Associations of non‐symbolic and symbolic numerical magnitude processing with mathematical competence: a meta‐analysis

Many studies have investigated the association between numerical magnitude processing skills, as assessed by the numerical magnitude comparison task, and broader mathematical competence, e.g. counting, arithmetic, or algebra. Most correlations were positive but varied considerably in their strengths. It remains unclear whether and to what extent the strength of these associations differs systematically between non‐symbolic and symbolic magnitude comparison tasks and whether age, magnitude comparison measures or mathematical competence measures are additional moderators. We investigated these questions by means of a meta‐analysis. The literature search yielded 45 articles reporting 284 effect sizes found with 17,201 participants. Effect sizes were combined by means of a two‐level random‐effects regression model. The effect size was significantly higher for the symbolic (r = .302, 95% CI [.243, .361]) than for the non‐symbolic (r = .241, 95% CI [.198, .284]) magnitude comparison task and decreased very slightly with age. The correlation was higher for solution rates and Weber fractions than for alternative measures of comparison proficiency. It was higher for mathematical competencies that rely more heavily on the processing of magnitudes (i.e. mental arithmetic and early mathematical abilities) than for others. The results support the view that magnitude processing is reliably associated with mathematical competence over the lifespan in a wide range of tasks, measures and mathematical subdomains. The association is stronger for symbolic than for non‐symbolic numerical magnitude processing. So symbolic magnitude processing might be a more eligible candidate to be targeted by diagnostic screening instruments and interventions for school‐aged children and for adults.     

Moving attention along the mental number line in preschool age: Study of the operational momentum in 3‐ to 5‐year‐old children's non‐symbolic arithmetic

People tend to underestimate subtraction and overestimate addition outcomes and to associate subtraction with the left side and addition with the right side. These two phenomena are collectively labeled 'operational momentum' (OM) and thought to have their origins in the same mechanism of 'moving attention along the mental number line'. OM in arithmetic has never been tested in children at the preschool age, which is critical for numerical development. In this study, 3–5 years old were tested with non‐symbolic addition and subtraction tasks. Their level of understanding of counting principles (CP) was assessed using the give‐a‐number task. When the second operand's cardinality was 5 or 6 (Experiment 1), the child's reaction time was shorter in addition/subtraction tasks after cuing attention appropriately to the right/left. Adding/subtracting one element (Experiment 2) revealed a more complex developmental pattern. Before acquiring CP, the children showed generalized overestimation bias. Underestimation in addition and overestimation in subtraction emerged only after mastering CP. No clear spatial‐directional OM pattern was found, however, the response time to rightward/leftward cues in addition/subtraction again depended on stage of mastering CP. Although the results support the hypothesis about engagement of spatial attention in early numerical processing, they point to at least partial independence of the spatial‐directional and magnitude OM. This undermines the canonical version of the number line‐based hypothesis. Mapping numerical magnitudes to space may be a complex process that undergoes reorganization during the period of acquisition of symbolic representations of numbers. Some hypotheses concerning the role of spatial‐numerical associations in numerical development are proposed.     

Asymmetric interference in 3‐ to 4‐month‐olds' sequential category learning

Three‐ to 4‐month‐old infants show asymmetric exclusivity in the acquisition of cat and dog perceptual categories. The cat perceptual category excludes dog exemplars, but the dog perceptual category does not exclude cat exemplars. We describe a connectionist autoencoder model of perceptual categorization that shows the same asymmetries as infants. The model predicts the presence of asymmetric retroactive interference when infants acquire cat and dog categories sequentially. A subsequent experiment conducted with 3‐ to 4‐month‐olds verifies the predicted pattern of looking time behaviors. We argue that bottom‐up, associative learning systems with distributed representations are appropriate for modeling the operation of short‐term visual memory in early perceptual category learning.     

