Core mathematical abilities in infants: Number and much more

Disparate processing of numerosity and associated continuous magnitudes in rats

The studies of number sense in different species are severely hampered by the inevitable entanglement of non-numerical attributes inherent in nonsymbolic stimuli representing numerosity, resulting in contrasting theories of numerosity processing. Here, we developed an algorithm and associated analytical methods to generate stimuli that not only minimized the impact of non-numerical magnitudes in numerosity perception but also allowed their quantification. We trained number-naïve rats with these stimuli as sound pulses representing two or three numbers and demonstrated that their numerical discrimination ability mainly relied on numerosity. Also, studying the learning process revealed that rats used numerosity before using magnitudes for choices. This numerical processing could be impaired specifically by silencing the posterior parietal cortex. Furthermore, modeling this capacity by neural networks shed light on the separation of numerosity and magnitudes extraction. Our study helps dissect the relationship between magnitude and numerosity processing, and the above different findings together affirm the independent existence of innate number and magnitudes sense in rats.

The interplay between math performances, spatial abilities, and affective factors: The role of task

Many studies have suggested that cognitive and affective abilities (such as math anxiety- MA and math self-efficacy) explain individual differences in math.

PURPOSE

The present study explores the interplay between MA, math self-efficacy, spatial anxiety and spatial abilities in explaining individual differences on two complex math tasks.

PROCEDURES

Ninety-three college students took part in the experiment and completed 3 emotional questionnaires, in addition to 2 math tasks and a mental rotation task.

FINDINGS

The interplay between math performances and cognitive and affective factors is related to task demand. MA and spatial abilities affected math performances directly, regardless of task. Spatial anxiety had only an indirect effect on math performances via MA, regardless of task.

CONCLUSIONS

These finding suggest that for math performances, contrary to MA, real spatial abilities rather than perceived spatial anxiety play a significant role in explaining individual differences.  Hence, the present result dissociates cognitive and emotional factors.

Adding and subtracting by hand: Metaphorical representations of arithmetic in spontaneous co-speech gestures

This study investigated the spontaneous co-speech gestures produced by speakers who were talking about the concepts of addition and subtraction in a television news setting. We performed a linguistic and co-speech gesture analysis of expressions related to the concepts of addition (N plus N, addition, add) and subtraction (N minus N, subtraction, subtract). First, we compared the linguistic frequency of these structures across several corpora. Second, we performed a multimodal gesture analysis, drawing data from a television news repository. We analyzed 423 co-speech gestures (169 for subtraction and 254 for addition) in terms of their axis (e.g., lateral, sagittal) and their direction (e.g., leftwards, away from their body). Third, we examined the semantic properties of the direct object that was added or subtracted. There were two main findings. First, low-frequency linguistic expressions were more likely to be accompanied by co-speech gestures. Second, most gestures about addition and subtraction were produced along the lateral or sagittal axes. When people spoke about addition, they tended to produce lateral, rightwards movements or movements away from the body. When people spoke about subtraction, they tended to produce lateral, leftwards movements or movements towards the body. This co-speech gesture data provides evidence that people activate two different metaphors for arithmetic in spontaneous behavior: arithmetic is motion along a path and arithmetic is collecting objects.

Characterizing ontogeny of quantity discrimination in zebrafish

A sense of non-symbolic numerical magnitudes is widespread in the animal kingdom and has been documented in adult zebrafish. Here, we investigated the ontogeny of this ability using a group size preference (GSP) task in juvenile zebrafish. Fish showed GSP from 21 days post-fertilization and reliably chose the larger group when presented with discriminations of between 1 versus 3, 2 versus 5 and 2 versus 3 conspecifics but not 2 versus 4 conspecifics. When the ratio between the number of conspecifics in each group was maintained at 1 : 2, fish could discriminate between 1 versus 2 individuals and 3 versus 6, but again, not when given a choice between 2 versus 4 individuals. These findings are in agreement with studies in other species, suggesting the systems involved in quantity representation do not operate separately from other cognitive mechanisms. Rather they suggest quantity processing in fishes may be the result of an interplay between attentional, cognitive and memory-related mechanisms as in humans and other animals. Our results emphasize the potential of the use of zebrafish to explore the genetic and neural processes underlying the ontogeny and function of number cognition.

Small-range numerical representations of linguistic sounds in 9- to 10-month-old infants

Coordinated studies provide evidence that very young infants, like human adults and nonhuman animals, readily discriminate small and large number of visual displays on the basis of numerical information. This capacity has been considerably less studied in the auditory modality. Surprisingly, the available studies yielded mixed evidence concerning whether numerical representations of auditory items in the small number range (1 to 3) are present early in human development. Specifically, while newborns discriminate 2- from 3-syllable sequences, older infants at 6 and 9 months of age fail to differentiate 2 from 3 tones. This study tested the hypothesis that infants can represent small sets more precisely when listening to ecologically relevant linguistic sounds. The aim was to probe 9- to 10-month-olds' (N = 74) ability to represent sound sets in a working memory test. In experiments 1 and 2, infants successfully discriminated 2- and 3-syllable sequences on the basis of their numerosity, when continuous variables, such as individual item duration, inter-stimulus duration, pitch, intensity, and total duration, were controlled for. In experiment 3, however, infants failed to discriminate 3- from 4-syllable sequences under similar conditions. Finally, in experiment 4, infants were tested on their ability to distinguish 2 and 3 tone sequences. The results showed no evidence that infants discriminated these non-linguistic stimuli. These findings indicate that, by means of linguistic sounds, infants can access a numerical system that yields precise auditory representations in the small number range.

