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We assessed whether the negative association between maternal postpartum depression (PPD) and infants' development of joint attention (gaze following) generalizes from WEIRD (Western, Educated, Industrialized, Rich, and Democratic) to Majority World contexts. The study was conducted in Bhutan (

Attentional control in infancy has been postulated as foundational for self-regulation later in life. However, the empirical evidence supporting this claim is inconsistent. In the current study, we examined the longitudinal data from a sample of Swedish infants (6, 10, and 18 months

During the first 2 years of life, an infant's vocabulary grows at an impressive rate. In the current study, we investigated the impact of three challenges that infants need to overcome to learn new words and expand the size of their vocabulary. We used longitudinal eye-tracking data (n = 118) to assess sequence learning, associative learning, and probability processing abilities at ages 6, 10, and 18 months. Infants' ability to efficiently solve these tasks was used to predict vocabulary size at age 18 months. We demonstrate that the ability to make audio-visual associations and to predict sequences of visual events predicts vocabulary size in toddlers (accounting for 20% of the variance). Our results indicate that statistical learning in some, but not all, domains have a role in vocabulary development.

In this novel study, we have used pupillometry to investigate if maths anxiety (MA) moderates the effect of difficulty level on cognitive effort in second-grade primary school children. Proficiency in mathematics is essential in today's society. Yet, a large number of people do not possess adequate skills in mathematics. Although there may be different reasons for low maths skills, one phenomenon that is consistently associated with low maths performance (MP) is MA. This negative relationship between MA and MP is sometimes explained by a negative effect of MA on working memory (WM) capacity, but the underlying mechanisms are still very much unknown. Previous studies have shown that pupil dilation is a valid measure of various forms of cognitive effort, providing a basis for pupil dilation as a measure of WM capacity being employed during arithmetic problem-solving. Using pupil dilation as a measure of cognitive effort, 98 second-grade pupils from 12 classrooms in public primary schools in an urban area in Norway solved addition problems presented on a computer screen while an eye tracker recorded their pupil size. In addition to measures of MA and cognitive effort, we also measured arithmetic skills, WM and general intelligence. The results of our linear mixed model analysis suggest that individuals with higher MA utilise relatively more cognitive effort compared to their low MA peers, even after controlling for arithmetic skills, WM and general intelligence, strengthening the assumption that MA negatively affects MP by occupying the WM capacity needed for problem-solving.

This study investigated the developmental trajectories and interrelationships of mathematics-related achieve-ment emotions and arithmetic fluency from first to third grade, and the effects of these on third grade mathe-matics performance. Participants were 232 Norwegian students. Students' emotions and arithmetic fluency were measured four times and mathematics performance once. Applying latent growth curve modeling, developmental patterns of decreasing enjoyment and increasing boredom were observed over time. The mean level of enjoyment remained fairly high, and of both boredom and anxiety quite low. Individual differences were observed in both the initial levels and development of all emotions and arithmetic fluency, indicating differences in developmental trajectories. Only the initial levels and rate of change in arithmetic fluency predicted mathematics performance at the third grade.

The ability to perceive approximate numerosity is present in many animal species, and emerges early in human infants. Later in life, it is moderately heritable and associated with mathematical abilities, but the etiology of the Approximate Number System (ANS) and its degree of independence from other cognitive abilities in infancy is unknown. Here, we assessed the phenotypic specificity as well as the influence of genetic and environmental factors on the ANS in a sample of 5-month-old twins (N = 514). We found a small-to-moderate but statistically significant effects of genetic factors on ANS acuity (heritability = 0.18, 95% CI: 0.02, 0.33), but only when differences in numerosity were relatively large (1:4 ratio). Non-verbal ability assessed with the Mullen Scales of Early Learning (MSEL) was found to be heritable (0.47; 95% CI: 0.34, 0.57) and the phenotypic association between ANS acuity and non-verbal ability performance was close to zero. Similarly, we found no association between ANS acuity and general attention during the task. An unexpected weak but statistically significant negative association between ANS auity and scores on the receptive language scale of the MSEL was found. These results suggest that early ANS function may be largely independent from other aspects of non-verbal development. Further, variability in ANS in infancy seems to, to some extent, reflect genotypic differences in the population. Assessing 514 infant twins with eye tracking, we found that infant’s sense of approximate numerosity is heritable and not positively associated with concurrent attentional, cognitive or motor abilities. These results have implications for our understanding of development of mathematical ability and the link between cognitive abilities early in postnatal life.