Integration versus separation in Stroop‐like counting interference tasks1

Abstract: Two versions of a Stroop‐like counting interference task were compared to examine how irrelevant information is ignored. In the integrated task, participants enumerated digits (inconsistent condition) or letters (neutral condition) while attempting to ignore the identity of the characters. In the newly created separated task, participants enumerated asterisks while attempting to ignore a single digit (inconsistent condition) or letter (neutral condition) at fixation. Interference (longer responses in the inconsistent condition than in the neutral condition) was small but significant in both tasks but was not reduced by separation. Contrasted with the pattern in the color–word Stroop task, these results suggest that dimensional separation has different effects on interference depending on the overall amount of interference.     

Young children's non‐numerical ordering ability at the start of formal education longitudinally predicts their symbolic number skills and academic achievement in maths

Ordinality is a fundamental feature of numbers and recent studies have highlighted the role that number ordering abilities play in mathematical development (e.g., Lyons et al., 2014 ), as well as mature mathematical performance (e.g., Lyons & Beilock, 2011 ). The current study tested the novel hypothesis that non‐numerical ordering ability, as measured by the ordering of familiar sequences of events, also plays an important role in maths development. Ninety children were tested in their first school year and 87 were followed up at the end of their second school year, to test the hypothesis that ordinal processing, including the ordering of non‐numerical materials, would be related to their maths skills both cross‐sectionally and longitudinally. The results confirmed this hypothesis. Ordinal processing measures were significantly related to maths both cross‐sectionally and longitudinally, and children's non‐numerical ordering ability in their first year of school (as measured by order judgements for everyday events and the parents’ report of their child's everyday ordering ability) was the strongest longitudinal predictor of maths one year later, when compared to several measures that are traditionally considered to be important predictors of early maths development. Children's everyday ordering ability, as reported by parents, also significantly predicted growth in formal maths ability between Year 1 and Year 2, although this was not the case for the event ordering task. The present study provides strong evidence that domain‐general ordering abilities play an important role in the development of children's maths skills at the beginning of formal education.     

Rostro‐caudal and dorso‐ventral gradients in medial and lateral prefrontal cortex during cognitive control of affective and cognitive interference

Characterizing the anatomical substrates of major brain functions such as cognition and emotion is of utmost importance to the ongoing efforts of understanding the nature of psychiatric ailments and their potential treatment. The aim of our study was to investigate how the brain handles affective and cognitive interferences on cognitive processes. Functional magnetic resonance imaging investigation was performed on healthy individuals, comparing the brain oxygenation level dependent activation patterns during affective and cognitive counting Stroop tasks. The affective Stroop task activated rostral parts of medial prefrontal cortex (PFC) and rostral and ventral parts of lateral PFC, while cognitive Stroop activated caudal parts of medial PFC and caudal and dorsal parts of lateral PFC. Our findings suggest that the brain may handle affective and cognitive interference on cognitive processes differentially, with affective interference preferentially activating rostral and ventral PFC networks and cognitive interference activating caudal and dorsal PFC networks.     

Typicality effects in picture‐word interference paradigm: An evaluation of the response exclusion hypothesis

The response exclusion hypothesis suggests that the polarity of semantic effects in the picture‐word interference paradigm is determined by the response‐relevant criteria. Semantic interference effects would be observed when semantically related distractor words satisfy the response‐relevant criteria; otherwise, semantic facilitation effects should be found. The purpose of this study was to further evaluate the response exclusion hypothesis by exploring the typicality effects in pictures naming. In two experiments, pictures of objects were named either in the context of verb distractor words with different typicality of passive functions or in the context of adjective distractor words with different typicality of characteristics. Facilitation effects were observed in context of typical verbs and adjectives, while interference effects were observed in the context of atypical verbs and adjectives. Given that neither typical nor atypical distractor words satisfy the response‐relevant criteria to produce noun, these findings are problematic for the response exclusion hypothesis. Role of syntagmatic relationships in lexical retrieval was invoked to explain present findings.     

Nine‐ to 11‐month‐old infants' reasoning about causality in anomalous human movements1

Two habituation experiments investigated 9–11‐month‐old infants' reasoning about causality in anomalous human movements. During habituation, infants saw an event in which a person walked toward a stationary person behind an occluder who fell down after an interval. Then, the infants were tested with two events without the occluder: the contact event in which the first person pushed the second one to fall down and the no‐contact event in which the second person fell down without any contact. In Experiment 1, in which the persons were face‐to‐back, infants looked at the no‐contact event for a longer time, whereas in Experiment 2, in which the persons were face‐to‐face, they looked at both the events for equal duration. Thus, infants considered it unnatural when a person fell down without external force in the absence of any action from a distance (e.g. communication). Infants seem to apply the physical contact principles to human movements in certain cases.     

