Numerical and non-numerical ordinality processing in children with and without developmental dyscalculia: Evidence from fMRI

Ordinality is – beyond numerical magnitude (i.e., quantity) – an important characteristic of the number system. There is converging empirical evidence that (intra)parietal brain regions mediate number magnitude processing. Furthermore, recent findings suggest that the human intraparietal sulcus (IPS) supports magnitude and ordinality in a domain-general way. However, the latter findings are derived from adult studies and with respect to children (i.e., developing brain systems) both the neural correlates of ordinality processing and the precise role of the IPS (domain-general vs. domain-specific) in ordinality processing are thus far unknown. The present study aims at filling this gap by employing functional magnetic resonance imaging (fMRI) to investigate numerical and non-numerical ordinality knowledge in children with and without developmental dyscalculia. In children (without DD) processing of numerical and non-numerical ordinality alike is supported by (intra)parietal cortex, thus extending the notion of a domain-general (intra)parietal cortex to developing brain systems. Moreover, activation extents in response to numerical ordinality processing differ significantly between children with and without dyscalculia in inferior parietal regions (supramarginal gyrus and IPS).     

Negative Numbers are not yet Automatically Associated with Space in 6th Graders

ABSTRACT

The metaphor of the mental number line accounts for numerous empirical effects of spatial-numerical associations. In the present study, we aimed at investigating directional spatial-numerical associations reflected by SNARC-like digit-direction and sign-direction congruency effects as well as the sign-digit compatibility effect when 6^th graders performed magnitude comparisons of multi-symbol numbers (i.e., positive and negative numbers). As spatial-numerical associations were associated with sensorimotor experiences, we used whole-body and finger tapping responses to manipulate the extent of motor responses. We only observed a SNARC-like digit-direction congruency effect, but neither a sign-direction congruency nor a sign-digit compatibility effect. This indicates that 6^th graders may already have developed spatial-numerical associations for absolute number magnitude, but not yet for polarity signs. Furthermore, not observing a sign-digit compatibility effect seemed to suggest that 6^th graders may not yet process multi-symbol numbers in the same parallel componential way as adults do. We argue that while 6^th graders are able to process negative numbers, they are not yet automatically associated with space or integrated in the place-value structure of the Arabic number system like multi-digit numbers are at this age.     

Multilevel analysis of individual differences in regularities of grapheme–color associations in synesthesia

Grapheme–color synesthesia is a neurological phenomenon where visual perception of letters and numbers stimulates perception of a specific color. Grapheme–color correspondences have been shown to be systematically associated with grapheme properties, including visual shape difference, ordinality, and frequency. However, the contributions of grapheme factors differ across individuals. In this study, we applied multilevel analysis to test whether individual differences in regularities of grapheme–color associations could be explained by individual styles of processing grapheme properties. These processing styles are reflected by the type of synesthetic experience. Specifically, we hypothesized that processing focusing on shape differences would be associated with projector synesthetes, while processing focusing on ordinality or familiarity would be associated with associator synesthetes. The analysis revealed that ordinality and familiarity factors were expressed more strongly among associators than among projectors. This finding suggests that grapheme–color associations are partly determined by the type of synesthetic experience.     

Language statistics explain the spatial–numerical association of response codes

The spatial–numerical association of response codes (SNARC) has shown that parity judgments with participants’ left hands yield faster response times (RTs) for smaller numbers than for larger numbers, with the opposite result for right-hand responses. These findings have been explained by participants perceptually simulating magnitude on a mental number line. In three RT experiments, we showed that the SNARC effect can also be explained by language statistics. Participants made parity judgments of number words (Exp. 1) and Arabic numerals (Exp. 2). Linguistic frequencies of the number words and numbers mirrored the SNARC effect, explaining aspects of processing that a perceptual simulation account could not. In Experiment 3, we investigated whether high- and low-frequency nonnumerical words would also elicit a SNARC-like effect. Again, RTs were faster for high-frequency words for left-hand responses, with the opposite result for right-hand responses. These results demonstrate that what has only been attributed to perceptual simulation should also be attributed to language statistics.     

The role of the motor system in conceptual processing: Effects of object affordances beyond response interference

Numerous behavioral and neuro-imaging studies have demonstrated that the motor system is activated when people are presented with manipulable objects. However it remains a matter of debate whether these results should be interpreted as evidence that certain conceptual processes employ motor programs. In order to address this issue, we conducted two experiments which required participants to assess the functions of tool-like objects and respond verbally. The results demonstrate that action affordances may constrain performance in tasks which are not based on the stimulus–response compatibility paradigm. We argue that this finding supports the causal role of the motor system in conceptual processing and that it cannot be explained by spreading of activation and response interference.     