Key issues in the behavioral sciences are if there exist stable risk preferences that generalize across domains and if these are best measured by revealed risk preference (RRP) in behavioral decisi ...

A negative relationship between mathematics anxiety (MA) and mathematics performance is well documented. One suggested explanation for this relationship is that MA interferes with the cognitive processes needed when solving mathematics problems. A demand for using more cognitive effort (e.g., when performing harder mathematics problems), can be traced as an increase in pupil dilation during the performance. However, we lack knowledge of how MA affects this relationship between the problem difficulty and cognitive effort. This study investigated, for the first time, whether MA moderates the effect of arithmetic (i.e., multiplication) problem difficulty on cognitive effort. Thirty-four university students from Norway completed multiplication tasks, including three difficulty levels of problems, while their cognitive effort was also measured by means of pupil dilation using an eyetracker. Further, the participants reported their MA using a questionnaire, and arithmetic competence, general intelligence, and working memory were measured with paper-pencil tasks. A linear mixed model analysis showed that the difficulty level of the multiplication problems affected the cognitive effort, so that the pupil dilated more with harder multiplication problems. However, we did not find a moderating effect of MA on cognitive effort, when controlling for arithmetic competence, general intelligence, and working memory. This suggests that MA does not contribute to cognitive effort when solving multiplication problems.

We assess fluid intelligence of 6–18 year-old children growing up in families that have fled from Syria and reside in Turkish communities (100 families, 394 individuals). We demonstrate that fluid intelligence of refugee children is related to maternal fluid intelligence and to the amount of time mothers spend reading to their child. These factors stood out in the analysis even when controlling for a large range of other factors such as demographics, parental mental health, parental fluid intelligence, home environment, and a large array of potential enrichment factors.

From planning daily activities with close others to passively overhearing a stranger’s conversation on the bus, humans spend roughly half of their waking life in the presence of other humans (US Bureau of Labor Statistics, 2003-2016). These social interactions constitute the source of a large proportion of the information that individuals gather on a daily basis. At the same time, people are often limited to only a small portion of information, or samples, in relation to all the possible information made available during a social experience (Ambady & Rosenthal, 1993; Fiedler, 2000). The fundamental question guiding this chapter is how group-motivated sampling of social information facilitates biased evaluations.

Poor maternal mental health negatively impacts cognitive development from infancy to childhood, affecting both behavior and brain architecture. In a non-western context (Thimphu, Bhutan), we demonstrate that culturally-moderated factors such as family, community social support, and enrichment may buffer and scaffold the development of infant cognition when maternal mental health is poor. We used eye-tracking to measure early building blocks of cognition: attention regulation and social perception, in 9-month-old Bhutanese infants (N = 121). The cognitive development of Bhutanese infants in richer social environments was buffered from poor maternal mental health, while for infants in environments with lower rates of protective social environment factors, worse maternal mental health significantly predicted greater costs for infant attention, a fundamental building block cognition. International policies and interventions geared to improve maternal mental health and child health outcomes should incorporate each regions’ unique family, cultural, and community support structures.

