Mapping numerical magnitudes onto symbols: the numerical distance effect and individual differences in children's mathematics achievement

Although it is often assumed that abilities that reflect basic numerical understanding, such as numerical comparison, are related to children’s mathematical abilities, this relationship has not been tested rigorously. In addition, the extent to which symbolic and nonsymbolic number processing play differential roles in this relationship is not yet understood. To address these questions, we collected mathematics achievement measures from 6- to 8-year-olds as well as reaction times from a numerical comparison task. Using the reaction times, we calculated the size of the numerical distance effect exhibited by each child. In a correlational analysis, we found that the individual differences in the distance effect were related to mathematics achievement but not to reading achievement. This relationship was found to be specific to symbolic numerical comparison. Implications for the role of basic numerical competency and the role of accessing numerical magnitude information from Arabic numerals for the development of mathematical skills and their impairment are discussed.     

The predictive value of numerical magnitude comparison for individual differences in mathematics achievement

Although it has been proposed that the ability to compare numerical magnitudes is related to mathematics achievement, it is not clear whether this ability predicts individual differences in later mathematics achievement. The current study addressed this question in typically developing children by means of a longitudinal design that examined the relationship between a number comparison task assessed at the start of formal schooling (mean age = 6 years 4 months) and a general mathematics achievement test administered 1 year later. Our findings provide longitudinal evidence that the size of the individual’s distance effect, calculated on the basis of reaction times, was predictively related to mathematics achievement. Regression analyses showed that this association was independent of age, intellectual ability, and speed of number identification.     

The Numerical Stroop Effect in Primary School Children: A Comparison of Low,Normal, and High Achievers

Sixty-six primary school children were selected, of which 21 scored low on a standardized math achievement test, 23 were normal, and 22 high achievers. In a numerical Stroop experiment, children were asked to make numerical and physical size comparisons on digit pairs. The effects of congruity and numerical distance were determined. All children exhibited congruity and distance effects in the numerical comparison. In the physical comparison, children of all performance groups showed Stroop effects when the numerical distance between the digits was large but failed to show them when the distance was small. Numerical distance effects depended on the congruity condition, with a typical effect of distance in the congruent, and a reversed distance effect in the incongruent condition. Our results are hard to reconcile with theories that suggest that deficits in the automaticity of numerical processing can be related to differential math achievement levels. Immaturity in the precision of mappings between numbers and their numerical magnitudes might be better suited to explain the Stroop effects in children. However, as the results for the high achievers demonstrate, in addition to numerical processing capacity per se, domain-general functions might play a crucial role in Stroop performance, too.     

Numerical comparison of two-digit numbers: How differences at encoding can involve differences in processing

The study of two-digit numbers processing has recently gathered a growing interest. Here, we examine whether differences at encoding of two-digit oral verbal numerals induce differences in the type of processing involved. Twenty-four participants were submitted to a comparison task to 55. Differences at encoding were introduced by the use of dichotic listening and synchronous (synchronous condition) or asynchronous presentation (tens-first and units-first conditions) of the two-digit numerals' components. Our results showed that differences at the encoding stage of two-digit numerals involve: (1) different comparison processes (tens-first and units-first conditions: parallel comparison; synchronous condition: parallel and holistic comparison); and (2) differences in the weight of the tens- and units-effects. Therefore, attentional mechanisms determining at the encoding stage how much attention is paid to the two-digit numerals' components might account for the different types of processing found with two-digit numbers.     

An electro-physiological temporal principal component analysis of processing stages of number comparison in developmental dyscalculia

Developmental dyscalculia (DD) still lacks a generally accepted definition. A major problem is that the cognitive component processes contributing to arithmetic performance are still poorly defined. By a reanalysis of our previous event-related brain potential (ERP) data (Soltész et al., 2007) here our objective was to identify and compare cognitive processes in adolescents with DD and in matched control participants in one-digit number comparison. To this end we used temporal principal component analysis (PCA) on ERP data. First, PCA has identified four major components explaining the 85.8% of the variance in number comparison. Second, the ERP correlate of the most frequently used marker of the so-called magnitude representation, the numerical distance effect, was intact in DD during all processing stages identified by PCA. Third, hemispheric differences in the first temporal component and group differences in the second temporal component suggest executive control differences between DD and controls.     

Intentional and automatic processing of numerical information in mathematical anxiety: testing the influence of emotional priming

ABSTRACT

Current theoretical approaches suggest that mathematical anxiety (MA) manifests itself as a weakness in quantity manipulations. This study is the first to examine automatic versus intentional processing of numerical information using the numerical Stroop paradigm in participants with high MA. To manipulate anxiety levels, we combined the numerical Stroop task with an affective priming paradigm. We took a group of college students with high MA and compared their performance to a group of participants with low MA. Under low anxiety conditions (neutral priming), participants with high MA showed relatively intact number processing abilities. However, under high anxiety conditions (mathematical priming), participants with high MA showed (1) higher processing of the non-numerical irrelevant information, which aligns with the theoretical view regarding deficits in selective attention in anxiety and (2) an abnormal numerical distance effect. These results demonstrate that abnormal, basic numerical processing in MA is context related.     

