its use is not recommended. If some of the abilities are nuisances, application of the criterion of A _s -optimality (or D _s -optimality), which focuses on the subset of intentional abilities is recommended. For the measurement of a linear combination of abilities, the criterion of c-optimality yielded the best results. The preferences of each of these criteria for items with specific patterns of parameter values was also assessed. It was found that the criteria differed mainly in their preferences of items with different patterns of values for their discrimination parameters. The first author is now at the Department of Methodology and Statistics, Statistics, Faculty of Social Sciences, Utrecht University, Heidelberglaan 1, 3854 Utrecht, The Netherlands. The second author is now at Research Department, CTB/McGraw-Hill, Monterey, CA, USA.