Stressful experiences in armed conflict incur intergenerational effects through parental behaviors with their children. A recent study reported that among Syrian refugee families, mothers’ (but not fathers’) post-traumatic stress (PTS) impacted children’s emotional processing. In this study, we aim to shed further light on this phenomenon by analyzing how the parenting practices in the context of post-traumatic stress confers protection or risk for children’s emotional processing. Participants were 6–18-year-old children (n = 212) and their mothers (n = 94), who fled from Syria and were residing in Turkish communities. We used the computer-based emotional processing task including photos of facial movements typically associated with different emotions to measure children’s capacity for emotional processing. Mothers reported their PTS and the discipline types they use, as well as the contextual factors related to their refugee background. Linear mixed effect models were constructed first, to find out the discipline types that are most strongly associated with emotional processing of the child, and second, to examine whether these discipline types moderate the effect of maternal PTS on children's emotional processing. Finally, generalized linear models were constructed to examine which contextual factors are associated with the use of these discipline types by mothers. We found that spanking as a discipline type was associated with poorer child emotional processing, whereas withholding of media access was associated with better emotional processing. Younger and less religious mothers were more prone to use spanking. The study underlines the need for parenting programs alongside with efforts to address mental health issues among mothers living under armed conflict.

How do children construct a concept of natural numbers? Past research addressing this question has mainly focused on understanding how children come to acquire the cardinality principle. However, at that point children already understand the first number words and have a rudimentary natural number concept in place. The question therefore remains; what gets children's number learning off the ground? We therefore, based on previous empirical and theoretical work, tested which factors predict the first stages of children's natural number understanding. We assessed if children's expressive vocabulary, visuospatial working memory, and ANS (Approximate number system) acuity at 18 months of age could predict their natural number knowledge at 2.5 years of age. We found that early expressive vocabulary and visuospatial working memory were important for later number knowledge. The results of the current study add to a growing body of literature showing the importance of language in children's learning about numbers.

Maternal distress is repeatedly reported to have negative impacts on the cognitive development in children. Studies examining the association between maternal distress and the development of attention in infancy are few. This study investigated the longitudinal relationships between maternal distress (depressive symptoms, anxiety symptoms, and exposure to childhood trauma) and the development of attention in infancy in 118 mother-infant dyads. We found that maternal exposure to non-interpersonal traumatic events in childhood and a large degree of anxiety during the 2nd trimester was associated with less attention of the infants to audio-visual stimuli at 6, 10, and 18 months. In addition, exposure to interpersonal traumatic events in childhood was identified as a moderator of the negative effect of maternal anxiety during the 2nd trimester on the development of attention in infants. We discuss the possible mechanisms accounting for these cross-generational effects. Our findings underscore the importance of maternal mental health to the development of attention in infancy and address the need for early screening of maternal mental health during pregnancy.

Past research on numerical cognition has suggested that both symbolic and non-symbolic numbers are mapped onto the same compressed mental analogue representation. However, experiments using magnitude estimation tasks show logarithmic compression of symbolic numbers while the compression of non-symbolic numbers has a power-function shape. This warrants closer inspection of what differentiates the two processes. In this study, we hypothesized that estimates of symbolic numbers are systematically shaped by the format in which they are represented, namely, the place value system. To investigate this, we tested adults (N = 188) on a magnitude estimation task with unfamiliar base-26 and base-5 scales. Results reveal that adults showed systematic, logarithmic-looking underestimation on both scales, indicating that the place value system itself can cause the pattern. Additionally, the observed shape of participants’ estimates on both scales could be well explained with a simple model that assumed insufficient understanding of exponential growth (i.e., a characteristic of place value systems). Taken together, our results suggest that the discrepancy between symbolic and non-symbolic number compression can be explained by taking the effect of the place value system into account.

Pervasive congruency effects characterize approximate number discrimination tasks. Performance is better on congruent (the more numerous stimulus consists of objects of larger size that occupy a larger area) than on incongruent (where the opposite holds) items. The congruency effects typically occur when controlling for nonnumeric variables such as cumulative area. Furthermore, only performance on incongruent stimuli seems to predict math abilities. Here, we present evidence for an attentional-bias induced by stimulus control (ABC) where preattentive features such as item size reflexively influence decisions, which can explain these congruency effects. In three experiments, we tested predictions derived from the ABC. In Experiment 1, as predicted, we found that manipulation of size introduced congruency effects and eliminated the correlation with math ability for congruent items. However, performance on incongruent items and neutral, nonmanipulated items were still predictive of math ability. A negative correlation between performance on congruent and incongruent items even indicated that they measure different underlying constructs. Experiment 2 demonstrated, in line with the ABC account, that increasing presentation time reduced congruency effects. By directly measuring overt attention using eye-tracking, Experiment 3 revealed that people direct their first gaze toward the array with items of larger individual size, biasing them towards these arrays. The ABC explains why the relation between performance on approximate number discrimination tasks and math achievement has been fragile and suggests that stimulus control manipulations have contaminated the results. We discuss the importance of using stimuli that are representative of the environment.

