The mental number line metaphor describes how numbers are associated with space. These spatial-numerical associations (SNA) are subserved by parietal structures (mainly intraparietal sulcus [IPS] and posterior superior parietal lobule [PSPL]). Generally, it is assumed that this association is a basic cornerstone for arithmetic skills. In this review, we present a taxonomy of SNAs and outline which of them are related to arithmetic skills. Recent research suggests that not all SNAs are related to arithmetic skills; for instance, the spatial-numerical association of response codes (SNARC) is not or at least less related to arithmetic skills than SNAs assessed in the number line estimation task. In general, we conclude that the relationship between SNAs and arithmetic skills are rather weak or caused by mediating variables. Nevertheless, interventions based on relations between space and numbers can be beneficial for arithmetic skills because space is a powerful tool to understand arithmetic concepts.
Spatial processing of numbers has emerged as one of the basic properties of humans' mathematical thinking. However, how and when number-space relations develop is a highly contested issue. One dominant view has been that a link between numbers and left/right spatial directions is constructed based on directional experience associated with reading and writing. However, some early forms of a number-space link have been observed in preschool children who cannot yet read and write. As literacy experience is evidently not necessary for number-space effects, we are searching for other potential sources of this association. Here we propose and test a hypothesis that the number-space link can be quickly constructed in preschool children's cognition on the basis of spatially oriented visuo-motor activities. We trained 3- and 4-year-old children with a non-numerical spatial movement task (left-to-right or right-to-left), where via touch screen children had to move a frog across a pond. After the training, children had to perform a numerosity comparison task. After left-to-right training, we observed a SNARC-like effect (reactions to smaller numbers were faster on the left side, and reactions to larger numbers on the right side), and after right-to-left training a reverse effect. These results are the first to show a causal link between visuo-motor activities and number-space associations in children before they learn to read and write. We argue that simple activities, such as manual games, dominant in a given society, might shape number-space associations in children in a way similar to lifelong reading training.
The last years of research on numerical development have provided evidence that spatial-numerical associations (SNA) can be formed independent of formal school training. However, most of these studies used various experimental paradigms that referred to slightly different aspects of number and space processing. This poses a question of whether all SNAs described in the developmental literature can be interpreted as a unitary construct, or whether they are rather examples of different, but related phenomena. Our review aims to provide a starting point for a systematic classification of SNA measures used from infancy to late preschool years, and their underlying representations. We propose to distinguish among four basic SNA categories: (i) cross-dimensional magnitude processing, (ii) associations between spatial and numerical intervals, (iii) associations between cardinalities and spatial directions, (iv) associations between ordinalities and spatial directions. Such systematization allows for identifying similarities and differences between processes and representations that underlie the described measures, and also for assessing the adequacy of using different SNA tasks at different developmental stages.
The directionality of space-number association (SNA) is shaped by cultural experiences. It usually follows the culturally dominant reading direction. Smaller numbers are generally associated with the starting side for reading (left side in Western cultures), while larger numbers are associated with the right endpoint side. However, SNAs consistent with cultural reading directions are present before children can actually read and write. Therefore, these SNAs cannot only be shaped by the direction of children’s own reading/writing behavior. We propose six distinct processes – one biological and five cultural/educational – underlying directional SNAs before formal reading acquisition: (i) Brain lateralization, (ii) Monitoring adult reading behavior, (iii) Pretend reading and writing, and rudimentary reading and writing skills, (iv) Dominant attentional directional preferences in a society, not directly related to reading direction, (v) Direct spatial-numerical learning, (vi) Other spatial-directional processes independent of reading direction. In this mini-review, we will differentiate between these processes, elaborate when in development they might emerge, discuss how they may create the SNAs observed in preliterate children and propose how they can be studied in the future.
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