Neurodynamics of time consciousness: An extensionalist explanation of apparent motion and the specious present via reentrant oscillatory multiplexing

This paper situates an original model of reentrant oscillatory multiplexing within the philosophy of time consciousness to argue for an extensionalist theory of the specious present. I develop a detailed differential latency model of apparent motion to show how the ordinality of experiential content is isomorphic to the ordinality of relevant brain processes. I argue that the theory presented has resources to account for other key features of the specious present, including the representational discreteness between successive conscious moments as well as the phenomenological continuity between them. This work not only shows the plausibility of an extensionalist philosophical theory, it also illustrates the utility of differential latency views in squaring temporal illusions with empirically supported neurodynamics.     

THE TROUBLE WITH LANGUAGE:

Abstract— Experiential avoidance is the attempt to escape or avoid certain private experiences, such as particular feelings, memories, behavioral predispositions, or thoughts. In this article, we discuss evidence that experiential avoidance is both pervasive and often harmful to human functioning. We argue that experiential avoidance can be explained by two verbal processes, and we provide basic behavioral evidence on both the bidirectionality of derived stimulus relations in verbal humans and the insensitivity to the effects of responding produced by verbal rules. If this analysis is correct, experiential avoidance is built into human language and thus can be undermined only with difficulty.     

Close monitoring as a contextual stimulator: How need for structure affects the relation between close monitoring and work outcomes

In this article, we argue and demonstrate that employees’ Personal Need for Structure (PNS) moderates the negative effects of close monitoring on job satisfaction, intrinsic work motivation, and innovative job performance (as rated by their supervisors). In a field study (N = 295), we found that employees low in PNS reacted unfavourably to close monitoring, whereas employees high in PNS reacted more favourably to close monitoring. Furthermore, we demonstrate that the negative effect of close monitoring on job satisfaction and intrinsic work motivation among low PNS employees can be explained by a reduction of perceived autonomy. In contrast, the positive effects of close monitoring on these favourable outcomes among high PNS employees were associated with increased role clarity.     

Visual search for expressions and anti-expressions

We used visual search to explore whether the preattentive mechanisms that enable rapid detection of facial expressions are driven by visual information from the displacement of features in expressions, or other factors such as affect. We measured search slopes for luminance and contrast equated images of facial expressions and anti-expressions of six emotions (anger, fear, disgust, surprise, happiness, and sadness). Anti-expressions have an equivalent magnitude of facial feature displacements to their corresponding expressions, but different affective content. There was a strong correlation between these search slopes and the magnitude of feature displacements in expressions and anti-expressions, indicating feature displacement had an effect on search performance. There were significant differences between search slopes for expressions and anti-expressions of happiness, sadness, anger, and surprise, which could not be explained in terms of feature differences, suggesting preattentive mechanisms were sensitive to other factors. A categorization task confirmed that the affective content of expressions and anti-expressions of each of these emotions were different, suggesting signals of affect might well have been influencing attention and search performance. Our results support a picture in which preattentive mechanisms may be driven by factors at a number of levels, including affect and the magnitude of feature displacement. We note that indirect effects of feature displacement, such as changes in local contrast, may well affect preattentive processing. These are most likely to be nonlinearly related to feature displacement and are, we argue, an important consideration for any study using images of expression to explore how affect guides attention. We also note that indirect effects of feature displacement (for example, changes in local contrast) may well affect preattentive processing. We argue that such effects are an important consideration for any study using images of expression to explore how affect guides attention.     

The analysis of morphological errors in a case of acquired dyslexia

An issue that is persistently raised in studies of subjects who produce morphological errors in reading and other tasks is whether these errors are the consequence of a morphological processing deficit, or whether they in any way reflect morphological principles of organization in the lexicon. We discuss the performance of one such subject on a number of tasks and evaluate standard arguments for attributing aspects of his performance to a morphological processing deficit. Although there are several features of his performance that are suggestive in this regard; we argue that, when these issues are addressed in the context of a sufficiently elaborated theory of lexical processing, a morphological processing deficit cannot be demonstrated. We also survey a number of recent reports that purport to provide evidence for a morphological processing deficit and argue that, in most cases, they fail to support such claims for similar reasons. An important moral to be drawn from a critique of these studies is that in order to make valid inferences concerning the role of morphology in organizing the lexicon, we must consider these errors in the context of theories of the lexicon that take seriously the effects of converging lexical factors in processing.     

