The development of symbolic and non-symbolic number line estimations: Three developmental accounts contrasted within cross-sectional and longitudinal data

Three theoretical accounts have been put forward for the development of children‟s response patterns on number line estimation (NLE) tasks: the log-to-linear representational shift, the two-linear-to-linear transformation and the proportion judgment account. Despite the ongoing debate, it remains to date unclear which of these three developmental accounts reflects best how children‟s NLE performance evolve through development. The present study is the first which contrasted these three accounts in both symbolic and non-symbolic NLE performance of children at different ages, cross-sectionally as well as longitudinally: In Experiment 1, first, second and sixth graders were examined. In Experiment 2, first and second graders were tested again one year later. In case of symbolic estimations, the proportion judgment account described the data best. Most young children‟s non-symbolic estimation patterns were best described by a logarithmic model (within the log-to-lin account), whereas those of most older children were best described by the simple power model (within the proportion judgment account). Together, in line with the integrative account proposed by Dackermann et al. (2015), these data suggest that the development of children‟s symbolic and non-symbolic NLE patterns does not reflect a developmental change in their mental representations of number per se, but rather the trajectory of when they start using (advanced) cognitive strategies on those number representations – a process that might be modulated by their numerical knowledge.status: publishe