The interplay between spatial ordinal knowledge, linearity of number-space mapping, and arithmetic skills

The ability to map numbers onto space has been widely investigated with the number line (NL) task. Accurate (linear) placement is typically preceded by a developmental phase in which children assign more space to small numbers and compress large numbers to the right part of the line, thereby resembling a biased log-like mapping. Here, we exploited a task that separately assesses direction, order and accuracy of spatial mapping (DOS task) to investigate the origin of the biased NL mapping in a sample of first and second graders. Children with reduced ordinal knowledge in the DOS task showed a more biased NL mapping, which was formally assessed using the leading mathematical models of the NL task. However, the log-like biased mapping did not emerge in the DOS task, thereby showing a lack of generalisation across different number-space mapping tasks. Both ordinal knowledge in the DOS task and linearity in the NL task related to arithmetic fluency beyond domain-general cognitive factors. We conclude that the NL task is a meter of children's arithmetic skills rather than an expression of the mental representation of numbers.