Learning and development of embodied numerosity

Recent empirical evidence indicates that seemingly abstract numerical cognitions are rooted in sensory and bodily experiences. In particular in finger counting finger-based representations reflect a specific case of embodied cognition, we termed embodied numerosity. Furthermore, we suggest that finger-based representations should be considered a distinct representation of number (magnitude) and argue that this representation is activated automatically whenever we encounter a number. We discuss in what way such a theoretical framework can account for the associations of fingers and numbers observed so far. In the final part, we evaluate whether the concept of embodied numerosity should be generalized beyond finger-based representations with particular focus on whether bodily-sensory experiences (such as moving the whole body along the mental number line) may corroborate numerical capabilities. In a series of intervention studies, we consistently observed more pronounced training effects for our embodied numerosity trainings for different age groups, different digital media, different number ranges, and different control conditions. Taken together, we conclude that embodied representations of number (magnitude) exist, are not limited to finger-based representations, and influence number processing in a systematic and functional way that can be used to foster the efficiency of numerical trainings.     

A quantum probability account of order effects in inference

Order of information plays a crucial role in the process of updating beliefs across time. In fact, the presence of order effects makes a classical or Bayesian approach to inference difficult. As a result, the existing models of inference, such as the belief-adjustment model, merely provide an ad hoc explanation for these effects. We postulate a quantum inference model for order effects based on the axiomatic principles of quantum probability theory. The quantum inference model explains order effects by transforming a state vector with different sequences of operators for different orderings of information. We demonstrate this process by fitting the quantum model to data collected in a medical diagnostic task and a jury decision-making task. To further test the quantum inference model, a new jury decision-making experiment is developed. Using the results of this experiment, we compare the quantum inference model with two versions of the belief-adjustment model, the adding model and the averaging model. We show that both the quantum model and the adding model provide good fits to the data. To distinguish the quantum model from the adding model, we develop a new experiment involving extreme evidence. The results from this new experiment suggest that the adding model faces limitations when accounting for tasks involving extreme evidence, whereas the quantum inference model does not. Ultimately, we argue that the quantum model provides a more coherent account for order effects that was not possible before.     

Representations of numerical and non‐numerical magnitude both contribute to mathematical competence in children

A growing body of evidence suggests that non‐symbolic representations of number, which humans share with nonhuman animals, are functionally related to uniquely human mathematical thought. Other research suggesting that numerical and non‐numerical magnitudes not only share analog format but also form part of a general magnitude system raises questions about whether the non‐symbolic basis of mathematical thinking is unique to numerical magnitude. Here we examined this issue in 5‐ and 6‐year‐old children using comparison tasks of non‐symbolic number arrays and cumulative area as well as standardized tests of math competence. One set of findings revealed that scores on both magnitude comparison tasks were modulated by ratio, consistent with shared analog format. Moreover, scores on these tasks were moderately correlated, suggesting overlap in the precision of numerical and non‐numerical magnitudes, as expected under a general magnitude system. Another set of findings revealed that the precision of both types of magnitude contributed shared and unique variance to the same math measures (e.g. calculation and geometry), after accounting for age and verbal competence. These findings argue against an exclusive role for non‐symbolic number in supporting early mathematical understanding. Moreover, they suggest that mathematical understanding may be rooted in a general system of magnitude representation that is not specific to numerical magnitude but that also encompasses non‐numerical magnitude.     

Second-order mappings in grapheme–color synesthesia

Typically, the search for order in grapheme–color synesthesia has been conducted by looking at the frequency of certain letter–color associations. Here, we report stronger associations when second-order similarity mappings are examined—specifically, mappings between the synesthetic colors of letters and letter shape, frequency, and position in the alphabet. The analyses demonstrate that these relations are independent of one other. More strikingly, our analyses show that each of the letter–color mappings is restricted to one dimension of color, with letter shape and ordinality linked to hue, and letter frequency linked to luminance. These results imply that synesthetic associations are acquired as the alphabet is learned, with associations involving letter shape, ordinality, and frequency being made independently and idiosyncratically. Because these mappings of similarity structure between domains (letters and colors) are similar to those found in numerous other cognitive and perceptual domains, they imply that synesthetic associations operate on principles common to many aspects of human cognition.     