We investigated the levels of and changes in mathematics anxiety (MA), symbolic numerical magnitude processing (SNMP) and arithmetic skills, and how those changes are linked to each other. Children's (n = 264) MA, SNMP and arithmetic skills were measured in Grade 1, and again in Grade 2, also including a mathematics performance test. All three constructs correlated significantly within each time point, and the rank-order stability over time was high, particularly in SNMP and arithmetic skills. By means of latent change score modelling, we found overall increases in SNMP and arithmetic skills over time, but not in MA. Most interestingly, changes in arithmetic skills and MA were correlated (i.e. steeper increase in arithmetic skills was linked with less steep increase in MA), as were changes in SNMP and arithmetic skills (i.e. improvement in SNMP was associated with improvement in arithmetic skills). Only the initial level of arithmetic skills and change in it predicted mathematics performance. The only gender difference, in favour of boys, was found in SNMP skills. The differential effects associated with MA (developmentally only linked with arithmetic skills) and gender (predicting only changes in SNMP) call for further longitudinal research on the different domains of mathematical skills.

More than 5.6 million people have fled Syria since 2011, about half of them children. These children grow up with parents that often suffer from war-related mental health problems. In this study, we assess emotional processing abilities of 6–18 year-old children growing up in families that have fled from Syria and reside in Turkish communities (100 families, 394 individuals). We demonstrate that mothers', but not fathers’, post-traumatic stress (PTS) impacts children's emotional processing abilities. A 4% reduction of mothers' PTS was equivalent to 1 year of development in children, even when controlling for parents’ traumatic experiences. Making a small investment in increased mental health of refugee mothers might have a positive impact on the lives of their children.

Item does not contain fulltext Likelihood estimations are crucial for dealing with the uncertainty of life. Here, infants' sensitivity to the difference in likelihood between two events was investigated. Infants aged 6, 12, and 18 months (N = 75) were shown animated movies of a machine simultaneously drawing likely and unlikely samples from a box filled with different colored balls. In different trials, the difference in likelihood between the two samples was manipulated. The infants' looking patterns varied as a function of the magnitude of the difference in likelihood and were modulated by the number of items in the samples. Looking patterns showed qualitative similarities across age groups. This study demonstrates that infants' looking responses are sensitive to the magnitude of the difference in likelihood between two events. 13 p.

Humans as well as some nonhuman animals can estimate object numerosities-such as the number of sheep in a flock-without explicit counting. Here, we report on a negative time-order effect (TOE) in this type of judgment: When nonsymbolic numerical stimuli are presented sequentially, the second stimulus is overestimated compared to the first. We examined this "recent is more" effect in two comparative judgment tasks: larger-smaller discrimination and same-different discrimination. Ideal-observer modeling revealed evidence for a TOE in 88.2% of the individual data sets. Despite large individual differences in effect size, there was strong consistency in effect direction: 87.3% of the identified TOEs were negative. The average effect size was largely independent of task but did strongly depend on both stimulus magnitude and interstimulus interval. Finally, we used an estimation task to obtain insight into the origin of the effect. We found that subjects tend to overestimate both stimuli but the second one more strongly than the first one. Overall, our findings are highly consistent with findings from studies on TOEs in nonnumerical judgments, which suggests a common underlying mechanism. (PsycINFO Database Record