Beyond quantity: Individual differences in working memory and the ordinal understanding of numerical symbols

In two different contexts, we examined the hypothesis that individual differences in working memory (WM) capacity are related to the tendency to infer complex, ordinal relationships between numerical symbols. In Experiment 1, we assessed whether this tendency arises in a learning context that involves mapping novel symbols to quantities by training adult participants to associate dot-quantities with novel symbols, the overall relative order of which had to be inferred. Performance was best for participants who were higher in WM capacity (HWMs). HWMs also learned ordinal information about the symbols that lower WM individuals (LWMs) did not. In Experiment 2, we examined whether WM relates to performance when participants are explicitly instructed to make numerical order judgments about highly enculturated numerical symbols by having participants indicate whether sets of three Arabic numerals were in increasing order. All participants responded faster when sequential sets (3-4-5) were in order than when they were not. However, only HWMs responded faster when non-sequential, patterned sets (1-3-5) were in order, suggesting they were accessing ordinal associations that LWMs were not. Taken together, these experiments indicate that WM capacity plays a key role in extending symbolic number representations beyond their quantity referents to include symbol-symbol ordinal associations, both in a learning context and in terms of explicitly accessing ordinal relationships in highly enculturated stimuli.     

Evidence for conditional sex differences in emotional but not in sexual jealousy at the automatic level of cognitive processing

The two evolutionary psychological hypotheses that men react more jealous than women to sexual infidelity and women react more jealous than men to emotional infidelity are currently controversial because of apparently inconsistent results. We suggest that these inconsistencies can be resolved when the two hypotheses are evaluated separately and when the underlying cognitive processes are considered. We studied jealousy with forced‐choice decisions and emotion ratings in a general population sample of 284 adults aged 20–30 years using six infidelity dilemmas and recordings of reaction times. The sex difference for emotional jealousy existed for decisions under cognitive constraint, was also evident in the decision speed, increased for faster decisions, and was stronger for participants with lower education. No evidence for a sex difference in sexual jealousy was found. Our results support the view of a specific female sensitivity to emotional infidelity that canalizes the development of an adaptive sex difference in emotional jealousy conditional to the sociocultural environment. Copyright © 2007 John Wiley & Sons, Ltd.     

Individual differences in self-attributed mindfulness levels are related to the experience of time and cognitive self-control

The objective of this correlational study was to investigate how dispositional mindfulness is related to the experience of time as operationalized by the assessment of the time perspectives, impulsiveness, and duration judgment tasks. A sample of students (N = 63) completed self-report measures of mindfulness (FMI, CHIME), the time perspectives (ZTPI), impulsiveness (BIS), conducted psychophysical tasks of (a) auditory duration discrimination in the milliseconds range, (b) visual duration reproduction in the multiple-second range, and performed an attention task, the Attention Network Test. Being more mindful in daily life was related to less impulsiveness, better emotional handling of the past, and a more pronounced future perspective. Mindfulness was also related to more accurate timing in the milliseconds and multiple-seconds range but not to attentional control. These findings suggest a close association between dispositional mindfulness with the temporal organization of behaviour and the perception of time.     

Social motivation and the use of distal,but not local,featural cues are related to ranging behavior in free-range chickens (Gallus gallus domesticus)

Animal Cognition - Animals can navigate an environment relying on different sources of information, such as geometrical or featural cues. The favoring of one type of information over another...     

In all questions, my interest is not in the individual people but in the analytic movement as a whole. It will be hard enough here in Europe in the times to come to keep it going. After all, we are just a handful of people who really have that in mind

The paper tries to deal with the difficult and at times contradictory decisions that the then leaders of the IPA, S. Freud, A. Freud, E. Jones etc. had to adopt as whether or not to clearly inform the readers of Die Internationale Zeitschrift für Psychoanalyse and the International Journal of Psychoanalysis, the official scientific periodicals of the IPA, of the tragic events concerning first the German Psychoanalytic Society and then the Vienna Psychoanalytic Society and the newborn Italian Psychoanalytic Society and other European psychoanalytic societies during the years 1933-1945. Because of the anti-Jewish persecution by the Nazi and fascist regimes the IPA had to face the extremely difficult task of helping its Continental Jewish members to emigrate to the USA, Great Britain and other countries in order to save their lives and to allow psychoanalysis to survive, with enormous radical consequences for the scientific and sociocultural future developments of the discipline.The following notes are dedicated to those non-Aryans and Aryans who could not find a proper rescue and whose graves became the wind which scattered the ashes of their bodies with the smoke coming out of the chimneys of the Nazi gas chambers.