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The development of numerosity estimation: Evidence for a linear number representation early in life
(2015)
Several studies investigating the development of approximate number representations used the number-to-position task and reported evidence for a shift from a logarithmic to a linear representation of numerical magnitude with increasing age. However, this interpretation as well as the number-to-position method itself has been questioned recently. The current study tested 5- and 8-year-old children on a newly established numerosity production task to examine developmental changes in number representations and to test the idea of a representational shift. Modelling of the children's numerical estimations revealed that responses of the 8-year-old children approximate a simple positive linear relation between estimated and actual numbers. Interestingly, however, the estimations of the 5-year-old children were best described by a bilinear model reflecting a relatively accurate linear representation of small numbers and no apparent magnitude knowledge for large numbers. Taken together, our findings provide no support for a shift of mental representations from a logarithmic to a linear metric but rather suggest that the range of number words which are appropriately conceptualised and represented by linear analogue magnitude codes expands during development.
Recent research has suggested that all types of size-related information are linked by a generalised system that codes for domain-independent magnitudes. This generalized system is further suggested to be acquired through everyday sensorimotor experiences with contingencies of size-related information in the real world. The aim of the present study was to investigate the existence of this common representation and its impact on the coupling of perception and action in early childhood. According to an embodied view on magnitude representation, an association between perceived magnitude information and size-related motor features, such as applied motor force, should emerge as soon as motor control is sufficiently developed. This hypothesis was tested in 2.5- to 3-year-old toddlers by engaging them in a computer game-like experimental task in which they were required to move objects placed on a platform upwards by pressing a button. The amount of objects was varied systematically (small amount: 3 vs. large amount: 15) and the force children applied on the button while moving the objects was recorded. Importantly, the amount of applied force was not relevant for successfully playing the game. The analysis of the peak force revealed that motor responses were executed more forcefully when children were presented with a large amount of objects compared to a small amount, irrespective of the toddler’s motor abilities which were evaluated by two additional measures (force control and general fine motor skills). This general effect of perceived magnitude information on the task-irrelevant applied motor force confirms our notion that a link between perceptual and motor magnitudes exists already in early childhood and provides new evidence for a sensorimotor grounding of magnitude concepts.