Numbers in Action: Origins and Developmental course – NUMACT

One set of behavioral studies with 8-month-old infants used a habituation paradigm (taking as measure of interest infants’ looking times), which was modeled after previous work investigating the number-length mapping, where infants are shown to create congruent mappings between the numerosity of a set and the length of a line (de Hevia & Spelke, 2010). This study found that infants successfully created number-length mappings only when number and length varied in a congruent way (i.e., the more numerous the array, the longer the accompanying line), but were unable to create them when the two dimensions varied in an incongruent way (i.e., the more numerous the array, the shorter the accompanying line). In the same vein, in NUMACT we investigated whether infants would similarly create expectations of congruency in magnitude changes when presented with information of number and of a hand opening (depicting a grasping action). One group of infants was habituated to a rule depicting a positive relationship between number and the amplitude of a hand opening (i.e., the larger the number, the greater the hand opening), while other group received the same information except that the relationship was inverse (i.e., the larger the number, the smaller the hand opening). During test trials, both groups of infants were shown new number-hand pairings, both in a congruent and in an incongruent mapping: if infants are able to learn the rule shown during habituation (either congruent or incongruent), in test they should discriminate between the new pairing conforming to the learnt rule (generalization of the rule) from the one non conforming to the learnt rule, testifying of their learning and discrimination. In a closely similar study we have explored whether the number-action mapping extends to other meaningful actions, such as observing an agent feeding. We showed infants videos of a Pacman character moving autonomously and adapting the amplitude of aperture of its mouth to the magnitude of the object to be eaten (the object varied in size in one experiment and in the number of elements in a second experiment). In another behavioral study newborns were tested in their ability to connect auditory number with the aperture of a hand in a meaningful way (mirroring their number-length mapping, de Hevia et al., 2014). Studies on children and adults measured their preferences for matching a set of magnitudes (including number and size) and hand shapes, which were presented in both static and dynamic displays. Finally, we measured 3- to 4-month-old infants’ electrical brain activity using EEG (electroencephalogram) when observing both congruent (i.e., a wide opened hand preceding a large numerosity -12-; a closed hand preceding a small numerosity -4-) and incongruent (i.e., a wide opened hand preceding a small numerosity -4-; a closed hand preceding a large numerosity -12-) pairings.

We have found evidence that across ages, from infancy through childhood and adulthood, there is a spontaneous link between the two quantities of number and amplitude of an action. We have found that 8-month-old infants that are shown a rule that establishes a positive relationship between number and amplitude of an action (i.e., the larger the number, the larger the amplitude of a hand opening) are able to learn the rule and generalize it to new exemplars; in contrast, when a different group of 8-month-old infants is shown the exact same numerical and action-related stimuli following an inverse rule (i.e., the larger the number, the smaller the amplitude of a hand opening), they are unable to learn and/or generalize the rule to new exemplars. This finding suggests the number-action link is functional in the first year of life, and that infants at this age create expectations of congruency between magnitude-related information across the numerical and action domains (published in Scientific Reports).

The number-action link is already functional at 3 months of age as measured by EEG methods. We measured the 3- to 4-m-o’s electrical brain activity across a broad region including frontal and occipito-parietal regions while presenting infants with both congruent (i.e., a wide opened hand precedes a large numerosity -12-; a closed hand precedes a small numerosity -4-) and incongruent (i.e., a wide opened hand precedes a small numerosity -4-; a closed hand precedes a large numerosity -12-) number-action couplings. Brain’s recorded activity was significantly modulated by the congruency of the pairings, suggesting an early, fully functional link between representations of numerosity and action even before infants perform accurate grasping actions (published in Brain Sciences).

Eight-month-old infants are able to learn a rule that establishes a positive relationship between number and the action performed by an autonomous agent: this ability is present for both size and numerical information (under review).

When children at different ages are asked to explicitly link one type of hand opening with one of two possible magnitudes (including numerical arrays and objects of different sizes) they show an adult-like performance from 8 years of age (published in Journal of Experimental Child Psychology).

We have shown that humans, from infancy, create expectations of congruency between a magnitude dimension, either size or numerosity, and the amplitude of the associated action, and that they do so only when pairings are congruent, implying that there is a predisposition for mapping these dimensions in a positive way. NUMACT studies support the existence of magnitude-action associations in preverbal infants, children and adults, and suggest that these associations may extend beyond hand openings depicting reaching and grasping, as studied in adults previously, but also to other meaningful actions. By using different magnitudes (size and number) in our studies, we contribute insights to a more comprehensive examination of humans’ processing regarding the coupling between the information of magnitude and action. Finally, these findings have relevance for understanding both early cognitive development and the potential links between numerical processing and action perception. Future research could further explore the developmental and evolutionary underpinnings of the connection between different magnitudes and action, examining how it emerges at birth, develops over time, to what magnitudes and actions it extends to, and whether and how it is shared with other non-human animals.

A fundamental link between magnitude (i.e., number, size, time) on the one hand, and visuo-spatial and motor abilities on the other, has been demonstrated in the adult human brain. While much insight has been recently gained on the number-space link, the origins and developmental course of the interaction between numbers and action is still poorly understood. A developmental account for human’s ability to relate number and action has become of paramount importance in a society where mathematics is at the centre of the children’s school curricula and one of the foundations of mathematics is the understanding of number. This project investigates the onset, properties and development of the number-action link using behavioral, electrophysiological, and electromyographic measures in human newborns and infants, by describing when and how the action perception system is sensitive to, and efficiently incorporates, information of number. Behavioral looking time (Task 1) and eye movement (Task 2) paradigms will test for the presence of a number-action link at birth, and the ability to detect and anticipate the goal of an action using numerical information during infancy. Electrophysiological paradigms (Task 3) will be used to investigate modulations of infants’ EEG activity during the observation of congruent and incongruent number-action couplings. Electromyographic paradigms will allow for testing when and how the activation of infants’ muscles is affected by numerical information. The results of this project will contribute knowledge with critical implications for education and neuropsychology.