Children's spatial-numerical associations on horizontal, vertical, and sagittal axes

Young children intuitively organize numbers on straight, horizontal lines from left to right before the onset of formal instruction

The number line estimation task is frequently used to measure children's numerical magnitude understanding. It is unclear whether the resulting straight, horizontal, left-to-right-oriented estimate patterns indicate task constraints or children's intuitive number-space mapping. Three- to six-year-old children (N = 72, Mage = 4.89, 56% girls, 94% German citizenship) were asked to explain the meaning of numbers to a teddy by laying out a rope and attaching cards showing non-symbolic numerosities (dots) to it. Most children intuitively created straight, horizontal, and left-to-right-oriented representations. Characteristics of the line correlated with age, mathematical competencies, and home numeracy. This demonstrates the usefulness of the number line estimation task for assessing how children intuitively map numbers onto space.

Effect of egocentric and allocentric reference frames on spatial-numerical associations

From an embodied view of cognition, sensorimotor mechanisms are strongly involved in abstract processing, such as Arabic number meanings. For example, spatial cognition can influence number processing. These spatial-numerical associations (SNAs) have been deeply explored since the seminal SNAs of response code (SNARC) effect (i.e., faster left/right sided responses to small/large magnitude numbers, respectively). Although these SNAs along the transverse plane (left-to-right axis) have been extensively studied in cognitive sciences, no systematic assessment of other planes of the tridimensional space has been afforded. Moreover, there is no evidence of how SNAs organise themselves throughout the changes in spatial body-reference frames (egocentric and allocentric). Hence, this study aimed to explore how SNAs organise themselves along the transverse and sagittal planes when egocentric and allocentric changes are processed during body displacements in the environment. In the first experiment, the results revealed that, when the participants used an egocentric reference, SNAs were observed only along the sagittal plane. In a second experiment that used an allocentric reference, the reversed pattern of results was observed: SNAs were present only along the transverse plane of the body. Overall, these findings suggest that, depending on the spatial reference frames of the body, SNAs are strongly flexible.

Children grow upwards, and so does the number line: Evidence from a directional number line paradigm

Technological advancements give researchers the opportunity to explore the internal metric that allows to mentally place numbers in a spatial and ordered way to establish relationships between quantities. In this study, we implement the cMNL, an embodied number line paradigm to investigate the configuration of children's number space mappings under multiple conditions. A sample of 185 primary school children aged 8-10years old completed digitally an embodied number line task encompassing directionality and modality as variables. Contrary to the premise of a fixed internal number line moving from left to right in many Western scripts, our results suggest that children's number-space mapping is more robust along a vertical axis. In addition, children's embodied number line estimation differed depending on input modality. The findings provide insight into the variability in children's number line estimation, and the usability of digital assessment in understanding the mechanisms of the developing number-space system.

Spatio-Numerical Mapping in 3D

The close link between number and space is illustrated by the Spatial Numerical Association of Response Codes (SNARC) effect. The current research focuses on the flexibility of the SNARC across three dimensions. Shaki and Fischer (2018) pointed out that spatial attributes of stimuli and response effectors can favor an ad hoc spatial representation. In this paper, we aimed to broaden this perspective using two Go/NoGo experiments with digits being presented at two spatial locations while a central response was required. In Experiment 1, stimuli appeared either to the left or right (horizontal) and below or above fixation (vertical). In Experiment 2, as the monitor was laying down flat on the desk, stimuli appeared either to the left or right (horizontal) and either close or far from the observer (midsagittal). The results of Experiment 1 show significant effects for the two dimensions (horizontal, vertical), while in Experiment 2, we observe only a barely significant effect for the sagittal axis. We interpret these findings as showing (1) the importance of motor response spatialization in eliciting the SNAs and (2) the dominance of the vertical axis over the horizontal when the spatial component of the motor response is removed.

The role of cognitive control in the SNARC effect: A review

The spatial-numerical association of response codes (SNARC) effect, in which people respond to small numbers faster with the left hand and to large numbers faster with the right hand, is a popular topic in cognitive psychology. Some well-known theoretical accounts explaining this effect include the mental number line model, polarity correspondence principle, dual-route model, and working memory account. However, these fail to explain the finding that the size of the SNARC effect is modulated by cognitive control. Here, we propose a new account-a cognitive control-based view of the SNARC effect. This view argues that the SNARC effect is fundamentally determined by cognitive control in resolving conflicts during stimulus-response mapping. Several subcomponents of cognitive control, such as working memory, mental or task set shifting, inhibition control, and conflict adaptation, can easily modulate the SNARC effect. The cognitive control-based view can account for the flexible SNARC effect observed in diverse task situations while providing new insight into its mechanism.

Children's use of egocentric reference frames in spatial language is related to their numerical magnitude understanding

Numerical magnitude information is assumed to be spatially represented in the form of a mental number line defined with respect to a body-centred, egocentric frame of reference. In this context, spatial language skills such as mastery of verbal descriptions of spatial position (e.g., in front of, behind, to the right/left) have been proposed to be relevant for grasping spatial relations between numerical magnitudes on the mental number line. We examined 4- to 5-year-old's spatial language skills in tasks that allow responses in egocentric and allocentric frames of reference, as well as their relative understanding of numerical magnitude (assessed by a number word comparison task). In addition, we evaluated influences of children's absolute understanding of numerical magnitude assessed by their number word comprehension (montring different numbers using their fingers) and of their knowledge on numerical sequences (determining predecessors and successors as well as identifying missing dice patterns of a series). Results indicated that when considering responses that corresponded to the egocentric perspective, children's spatial language was associated significantly with their relative numerical magnitude understanding, even after controlling for covariates, such as children's SES, mental rotation skills, and also absolute magnitude understanding or knowledge on numerical sequences. This suggests that the use of egocentric reference frames in spatial language may facilitate spatial representation of numbers along a mental number line and thus seem important for preschoolers' relative understanding of numerical magnitude.