Set size, individuation, and attention to shape

Bidirectional Mapping Between the Symbolic Number System and the Approximate Number System

Abstract. Previous studies have discussed the symmetry of bidirectional mapping between approximate number system (ANS) and symbolic number system (SNS). However, these studies neglected the essential significance of bidirectional mapping in the development of numerical cognition. That is, with age, the connection strength between the ANS and SNS in ANS-SNS mapping could be higher than that in SNS-ANS mapping. Therefore, this study attempted to explore the symmetry of bidirectional mapping by examining whether the connection between the ANS and SNS is the same. Using two types of dot array materials (extensive and intensive) and sequence priming paradigms, this study found a stable negative priming effect in the ANS-SNS priming task, but no priming effect in the SNS-ANS priming task. In addition, although sensory cues (extensive and intensive) could affect performance in the ANS-SNS mapping task, these cues did not affect performance in the ANS-SNS priming task. In general, this study provides valuable insight into the symmetry of bidirectional mapping.

A MEG Study on the Processing of Time and Quantity: Parietal Overlap but Functional Divergence

A common magnitude system for the processing of time and numerosity, supported by areas in the posterior parietal cortex, has been proposed by some authors. The present study aims to investigate possible intersections between the neural processing of non-numerical (time) and numerical magnitudes in the posterior parietal lobe. Using Magnetoencephalography for the comparison of brain source activations during the processing of duration and numerosity contrasts, we demonstrate parietal overlap as well as dissociations between these two dimensions. Within the parietal cortex, the main areas of overlap were bilateral precuneus, bilateral intraparietal sulci, and right supramarginal gyrus. Interestingly, however, these regions did not equivalently correlated with the behavior for the two dimensions: left and right precuneus together with the right supramarginal gyrus accounted functionally for durational judgments, whereas numerosity judgments were accounted by the activation pattern in the right intraparietal sulcus. Present results, indeed, demonstrate an overlap between the neural substrates for processing duration and quantity. However, the functional relevance of parietal overlapping areas for each dimension is not the same. In fact, our data indicates that the same parietal sites rule differently non-numerical and numerical dimensions, as parts of broader networks.

Words affect visual perception by activating object shape representations

Linguistic labels are known to facilitate object recognition, yet the mechanism of this facilitation is not well understood. Previous psychophysical studies have suggested that words guide visual perception by activating information about visual object shape. Here we aimed to test this hypothesis at the neural level, and to tease apart the visual and semantic contribution of words to visual object recognition. We created a set of object pictures from two semantic categories with varying shapes, and obtained subjective ratings of their shape and category similarity. We then conducted a word-picture matching experiment, while recording participants’ EEG, and tested if the shape or the category similarity between the word’s referent and target picture explained the spatiotemporal pattern of the picture-evoked responses. The results show that hearing a word activates representations of its referent’s shape, which interacts with the visual processing of a subsequent picture within 100 ms from its onset. Furthermore, non-visual categorical information, carried by the word, affects the visual processing at later stages. These findings advance our understanding of the interaction between language and visual perception and provide insights into how the meanings of words are represented in the brain.

Numerical distance effect size is a poor metric of approximate number system acuity

Individual differences in the ability to compare and evaluate nonsymbolic numerical magnitudes-approximate number system (ANS) acuity-are emerging as an important predictor in many research areas. Unfortunately, recent empirical studies have called into question whether a historically common ANS-acuity metric-the size of the numerical distance effect (NDE size)-is an effective measure of ANS acuity. NDE size has been shown to frequently yield divergent results from other ANS-acuity metrics. Given these concerns and the measure's past popularity, it behooves us to question whether the use of NDE size as an ANS-acuity metric is theoretically supported. This study seeks to address this gap in the literature by using modeling to test the basic assumption underpinning use of NDE size as an ANS-acuity metric: that larger NDE size indicates poorer ANS acuity. This assumption did not hold up under test. Results demonstrate that the theoretically ideal relationship between NDE size and ANS acuity is not linear, but rather resembles an inverted J-shaped distribution, with the inflection points varying based on precise NDE task methodology. Thus, depending on specific methodology and the distribution of ANS acuity in the tested population, positive, negative, or null correlations between NDE size and ANS acuity could be predicted. Moreover, peak NDE sizes would be found for near-average ANS acuities on common NDE tasks. This indicates that NDE size has limited and inconsistent utility as an ANS-acuity metric. Past results should be interpreted on a case-by-case basis, considering both specifics of the NDE task and expected ANS acuity of the sampled population.

Universal and uniquely human factors in spontaneous number perception

A capacity for nonverbal numerical estimation is widespread among humans and animals. However, it is currently unclear whether numerical percepts are spontaneously extracted from the environment and whether nonverbal perception is influenced by human exposure to formal mathematics. We tested US adults and children, non-human primates, and numerate and innumerate Tsimane' adults on a quantity task in which they could choose to categorize sets of dots on the basis of number alone, surface area alone or a combination of the two. Despite differences in age, species and education, subjects are universally biased to base their judgments on number as opposed to the alternatives. Numerical biases are uniquely enhanced in humans compared to non-human primates, and correlated with degree of mathematics experience in both the US and Tsimane' groups. We conclude that humans universally and spontaneously extract numerical information, and that human nonverbal numerical perception is enhanced by symbolic numeracy.