Complications travel: A cross‐cultural comparison of the proportion of complications as a verbal cue to deceit

Verbal lie detection tools are almost exclusively examined in Western Europe and North America, but practitioners worldwide show interest in such tools. Because cultural differences in the efficacy of such tools may occur, it is important to examine their efficacy in different cultures. In this article, we focus on proportion of complications, which in previous research was more diagnostic than “total details” in two British samples and in three samples that each included Hispanic, Russian, and South Korean participants. In the present article, we merged the three non‐British samples and analysed the data by presenting them for each cultural group separately. Truth tellers disclosed the details of a trip away they had made, whereas liars fabricated such details. Proportion of complications discriminated truth tellers from liars in all three groups and was consistently a better indicator of veracity than total details. Implications of the findings are discussed.     

Actions speak louder than words: Differences in memory flexibility between monolingual and bilingual 18‐month‐olds

Bilingual infants from 6‐ to 24‐months of age are more likely to generalize, flexibly reproducing actions on novel objects significantly more often than age‐matched monolingual infants are. In the current study, we examine whether the addition of novel verbal labels enhances memory generalization in a perceptually complex imitation task. We hypothesized that labels would provide an additional retrieval cue and aid memory generalization for bilingual infants. Specifically, we hypothesized that bilinguals might be more likely than monolinguals to map multiple perceptual features onto a novel label and therefore show enhanced generalization. Eighty‐seven 18‐month‐old monolingual and bilingual infants were randomly assigned to one of two experimental conditions or a baseline control condition. In the experimental conditions, either no label or a novel label was added during demonstration and again at the beginning of the test session. After a 24‐hr delay, infants were tested with the same stimulus set to test cued recall and with a perceptually different but functionally equivalent stimulus set to test memory generalization. Bilinguals performed significantly above baseline on both cued recall and memory generalization in both experimental conditions, whereas monolinguals performed significantly above baseline only on cued recall in both experimental conditions. These findings show a difference between monolinguals and bilinguals in memory generalization and suggest that generalization differences between groups may arise from visual perceptual processing rather than linguistic processing. A video abstract of this article can be viewed at https://youtu.be/yXB4pM3fF2k     

Pointing and the interference effect in obsessive‐compulsive disorder (OCD)

The interference effect in obsessive‐compulsive disorder (OCD) was investigated in order to analyze cognitive aspects of motor stereotypy in OCD‐related compulsions. So far, the domain of cognitive control in compulsive behavior has been under‐investigated. Twelve participants (OCD patients and healthy controls) completed a newly created computer‐based pointing task as well as standard clinical and psychological background measures. Findings showed that the patients displayed a larger visual interference effect compared to the controls and pointing paths were longer in time as well as distance when a distractor stimulus was present. It is concluded that, for compensation, patients would need to generate excessive amounts of attentional resources not available to overcome motor rigidity on the one side and visual distraction on the other side.     

Connection‐based and object‐based grouping in multiple‐object tracking: A developmental study

Developmental research on Gestalt laws has previously revealed that, even as young as infancy, we are bound to group visual elements into unitary structures in accordance with a variety of organizational principles. Here, we focus on the developmental trajectory of both connection‐based and object‐based grouping, and investigate their impact on object formation in participants, aged 9–21 years old (N = 113), using a multiple‐object tracking paradigm. Results reveal a main effect of both age and grouping type, indicating that 9‐ to 21‐year‐olds are sensitive to both connection‐based and object‐based grouping interference, and tracking ability increases with age. In addition to its importance for typical development, these results provide an informative baseline to understand clinical aberrations in this regard.

Statement of contribution

What is already known on this subject?

