Operational momentum and size ordering in preverbal infants

Does the Brain Care Which Direction We Read? A Cross-Cultural tDCS Study on Functional Lateralization of Number Processing

PURPOSE

The potential influence of culture on functional lateralization was rarely investigated, yet it may be an important factor in our understanding of the human brain. In numerical processing, evidence was found for differential directional preferences of space-number associations in cultures with opposite reading direction systems. This may affect finger-counting preferences like the starting hand, which in turn have previously been associated with differing lateralization. Such studies raise the question of whether number culture may also play a distinct role in the lateralization of the intraparietal sulcus (IPS), the hallmark region of numerical magnitude processing.

METHOD

In our preregistered cross-cultural study, we applied anodal transcranial direct current stimulation (tDCS) over the left versus right IPS to investigate the effect of stimulation as compared to sham in Iranians (with right-to-left reading system) and Germans (with left-to-right reading system).

FINDING

Results indicated no overall effect of stimulation; however, exploratory analyses revealed that tDCS over the left and right IPS facilitated number processing in Iranians compared to Germans after controlling for training effects. Finger-counting direction was not found to be decisive for this effect.

CONCLUSION

At the end, number processing might be bilaterally represented in the IPS; however, our exploratory analyses emphasize the need for further investigation on the potential role of culture in the representations of numbers.

Space modulates cross-domain transfer of abstract rules in infants

Developmental studies have shown that infants exploit ordinal information to extract and generalize repetition-based rules from a sequence of items. Within the visual modality, this ability is constrained by the spatial layout within which items are delivered given that a left-to-right orientation boosts infants' rule learning, whereas a right-to-left orientation hinders this ability. Infants' rule learning operates across different domains and can also be transferred across modalities when learning is triggered by speech. However, no studies have investigated whether the transfer of rule learning occurs across different domains when language is not involved. Using a visual habituation procedure, we tested 7-month-old infants' ability to extract rule-like patterns from numerical sequences and generalize them to non-numerical sequences of visual shapes and whether this ability is affected by the spatial orientation. Infants were first habituated to left-to-right or right-to-left oriented numerical sequences instantiating an ABB rule and were then tested with the familiar rule instantiated across sequences of single geometrical shapes and a novel (ABA) rule. Results showed a transfer of learning from number to visual shapes for left-to-right oriented sequences but not for right-to-left oriented ones (Experiment 1) even when the direction of the numerical change (increasing vs. decreasing) within the habituation sequences violated a small-left/large-right number-space association (Experiment 2). These results provide the first demonstration that visual rule learning mechanisms in infancy operate at a high level of abstraction and confirm earlier findings that left-to-right oriented directional cues facilitate infants' representation of order.

Operational momentum during children's approximate arithmetic relates to symbolic math skills and space-magnitude association

Operational momentum (OM) refers to the behavioral tendency to overestimate or underestimate the results of addition or subtraction, respectively. The cognitive mechanism of the OM effect and how it is related to the development of symbolic math abilities are not well understood. The current study examined whether individual differences in the OM effect are related to symbolic arithmetic abilities, number line estimation performance, and the space-magnitude association effect in young children. In this study, first-grade elementary school children manifested the OM effect during approximate addition and subtraction. Individual differences in the OM effect were not correlated with number line estimation error. Interestingly, children who showed a greater degree of the OM effect performed not worse, but better on the symbolic arithmetic task. In addition, the OM effect was correlated with the space-magnitude association (size congruity) effect measured with the Numerical Stroop task. More specifically, the OM bias was correlated with the ability to inhibit interference from competing information on the incongruent trials of the Numerical Stroop task. Our results suggest that the inaccuracy of numerical magnitude representations is not the source of the OM effect. Given that children with better math ability showed a greater OM bias, a stronger OM effect may reflect better intuition in arithmetic operations. Altogether, we carefully interpret these findings as suggesting that a greater OM effect reflects superior intuition or fundamental knowledge of arithmetic operations and a more adult-like maturation of the reorienting component of the attentional system.

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.