Is 26 + 26 smaller than 24 + 28? Estimating the approximate magnitude of repeated versus different numbers

It has recently been suggested that regardless of the dimension at hand (i.e., numerosity, length, time), similar operational mechanisms are involved in the comparison process based on approximate magnitude representation. One piece of evidence for this hypothesis lies in the presence of similar behavioral effects for any comparison (i.e., the distance effect). In the case of length comparison, the comparison process can be biased by summation toward either an underestimation or an overestimation: The sum of equal-size stimuli is underestimated, whereas the sum of different-size stimuli is overestimated. Relying on the hypothesis that similar operational mechanisms underlie the comparison process of any magnitude, we aim at extending these findings to another magnitude dimension. A number comparison task with digit numbers was used in the two experiments reported presently. The objective was to investigate whether summation also biases magnitude representation of numerical and symbolic information. The results provided evidence that the summation bias can also apply to numerical magnitude comparison, since the sum of repeated numbers (26 + 26) was underestimated whereas the sum of different numbers (24 + 28) was overestimated. We propose that these effects could be accounted for by a heuristic linking cognitive effort and magnitude estimation.     

Isolation,not locality

There is a long tradition of preferring local theories to ones that posit lawful or causal influence at a spacetime distance. In this paper, we argue against this preference. We argue that nonlocality is scientifically unobjectionable and that nonlocal theories can be known. Scientists can gather evidence for them and confirm them in much the same way that they do for local theories. We think these observations point to a deeper constraint on scientific theorizing and experimentation: the (quasi-) isolation of causal or lawful influence. We argue that this requirement ought to replace the locality desideratum in science. We then explore the possibility that the order of explanation has been reversed: perhaps it is isolatable influence that determines what counts as local in the first place.     

Tripartite model of anxiety and depression: psychometric evidence and taxonomic implications

We review psychometric and other evidence relevant to mixed anxiety-depression. Properties of anxiety and depression measures, including the convergent and discriminant validity of self- and clinical ratings, and interrater reliability, are examined in patient and normal samples. Results suggest that anxiety and depression can be reliably and validly assessed; moreover, although these disorders share a substantial component of general affective distress, they can be differentiated on the basis of factors specific to each syndrome. We also review evidence for these specific factors, examining the influence of context and scale content on ratings, factor analytic studies, and the role of low positive affect in depression. With these data, we argue for a tripartite structure consisting of general distress, physiological hyperarousal (specific anxiety), and anhedonia (specific depression), and we propose a diagnosis of mixed anxiety-depression.     

Function, goals and intention: children's teleological reasoning about objects

A fundamental aspect of adult thought is the 'teleological' tendency to assume that objects exist for a purpose. When seeing an unfamiliar artifact or strange anatomical part on an animal, the first question an adult will usually ask is 'what's that for?' - a query that assumes that the object can be teleologically explained in terms of its function. Current debate focuses on the origin and scope of teleological thought, and its role in children's emerging theories of the biological world. The bias to view objects as 'designed for a purpose' probably derives from children's privileged understanding of intentional behavior and artifacts. This makes children prone to a 'promiscuous teleology' in which artifacts and natural objects of all types are viewed as existing for a function. Because of this, I argue that we should be cautious about taking the existence of an early teleological bias as evidence that there is biological understanding that exists independently of a psychological construal of living things.     

Is Emotional Magnitude Spatialized? A Further Investigation

Accumulating evidence suggests that different magnitudes (e.g., number, size, and duration) are spatialized in the mind according to a common left–right metric, consistent with a generalized system for representing magnitude. A previous study conducted by two of us (Holmes & Lourenco, 2011 ) provided evidence that this metric extends to the processing of emotional magnitude, or the intensity of emotion expressed in faces. Recently, however, Pitt and Casasanto ( 2018 ) showed that the earlier effects may have been driven by a left–right mapping of mouth size rather than emotional magnitude, and they found no evidence for an emotional magnitude mapping when using words as stimuli. Here, we report two new experiments that further examine these conclusions. In Experiment 1, using face stimuli with mouths occluded, we replicate the original finding: Less emotional faces were associated with the left and more emotional faces with the right. However, we also find that people can reliably infer the sizes of the occluded mouths, and that these inferred mouth sizes can explain the observed left–right mapping. In Experiment 2, we show that comparative judgments of emotional words yield a left–right mapping of emotional magnitude not attributable to stimulus confounds. Based on these findings, we concur with Pitt and Casasanto that faces pose challenges for isolating the forces driving spatialization, but we suggest that emotional magnitude, when assessed using unconfounded stimuli in a sufficiently sensitive task, may indeed be spatialized as originally proposed. Suggestions for further research on the spatialization of emotional magnitude are discussed.