Does ingroup favoritism reflect experience or some preset motivation? The latter possibility is well examined in social psychology, but models from cognitive psychology suggest that unrepresentative samples of experience can generate biases even in the absence of motivational concerns. It remains unclear, however, how motivation and initially sampled experiences interact when both influences are possible, and people encounter new groups. Extending classic arguments about motivated information gathering, we propose that people can be described as "group-motivated samplers"-marked by a tendency to primarily seek out information about one's own group, and to attend more to information that portrays the ingroup in a positive light. Four experiments showed that information seeking almost always starts with the ingroup, and that people chose to gather more information from the ingroup compared to an outgroup. In subsequent group evaluations, people were excessively positive about ingroups giving a good initial impression. Participants were also fairly accurate, on average, about the direction and magnitude of group differences when the ingroup was de facto better, but downplayed those differences in the opposite situation. Further analyses indicated that first experiences led to biased evaluations because people failed to discount for nonrepresentative (positive) ingroup experiences, whereas interpretive biases seem responsible for evaluations based on belonging to a better/worse performing group. Taken together, while social psychologists know that people tend to portray ingroups in a flattering light, we show how people selectively incorporate early experiences to build those impressions. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Using eye tracking, we investigated if 10-month-old infants could discriminate between members of a set of small forms based on geometric properties in a deviant-detection paradigm, as suggested by the idea of a core cognitive system for Euclidian geometry. We also investigated the precision of infants’ ability to discriminate as well as how the discrimination process unfolds over time. Our results show that infants can discriminate between small forms based on geometrical properties, but only when the difference is sufficiently large. Furthermore, our results also show that it takes infants, on average, less than 3.5 seconds to detect a deviant form. Our findings extend previous research in three ways: by showing that infants can make similar discriminative judgments as children and adults with respect to geometric properties; by providing a first crude estimate on the limit of the discriminative abilities in infants, and finally; by providing a first demonstration of how the discrimination process unfolds over time.

Motor experiences and active exploration during early childhood may affect individual differences in a wide range of perceptual and cognitive abilities. In the current study, we suggest that active exploration of objects facilitates the ability to process object forms and magnitudes, which in turn impacts the development of numerosity perception. We tested our hypothesis by conducting a preregistered active exploration intervention with 59 8‐month‐old infants. The minimal intervention consisted of actively playing with and exploring blocks once a day for 8 weeks. In order to control for possible training effects on attention, we used book reading as a control condition. Pre‐ and post‐test assessments using eye‐tracking showed that block play improved visual form perception, where infants became better at detecting a deviant shape. Furthermore, using three control tasks, we showed that the intervention specifically improved infants' ability to process visual forms and the effect could not be explained by a domain general improvement in attention or visual perception. We found that the intervention did not improve numerosity perception and suggest that because of the sequential nature of our hypothesis, a longer time frame might be needed to see improvements in this ability. Our findings indicate that if infants are given more opportunities for play and exploration, it will have positive effects on their visual form perception, which in turn could help their understanding of geometrical concepts., Playing with blocks leads 8‐month‐old infants to develop better visual form perception, conceptualized here as detecting a deviant shape, compared to infants who were assigned to a reading control group.

Two recent studies - one of which was published in this journal - claimed to have found that learning on a non-symbolic arithmetic task improved performance on a symbolic arithmetic task (Park & Brannon, 2013, 2014). This finding has potentially far-reaching implications, because it would constitute evidence for a causal link between the Approximate Number System (ANS) and symbolic-math ability. Here, we argue that, due to the methodology used in both studies, the interpretation of data in terms of an improvement in ANS performance is problematic. We provide arguments and simulations showing that the trends in the data are similar to what one would expect for a non-learning observer. We discuss the implications for the original interpretation in terms of causality between non-symbolic and symbolic arithmetic performance.

In this study, we propose that infant social cognition may 'bootstrap' the successive development of domain-general cognition in line with the cultural intelligence hypothesis. Using a longitudinal design, 6-month-old infants (N = 118) were assessed on two basic social cognitive tasks targeting the abilities to share attention with others and understanding other peoples' actions. At 10 months, we measured the quality of the child's social learning environment, indexed by parent's abilities to provide scaffolding behaviors during a problem-solving task. Eight months later, the children were followed up with a cognitive test-battery, including tasks of inhibitory control and working memory. Our results showed that better infant social action understanding interacted with better parental scaffolding skills in predicting simple inhibitory control in toddlerhood. This suggests that infants' who are better at understanding other's actions are also better equipped to make the most of existing social learning opportunities, which in turn may benefit future non-social cognitive outcomes.