Operational momentum for magnitude ordering in preschool children and adults

When adding or subtracting quantities, adults tend to overestimate addition outcomes and underestimate subtraction outcomes. They also shift visuospatial attention to the right when adding and to the left when subtracting. These operational momentum phenomena are thought to reflect an underlying representation in which small magnitudes are associated with the left side of space and large magnitudes with the right side of space. Currently, there is limited research on operational momentum in early childhood or for operations other than addition and subtraction. The current study tested whether English-speaking 3- and 4-year-old children and college-aged adults exhibit operational momentum when ordering quantities. Participants were presented with two experimental blocks. In one block of trials, they were tasked with choosing the same quantity they had previously seen three times; in the other block, they were asked to generate the next quantity in a doubling sequence composed of three ascending quantities. A bias to shift attention to the right after an ascending operation was found in both age groups, and a bias to overestimate the next sequential quantity during an ascending ordering operation was found in adults under conditions of uncertainty. These data suggest that, for children, the spatial biases during operating are more pronounced than the mis-estimation biases. These findings highlight the spatial underpinnings of operational momentum and suggest that both very young children and adults conceptualize quantity along a horizontal continuum during ordering operations, even before formal schooling.

Spatial Presentations, but Not Response Formats Influence Spatial-Numerical Associations in Adults

According to theories of embodied numerosity, processing of numerical magnitude is anchored in bodily experiences. In particular, spatial representations of number interact with movement in physical space, but it is still unclear whether the extent of the movement is relevant for this interaction. In this study, we compared spatial-numerical associations over response movements of differing spatial expansion. We expected spatial-numerical effects to increase with the extent of physical response movements. In addition, we hypothesized that these effects should be influenced by whether or not a spatial representation of numbers was presented. Adult participants performed two tasks: a magnitude classification (comparing numbers to the fixed standard 5), from which we calculated the Spatial Numerical Association of Response Codes (SNARC) effect; and a magnitude comparison task (comparing two numbers against each other), from which we calculated a relative numerical congruity effect (NCE), which describes that when two relatively small numbers are compared, responses to the smaller number are faster than responses to the larger number; and vice versa for large numbers. A SNARC effect was observed across all conditions and was not influenced by response movement extent but increased when a number line was presented. In contrast, an NCE was only observed when no number line was presented. This suggests that the SNARC effect and the NCE reflect two different processes. The SNARC effect seems to represent a highly automated classification of numbers as large or small, which is further emphasized by the presentation of a number line. In contrast, the NCE likely results from participants not only classifying numbers as small or large, but also processing their relative size within the relevant section of their mental number line representation. An additional external presentation of a number line might interfere with this process, resulting in overall slower responses. This study follows up on previous spatial-numerical training studies and has implications for future spatial-numerical trainings. Specifically, similar studies with children showed contrasting results, in that response format but not number line presentation influenced spatial-numerical associations. Accordingly, during development, the relative relevance of physical experiences and presentation format for spatial-numerical associations might change.

Infants learn better from left to right: a directional bias in infants' sequence learning

A wealth of studies show that human adults map ordered information onto a directional spatial continuum. We asked whether mapping ordinal information into a directional space constitutes an early predisposition, already functional prior to the acquisition of symbolic knowledge and language. While it is known that preverbal infants represent numerical order along a left-to-right spatial continuum, no studies have investigated yet whether infants, like adults, organize any kind of ordinal information onto a directional space. We investigated whether 7-month-olds' ability to learn high-order rule-like patterns from visual sequences of geometric shapes was affected by the spatial orientation of the sequences (left-to-right vs. right-to-left). Results showed that infants readily learn rule-like patterns when visual sequences were presented from left to right, but not when presented from right to left. This result provides evidence that spatial orientation critically determines preverbal infants' ability to perceive and learn ordered information in visual sequences, opening to the idea that a left-to-right spatially organized mental representation of ordered dimensions might be rooted in biologically-determined constraints on human brain development.

Core mathematical abilities in infants: Number and much more

Adults' ability to process numerical information can be traced back to the first days of life. The cognitive mechanisms underlying numerical representations are functional in preverbal infants, who are able to both track a small number of individuals and to estimate the numerosity of large sets across different modalities. This ability is closely linked to their ability to compute other quantitative dimensions such as spatial extent and temporal duration. In fact, the human mind establishes, early in life, spontaneous links between number, space, and time, which are privileged relative to links with other continuous dimensions (like loudness and brightness). Finally, preverbal infants do not only associate numbers to corresponding spatial extents but also to different spatial positions along a spatial axis. It is argued that these number-space mappings are at the origins of the "mental number line" representation, which is already functional in the first year of life.