• The origin of the Gestalt principles is still an ongoing debate: Are they innate, learned over time, or both?
• Developmental research has revealed how each Gestalt principle has its own trajectory and unique relationship to visual experience.
• Both connectedness and object‐based grouping play an important role in object formation during childhood.

What does this study add?

• The study identifies how sensitivity to connectedness and object‐based grouping evolves in individuals, aged 9–21 years old.
• Using multiple‐object tracking, results reveal that the ability to track multiple objects increases with age.
• These results provide an informative baseline to understand clinical aberrations in different types of grouping.

     

The impact of mothers' trait anxiety on their expectations of approach‐avoidance behaviour in anxious and non‐anxious children

This study investigated estimates of approach and avoidance behaviour in clinically anxious and non‐anxious children, and whether mothers' expectations of their children's avoidance differed as a function of high trait anxiety (HTA) versus low trait anxiety (LTA). Participants were 62 clinically anxious and 60 non‐anxious children aged 7–12 years and their mothers. Estimates of avoidance were obtained using an analogue task in which children and mothers were given threat and pleasant information about two novel animals and were asked to estimate children's avoidance of the threat animal's habitat when the threat animal was present (threat condition) and absent (safe condition) from the habitat and when its presence was uncertain (ambiguous condition). Contrary to expectation, anxious children did not differ from controls in estimates of avoidance in any condition. However, relative to HTA mothers of anxious children and LTA mothers of non‐anxious children, HTA mothers estimated greater approach behaviour by their non‐anxious children in the threat condition. Findings suggest that mothers' expectations of children's approach‐avoidance behaviour is influenced by both maternal and child factors.     

The impact of balance‐focused attitudes on job stress: Gender differences evidenced in American and Chinese samples

Based on gender role expectations model, we examined how balance‐focused attitudes would affect job stress by influencing individuals' perceptions of family interference with work (FIW), and investigated whether a gender difference would exist in the relationships among balance‐focused attitudes, FIW and job stress. Using two independent samples from the United States and China, we found support for the indirect influence of balance‐focused attitudes on job stress, through FIW. Participants with balance‐focused attitudes experienced lower levels of job stress as they perceived less interference from family to work. As expected, such indirect effect was more pronounce among male participants, meaning that the male participants benefited more from having balance‐focused attitudes. Discussion, theoretical and practical implications are provided.     

Elaboration and numerical anchoring: Breadth,depth, and the role of (non‐)thoughtful processes in anchoring theories

Noted Judgment and Decision Making (JDM) researchers differ in their opinions of whether and how an attitudes and persuasion (A&;P) view of anchoring might add to the existing anchoring literature. Epley and Gilovich (2010) and Russo (2010) supported the breadth of variables that an attitudinal view of brings to bear on anchoring phenomena and the potential operation of different psychological processes across different contexts. They also suggest extensions to other types of anchors (along with Frederick et al. 2010), to alternative paradigms, and to other classes of moderators, such as goals. Authors of all three commentaries wondered if the evidence we presented speaks to traditional issues related to processes underlying anchoring. Frederick et al. (2010) also took a different approach in suggesting that anchoring is always due to non-thoughtful processes despite the fact that thoughtful processes can also influence judgments. This approach diverges from prominent reviews of the anchoring literature and implies that the presence of any simple, associative mechanism makes the overall process that involves that mechanism “non-thoughtful.” We discuss how this approach differs from our own, and we discuss the implications of the other observations in each commentary.     

The impact of non‐aggressive behaviour early in aggressive interactions: Sex differences in direct and indirect aggression in response to provocation

Using an adapted form of the Taylor competitive reaction time task (TCRT: Taylor, 1967), we examined the effect of initially non‐aggressive behaviour during aggressive encounters. Specifically, if a person is initially non‐aggressive, but becomes more aggressive later, does an opponent respond more or less aggressively in response? Participants (N = 148) played a competitive reaction time task against a bogus partner, who was either initially non‐aggressive, or initially moderately aggressive, and then delivered increasingly loud noise blasts to participants on trials when the participant lost. Both direct (noise blasts delivered to the partner) and indirect aggression (damage to partner's reputation) were assessed. The impact of whether or not participants expected to meet the partner on direct and indirect aggression was also examined. All participants reduced their direct aggression towards an initially non‐aggressive partner and a partner they expected to meet. However, for females, the switch from initial non‐aggression to later aggression generated a negative evaluation of the partner, exhibited by indirect but not direct aggression.     

