Quantifying a threat: Evidence of a numeric processing bias

Understanding the social-emotional components of our "number sense": insights from a novel non-symbolic numerical comparison task

Introduction

A large body of work has identified a core sense of number supported by the Approximate Number System (ANS) that is present in infancy and across species. Although it is commonly assumed that the ANS directly processes perceptual input and is relatively independent from affective factors, some evidence points at a correlation between ANS performance and math anxiety. However, the evidence is mixed. We tested whether giving participants active control in completing a numerical task would change the relationship between math anxiety on performance.

Methods

Adult participants (N = 103) completed a novel four-alternative-forced-choice non-symbolic numerical comparison task. In a repeated-measures design, participants either passively viewed different dot arrays or actively chose to view each array (i.e., active information-seeking) before deciding on the largest quantity. Participants also provided confidence judgments during the passive version of the task.

Results

We replicated the ratio-dependent signature in participants' accuracy in both the passive and active versions of the task using this novel paradigm, as well as in trial-level confidence judgments and information-seeking behavior. Participants' self-reported math anxiety significantly correlated with their accuracy on the passive version of the task. Critically, the correlation disappeared in the active version of the task. Gender also emerged as a predictor of confidence judgments and a moderator of the effect of task on overall accuracy and the effect of active information seeking on accuracy in the active version of the task. Exploratory analysis of estimated Weber Fraction suggests that these results may be driven by auxiliary factors instead of changes in ANS acuity.

Conclusion

These findings have implications for understanding the relationship between math anxiety and performance on numerical tasks.

How negative emotions influence arithmetic performance: a comparison of young and older adults

We investigated the influence of negative emotions on arithmetic problem-solving performance and age-related differences therein. Participants were asked to verify complex multiplication problems that were either true (e.g., 4 × 26 = 104) or false (e.g., 5 × 41 = 201). Half the problems were five problems (e.g., 5 × 28 = 140) and half were non-five problems (e.g., 6 × 36 = 216). False five problems violated the five-rule, the parity-rule, both rules, or no rule. Problems were preceded by emotionally neutral or negative pictures. For true problems, emotions impaired performance while verifying non-five problems in young adults only and while verifying five problems in older adults only. For false five problems, negative emotions influenced young adults’ performance while verifying both-rule and no-rule violation problems but not when verifying parity-rule violation or five-rule violation problems. Negative emotions did not influence older adults’ performance whichever false five problems they solved. These findings suggest that negative emotions may change the mechanisms that participants use to solve arithmetic problems and that emotions influence young and older adults via different mechanisms.

Exploring spatiotemporal interactions: On the superiority of time over space

Space and time mutually influence each other such that space affects time estimation (space-on-time effect), and conversely (time-on-space effect). These reciprocal interferences suggest that space and time are intrinsically linked in the human mind. Yet, recent evidence for an asymmetrical advantage for space over time challenges the classical theoretical interpretation. In the present study, we tested whether the superiority of space over time in magnitude interference depends on the cognitive resources engaged in the spatial task. We conducted three experiments in which participants performed judgments on temporal intervals and spatial distances in separate blocks. In each trial, two dots were successively flashed at various locations, and participants were to judge whether the duration or distance between the dots was short or long. To manipulate cognitive demands in the spatial task, distances varied across experiments (highly discriminable for the non-demanding spatial task in Experiment 1 and scarcely discriminable for the demanding spatial task in Experiment 2). Importantly, this manipulation tended to enhance perceptual sensitivity (as indexed by Weber Ratios) but slowed down the decision process (as indexed by response times) in the demanding experiment. Our results provide evidence for robust space-on-time and time-on-space effects (Experiments 1 and 2). More crucially, the involvement of cognitive resources in a demanding spatial task causes a massive time-on-space effect: Spatial judgments are indeed more influenced by irrelevant temporal information than the reverse (Experiments 2 and 3). Overall, the flexibility of spatiotemporal interferences has direct theoretical implications and questions the origins of space-time interaction.

EXPRESS: How negative emotions affect young and older adults' numerosity estimation performance

In this study, we investigated the influence of negative emotions on numerosity estimation and whether this influence changes with aging during adulthood. Young and older adults were asked to estimate and compare the numerosity of collections of elements (cars or dots) with a two-digit number. Collections of elements were preceded by emotionally neutral (e.g., mushrooms) or emotionally negative (e.g., a corpse) pictures. Stimuli were easier (i.e., small-ratio) or harder (i.e., large-ratio) items. Young and older participants obtained similar numerosity estimation performance. Interestingly, participants were less accurate under negative emotions than under neutral emotions when they estimated numerosity of collections of abstract elements (i.e., dots). In contrast, participants improved their performance under negative emotions while estimating collections of non-abstract, daily-life elements (i.e., cars). These findings have important implications for furthering our understanding of the role of negative emotions in numerosity estimation and age-related differences therein.