A dissociation between small and large numbers in young children's ability to "solve for x" in non-symbolic math problems

Solving for an unknown addend in problems like 5+x=17 is challenging for children. Yet, previous work (Kibbe & Feigenson, 2015) found that even before formal math education, young children, aged 4- to 6-years, succeeded when problems were presented using non-symbolic collections of objects rather than symbolic digits. This reveals that the Approximate Number System (ANS) can support pre-algebraic intuitions. Here, we asked whether children also could intuitively "solve for x" when problems contained arrays of four or fewer objects that encouraged representations of individual objects instead of ANS representations. In Experiment 1, we first confirmed that children could solve for an unknown addend with larger quantities, using the ANS. Next, in Experiment 2a, we presented addend-unknown problems containing arrays of four or fewer objects (e.g., 1+x=3). This time, despite the identical task conditions, children were unable to solve for the unknown addend. In Experiment 2b, we replicated this failure with a new sample of children. Finally, in Experiment 3, we confirmed that children's failures in Experiments 2a and b were not due to lack of motivation to compute with small arrays, or to the discriminability of the quantities used: children succeeded at solving for an unknown sum with arrays containing four or fewer objects. Together, these results suggest that children's ability to intuitively solve for an unknown addend may be limited to problems that can be represented using the ANS.

Sensory-integration system rather than approximate number system underlies numerosity processing: A critical review

It is widely accepted that human and nonhuman species possess a specialized system to process large approximate numerosities. The theory of an evolutionarily ancient approximate number system (ANS) has received converging support from developmental studies, comparative experiments, neuroimaging, and computational modelling, and it is one of the most dominant and influential theories in numerical cognition. The existence of an ANS system is significant, as it is believed to be the building block of numerical development in general. The acuity of the ANS is related to future arithmetic achievements, and intervention strategies therefore aim to improve the ANS. Here we critically review current evidence supporting the existence of an ANS. We show that important shortcomings and confounds exist in the empirical studies on human and non-human animals as well as the logic used to build computational models that support the ANS theory. We conclude that rather than taking the ANS theory for granted, a more comprehensive explanation might be provided by a sensory-integration system that compares or estimates large approximate numerosities by integrating the different sensory cues comprising number stimuli.

A texture-processing model of the 'visual sense of number'

It has been suggested that numerosity is an elementary quality of perception, similar to colour. If so (and despite considerable investigation), its mechanism remains unknown. Here, we show that observers require on average a massive difference of approximately 40% to detect a change in the number of objects that vary irrelevantly in blur, contrast and spatial separation, and that some naive observers require even more than this. We suggest that relative numerosity is a type of texture discrimination and that a simple model computing the contrast energy at fine spatial scales in the image can perform at least as well as human observers. Like some human observers, this mechanism finds it harder to discriminate relative numerosity in two patterns with different degrees of blur, but it still outpaces the human. We propose energy discrimination as a benchmark model against which more complex models and new data can be tested.

Set size and culture influence children's attention to number

Much research evidences a system in adults and young children for approximately representing quantity. Here we provide evidence that the bias to attend to discrete quantity versus other dimensions may be mediated by set size and culture. Preschool-age English-speaking children in the United States and Japanese-speaking children in Japan were tested in a match-to-sample task where number was pitted against cumulative surface area in both large and small numerical set comparisons. Results showed that children from both cultures were biased to attend to the number of items for small sets. Large set responses also showed a general attention to number when ratio difficulty was easy. However, relative to the responses for small sets, attention to number decreased for both groups; moreover, both U.S. and Japanese children showed a significant bias to attend to total amount for difficult numerical ratio distances, although Japanese children shifted attention to total area at relatively smaller set sizes than U.S. children. These results add to our growing understanding of how quantity is represented and how such representation is influenced by context--both cultural and perceptual.

Neural substrates of numerosity estimation in autism

Visual skills, including numerosity estimation are reported to be superior in autism spectrum disorders (ASD). This phenomenon is attributed to individuals with ASD processing local features, rather than the Gestalt. We examined the neural correlates of numerosity estimation in adults with and without ASD, to disentangle perceptual atypicalities from numerosity processing. Fourteen adults with ASD and matched typically developed (TD) controls estimated the number of dots (80-150) arranged either randomly (local information) or in meaningful patterns (global information) while brain activity was recorded with magnetoencephalography (MEG). Behavioral results showed no significant group difference in the errors of estimation. However, numerical estimation in ASD was more variable across numerosities than TD and was not affected by the global arrangement of the dots. At 80-120 ms, MEG analyses revealed early significant differences (TD > ASD) in source amplitudes in visual areas, followed from 120 to 400 ms by group differences in temporal, and then parietal regions. After 400 ms, a source was found in the superior frontal gyrus in TD only. Activation in temporal areas was differently sensitive to the global arrangement of dots in TD and ASD. MEG data show that individuals with autism exhibit widespread functional abnormalities. Differences in temporal regions could be linked to atypical global perception. Occipital followed by parietal and frontal differences might be driven by abnormalities in the processing and conversion of visual input into a number-selective neural code and complex cognitive decisional stages. These results suggest overlapping atypicalities in sensory, perceptual and number-related processing during numerosity estimation in ASD.