Humans can estimate numerosities–such as the number sheep in a flock–without deliberate counting. A number of biases have been identified in these estimates, which seem primarily rooted in the spatial organization of objects (grouping, symmetry, etc). Most previous studies on the number sense used static stimuli with extremely brief exposure times. However, outside the laboratory, visual scenes are often dynamic and freely viewed for prolonged durations (e.g., a flock of moving sheep). The purpose of the present study is to examine grouping-induced numerosity biases in stimuli that more closely mimic these conditions. To this end, we designed two experiments with limited-dot-lifetime displays (LDDs), in which each dot is visible for a brief period of time and replaced by a new dot elsewhere after its disappearance. The dynamic nature of LDDs prevents subjects from counting even when they are free-viewing a stimulus under prolonged presentation. Subjects estimated the number of dots in arrays that were presented either as a single group or were segregated into two groups by spatial clustering, dot size, dot color, or dot motion. Grouping by color and motion reduced perceived numerosity compared to viewing them as a single group. Moreover, the grouping effect sizes between these two features were correlated, which suggests that the effects may share a common, feature-invariant mechanism. Finally, we find that dot size and total stimulus area directly affect perceived numerosity, which makes it difficult to draw reliable conclusions about grouping effects induced by spatial clustering and dot size. Our results provide new insights into biases in numerosity estimation and they demonstrate that the use of LDDs is an effective method to study the human number sense under prolonged viewing. Leo Poom and Ronald van der Berg contributed equally to this work.

While a wealth of evidence suggests that humans tend to rely on additive cue combination to make controlled judgments, many of the normative rules for probability combination require multiplicative combination. In this article, the authors combine the experimental paradigms on probability reasoning and multiple-cue judgment to allow a comparison between formally identical tasks that involve probability vs. other task contents. The purpose was to investigate if people have cognitive algorithms for the combination, specifically, of probability, affording multiplicative combination in the context of probability. Three experiments suggest that, although people show some signs of a qualitative understanding of the combination rules that are specific to probability, in all but the simplest cases they lack the cognitive algorithms needed for multiplication, but instead use a variety of additive heuristics to approximate the normative combination. Although these heuristics are surprisingly accurate, normative combination is not consistently achieved until the problems are framed in an additive way.

Recent research has highlighted the importance of considering an individual's level of numeracy, that is their numerical abilities, in a vast variety of judgment and decision making tasks. To accurately evaluate the influence of numeracy requires good and valid measures of the construct. In the present study we validate a Swedish version of the Berlin Numeracy Test (Cokely, Galesic, Schulz, Ghazal & Garcia-Retamero, 2012). The validation was carried out on both a student sample and a sample representative of the Swedish population. The Swedish BNT showed sound psychometrical properties in both samples. Further, in both samples the BNT had satisfactory convergent and discriminant validity when correlating with other measures of numeracy, while not being significantly related to measures of personality. With respect to predictive validity the results indicated divergent patterns in the two samples. In the student sample, participants scoring highest on the BNT outperformed those in the other three levels, which did not differ in performance. In contrast, in the population sample participants scoring lowest on the BNT performed worse than those in the other three levels, which did not differ in performance. Taken together, however, the results suggest that the Swedish version of the BNT should be considered a valid measure of numeracy in both Swedish student and population representative samples.