Cognitive control in belief‐laden reasoning during conclusion processing: An ERP study

Belief bias is the tendency to accept conclusions that are compatible with existing beliefs more frequently than those that contradict beliefs. It is one of the most replicated behavioral findings in the reasoning literature. Recently, neuroimaging studies using functional magnetic resonance imaging (fMRI) and event‐related potentials (ERPs) have provided a new perspective and have demonstrated neural correlates of belief bias that have been viewed as supportive of dual‐process theories of belief bias. However, fMRI studies have tended to focus on conclusion processing, while ERPs studies have been concerned with the processing of premises. In the present research, the electrophysiological correlates of cognitive control were studied among 12 subjects using high‐density ERPs. The analysis was focused on the conclusion presentation phase and was limited to normatively sanctioned responses to valid–believable and valid–unbelievable problems. Results showed that when participants gave normatively sanctioned responses to problems where belief and logic conflicted, a more positive ERP deflection was elicited than for normatively sanctioned responses to nonconflict problems. This was observed from ?400 to ?200 ms prior to the correct response being given. The positive component is argued to be analogous to the late positive component (LPC) involved in cognitive control processes. This is consistent with the inhibition of empirically anomalous information when conclusions are unbelievable. These data are important in elucidating the neural correlates of belief bias by providing evidence for electrophysiological correlates of conflict resolution during conclusion processing. Moreover, they are supportive of dual‐process theories of belief bias that propose conflict detection and resolution processes as central to the explanation of belief bias.     

A meta‐mood model of rumination and depression: Preliminary test in a non‐clinical population

Depressive rumination and trait meta‐mood (emotional attention, emotional clarity and emotional repair) have been suggested as vulnerability factors leading to depression, but less is known about the associations among them. In this study, we examined the relationships between trait meta‐mood, rumination and depressive symptomatology. Using structural equation analysis in a large sample of a non‐clinical population we found a preliminary test of the role of trait meta‐mood dimensions in rumination and depressive symptomatology. Results indicated that attention to feelings has two pathways in its relation with rumination and depressive mood. On the one hand, emotional attention was associated with emotional clarity, and emotional clarity with emotional repair, which was related to lower depressive symptomatology, in part, by reducing rumination. On the other hand, emotional attention was directly associated with ruminative thoughts which, in turn, were related to higher depressive mood. Findings are discussed in terms of the implications of beliefs about emotions in the treatment of depression.     

Colour fluctuations in grapheme‐colour synaesthesia: The effect of clinical and non‐clinical mood changes

Synaesthesia is a condition that gives rise to unusual secondary sensations (e.g., colours are perceived when listening to music). These unusual sensations tend to be reported as being stable throughout adulthood (e.g., Simner & Logie, 2007, Neurocase, 13, 358) and the consistency of these experiences over time is taken as the behavioural hallmark of genuineness. Our study looked at the influence of mood states on synaesthetic colours. In Experiment 1, we recruited grapheme‐colour synaesthetes (who experience colours from letters/digits) and elicited their synaesthetic colours, as well as their mood and depression states, in two different testing sessions. In each session, participants completed the PANAS‐X (Watson & Clark, 1999) and the BDI‐II (Beck, Steer, & Brown, 1996, Manual for Beck Depression Inventory‐II), and chose their synaesthetic colours for letters A‐Z from an interactive colour palette. We found that negative mood significantly decreased the luminance of synaesthetic colours. In Experiment 2, we showed that synaesthetic colours were also less luminant for synaesthetes with anxiety disorder, versus those without. Additional evidence suggests that colour saturation, too, may inversely correlate with depressive symptoms. These results show that fluctuations in mood within both a normal and clinical range influence synaesthetic colours over time. This has implications for our understanding about the longitudinal stability of synaesthetic experiences, and of how mood may interact with the visual (imagery) systems.