Age-related differences in how negative emotions influence arithmetic performance

In this study, we investigated the role of negative emotions on arithmetic and whether this role changes with aging during adulthood. Young and older adults were asked to verify one-digit addition problems (Experiment 1) and to estimate the results of two-digit multiplication problems (Experiment 2). In both experiments, easier and harder problems were displayed superimposed on emotionally neutral (e.g. mushrooms) or emotionally negative (e.g. a corpse) pictures. In both simple and complex arithmetic, young and older adults obtained poorer arithmetic performance under negative emotion conditions, especially while solving harder problems. Most interesting, deleterious effects of negative emotions on arithmetic performance were larger in young than in older adults. These findings have important implications for further our understanding of the role of negative emotions in the domain of arithmetic and age-related differences in this role.

Disentangling the facilitating and hindering effects of threat-related stimuli - A visual search study

Although large body of research has demonstrated the attention-grabbing nature of threat-related stimuli, threat could also facilitate attentional processes. Previous studies suggest a linear relationship between the facilitating effect of the arousal level conveyed by threat and performance on visual search tasks. Due to the temporal competition bias favouring stimuli with higher arousal level, this could be more pronounced for shorter onset times. Here, through two experiments we aimed to disentangle the two effects by using a visual search paradigm that allowed us to separate the emotional stimuli and the cognitive task. We manipulated stimulus onset time and threat intensity. Participants saw neutral and threatening pictures as priming stimuli, and then, they had to find numbers in ascending order in a matrix array. We measured the reaction time for finding the first number, and search time for finding all the numbers. Our results showed that when the priming stimulus is presented, longer threatening pictures produced longer reaction times compared to neutral ones, which was reversed with increase in arousal. We did not find any significant effects for the shorter onset time. Further theoretical and methodological implications are discussed.

Number, time, and space are not singularly represented: Evidence against a common magnitude system beyond early childhood

Our ability to represent temporal, spatial, and numerical information is critical for understanding the world around us. Given the prominence of quantitative representations in the natural world, numerous cognitive, neurobiological, and developmental models have been proposed as a means of describing how we track quantity. One prominent theory posits that time, space, and number are represented by a common magnitude system, or a common neural locus (i.e., Bonn & Cantlon in Cognitive Neuropsychology, 29(1/2), 149-173, 2012; Cantlon, Platt, & Brannon in Trends in Cognitive Sciences, 13(2), 83-91, 2009; Meck & Church in Animal Behavior Processes, 9(3), 320, 1983; Walsh in Trends in Cognitive Sciences, 7(11), 483-488, 2003). Despite numerous similarities in representations of time, space, and number, an increasing body of literature reveals striking dissociations in how each quantity is processed, particularly later in development. These findings have led many researchers to consider the possibility that separate systems may be responsible for processing each quantity. This review will analyze evidence in favor of a common magnitude system, particularly in infancy, which will be tempered by counter evidence, the majority of which comes from experiments with children and adult participants. After reviewing the current data, we argue that although the common magnitude system may account for quantity representations in infancy, the data do not provide support for this system throughout the life span. We also identify future directions for the field and discuss the likelihood of the developmental divergence model of quantity representation, like that of Newcombe (Ecological Psychology, 2, 147-157, 2014), as a more plausible account of quantity development.

Cognitive Load Affects Numerical and Temporal Judgments in Distinct Ways

Prominent theories suggest that time and number are processed by a single neural locus or a common magnitude system (e.g., Meck and Church, 1983; Walsh, 2003). However, a growing body of literature has identified numerous inconsistencies between temporal and numerical processing, casting doubt on the presence of such a singular system. Findings of distinct temporal and numerical biases in the presence of emotional content (Baker et al., 2013; Young and Cordes, 2013) are particularly relevant to this debate. Specifically, emotional stimuli lead to temporal overestimation, yet identical stimuli result in numerical underestimation. In the current study, we tested adults’ temporal and numerical processing under cognitive load, a task that compromises attention. Under the premise of a common magnitude system, one would predict cognitive load to have an identical impact on temporal and numerical judgments. Inconsistent with the common magnitude account, results revealed baseline performance on the temporal and numerical task was not correlated and importantly, cognitive load resulted in distinct and opposing quantity biases: numerical underestimation and marginal temporal overestimation. Together, our data call into question the common magnitude account, while also providing support for the role of attentional processes involved in numerical underestimation.

The impact of emotion on numerical estimation: A developmental perspective

Recent literature has revealed underestimation effects in numerical judgments when adult participants are presented with emotional stimuli (as opposed to neutral). Whether these numerical biases emerge early in development however, or instead reflect overt, learned responses to emotional stimuli across development are unclear. Moreover, reported links between numerical acuity and mathematics achievement point to the importance of exploring how numerical approximation abilities in childhood may be influenced in real-world affective contexts. In this study, children (aged 6-10 years) and adults were presented with happy and neutral facial stimuli in the context of a numerical bisection task. Results reveal that children, like adults, underestimate number following emotional (i.e., happy) faces (relative to neutral). However, children's, but not adult's, responses were also significantly more precise following emotional stimuli. In a second experiment, adult judgments revealed a similar increase in precision following emotional stimuli when numerical discriminations were more challenging (involving larger sets). Together, results are the first to reveal children, like adults, underestimate number in the context of emotional stimuli and this underestimation bias is accompanied with enhanced response precision.