Excessive visual crowding effects in developmental dyscalculia

Visual crowding refers to the inability to identify objects when surrounded by other similar items. Crowding-like mechanisms are thought to play a key role in numerical perception by determining the sensory mechanisms through which ensembles are perceived. Enhanced visual crowding might hence prevent the normal development of a system involved in segregating and perceiving discrete numbers of items and ultimately the acquisition of more abstract numerical skills. Here, we investigated whether excessive crowding occurs in developmental dyscalculia (DD), a neurodevelopmental disorder characterized by difficulty in learning the most basic numerical and arithmetical concepts, and whether it is found independently of associated major reading and attentional difficulties. We measured spatial crowding in two groups of adult individuals with DD and control subjects. In separate experiments, participants were asked to discriminate the orientation of a Gabor patch either in isolation or under spatial crowding. Orientation discrimination thresholds were comparable across groups when stimuli were shown in isolation, yet they were much higher for the DD group with respect to the control group when the target was crowded by closely neighbouring flanking gratings. The difficulty in discriminating orientation (as reflected by the combination of accuracy and reaction times) in the DD compared to the control group persisted over several larger target flanker distances. Finally, we found that the degree of such spatial crowding correlated with impairments in mathematical abilities even when controlling for visual attention and reading skills. These results suggest that excessive crowding effects might be a characteristic of DD, independent of other associated neurodevelopmental disorders.

Learning disabilities: Developmental dyscalculia

Developmental dyscalculia (DD) is a developmental learning disability that manifests as a persistent difficulty in comprehending even the most basic numeric and arithmetic concepts, despite normal intelligence and schooling opportunities. Given the predominant use of numbers in modern society, this condition can pose major challenges in the sufferer's everyday life, both in personal and professional development. Since, to date, we still lack a universally recognized and psychometrically driven definition of DD, its diagnosis has been applied to a wide variety of cognitive profiles. In this chapter, we review the behavioral and neural characterization of DD as well as the different neurocognitive and etiologic accounts of this neurodevelopmental disorder. We underline the multicomponential nature of this heterogeneous disability: different aspects of mathematical competence can be affected by both the suboptimal recruitment of general cognitive functions supporting mathematical cognition (such as attention, memory, and cognitive control) and specific deficits in mastering numeric concepts and operations. Accordingly, both intervention paradigms focused on core numeric abilities and more comprehensive protocols targeting multiple neurocognitive systems have provided evidence for effective positive outcomes.

Implications of Change/Stability Patterns in Children's Non-symbolic and Symbolic Magnitude Judgment Abilities Over One Year: A Latent Transition Analysis

Non-symbolic magnitude abilities are often claimed to support the acquisition of symbolic magnitude abilities, which, in turn, are claimed to support emerging math abilities. However, not all studies find links between non-symbolic and symbolic magnitude abilities, or between them and math ability. To investigate possible reasons for these different findings, recent research has analyzed differences in non-symbolic/symbolic magnitude abilities using latent class modeling and has identified four different magnitude ability profiles residing within the general magnitude ability distribution that were differentially related to cognitive and math abilities. These findings may help explain the different patterns of findings observed in previous research. To further investigate this possibility, we (1) attempted to replicate earlier findings, (2) determine whether magnitude ability profiles remained stable or changed over 1 year; and (3) assessed the degree to which stability/change in profiles were related to cognitive and math abilities. We used latent transition analysis to investigate stability/changes in non-symbolic and symbolic magnitude abilities of 109 5- to 6-year olds twice in 1 year. At Time 1 and 2, non-symbolic and symbolic magnitude abilities, number transcoding and single-digit addition abilities were assessed. Visuospatial working memory (VSWM), naming numbers, non-verbal IQ, basic RT was also assessed at Time 1. Analysis showed stability in one profile and changes in the three others over 1 year. VSWM and naming numbers predicted profile membership at Time 1 and 2, and profile membership predicted math abilities at both time points. The findings confirm the existence of four different non-symbolic-symbolic magnitude ability profiles; we suggest the changes over time in them potentially reflect deficit, delay, and normal math developmental pathways.

Infants' intermodal numerical knowledge

Two-system theory as the dominant approach in the field of infant numerical representation is characterized by three features: precise representation of small sets of objects, approximate representation of large magnitudes and failure to compare small and large sets. Comparison of single- and multimodal numerical abilities suggests that infants' performance in multimodal conditions is consistent with these three features. Nevertheless, the influence of multimodal stimulation on infants' numerical representation is characterized by preventing the formation of perceptual overlaps across different sensory modalities which can lead to an understanding of numerical values of small sets and also by creating a conceptual overlap about numbers that increases infants' accuracy for discriminating quantities when numerical information is presented bimodally and synchronously. Such multisensory benefits provide numerical capabilities beyond what is depicted by the two-system view.