Prospective motor control, a key element of action planning, is the ability to adjust one's actions with respect to task demands and action goals in an anticipatory manner. The current study investigates whether 14-month-olds can prospectively control their reaching actions based on the difficulty of the subsequent action. We used a reach-to-place task, with difficulty of the placing action varied by goal size and goal distance. To target prospective motor control, we determined the kinematics of the prior reaching movements using a motion-tracking system. Peak velocity of the first movement unit of the reach served as indicator for prospective motor control. Both difficulty aspects (goal size and goal distance) affected prior reaching, suggesting that both these aspects of the subsequent action have an impact on the prior action. The smaller the goal size and the longer the distance to the goal, the slower infants were in the beginning of their reach toward the object. Additionally, we modeled movement times of both reaching and placing actions using a formulation of Fitts' law (as in heading). The model was significant for placement and reaching movement times. These findings suggest that 14-month-olds can plan their future actions and prospectively control their related movements with respect to future task difficulties. (PsycINFO Database Record

Research on people's ability to act as intuitive statisticians has mainly focused on the accuracy of estimates of central tendency and variability. In this paper, we investigate two hypothesised cognitive processes by which people make judgements of distribution shape. The first claims that people spontaneously induce abstract representations of distribution properties from experience, including about distribution shape. The second process claims that people construct beliefs about distribution properties post hoc by retrieval from long-term memory of small samples from the distribution, implying format dependence with accuracy that differs depending on judgement format. Results from two experiments confirm the predicted format dependence, suggesting that people are often constrained by the post hoc assessment of distribution properties by sampling from long-term memory. The results, however, also suggest that, although post hoc sampling from memory seems to be the default process, under certain predictab...

The capacity of short-term memory is a key constraint when people make online judgments requiring them to rely on samples retrieved from memory (e.g., Dougherty & Hunter, 2003). In this article, the authors compare 2 accounts of how people use knowledge of statistical distributions to make point estimates: either by retrieving precomputed large-sample representations or by retrieving small samples of similar observations post hoc at the time of judgment, as constrained by short-term memory capacity (the naive sampling model: Juslin, Winman, & Hansson, 2007). Results from four experiments support the predictions by the naive sampling model, including that participants sometimes guess values that they, when probed, demonstrably know have the lowest probability of occurring. Experiment 1 also demonstrated the operations of an unpredicted recognition-based inference. Computational modeling also incorporating this process demonstrated that the data from all 4 experiments were better predicted by assuming a post hoc sampling process constrained by short-term memory capacity than by assuming abstraction of large-sample representations of the distribution.

The Approximate Number System (ANS) is thought to support non-symbolic representations of numerical magnitudes in humans. Recently much debate has focused on the causal direction for an observed relation between ANS acuity and arithmetic fluency. Here we investigate if arithmetic training can improve ANS acuity. We show with an experimental training study consisting of six 45-minute training sessions that although feedback during arithmetic training improves arithmetic performance substantially, it does not influence ANS acuity. Hence, we find no support for a causal link where symbolic arithmetic training influences the ANS acuity. Further, although short-term number memory is likely involved in arithmetic tasks we did not find that short-term memory capacity for numbers, measured by a digit-span test, was effected by arithmetic training. This suggests that the improvement in arithmetic fluency may have occurred independent of short-term memory efficiency, but rather due to long-term memory processes and/or mental calculation strategy development. The theoretical implications of these findings are discussed.

Math anxiety (MA) involves negative affect and tension when solving mathematical problems, with potentially life-long consequences. MA has been hypothesized to be a consequence of negative learning experiences and cognitive predispositions. Recent research indicates genetic and neurophysiological links, suggesting that MA stems from a basic level deficiency in symbolic numerical processing. However, the contribution of evolutionary ancient purely nonverbal processes is not fully understood. Here we show that the roots of MA may go beyond symbolic numbers. We demonstrate that MA is correlated with precision of the Approximate Number System (ANS). Individuals high in MA have poorer ANS functioning than those low in MA. This correlation remains significant when controlling for other forms of anxiety and for cognitive variables. We show that MA mediates the documented correlation between ANS precision and math performance, both with ANS and with math performance as independent variable in the mediation model. In light of our results, we discuss the possibility that MA has deep roots, stemming from a non-verbal number processing deficiency. The findings provide new evidence advancing the theoretical understanding of the developmental etiology of MA.