An Assessment of Lee and Sarnecka's (2010) Knower-level Model of Children's Numeracy Learning

How do children learn to count? Acquisition of number words and their representation of quantity (Cardinality Principle; CP) is commonly assessed with Wynn’s (1990; 1992) give-a-number (Give-N) task. However, results and methods are inconsistent across studies with this task, contributing to theoretical debates about how children acquire number knowledge. The primary aim of this project was to review these debates, and to evaluate systematically a graphical knower-level model of number word acquisition (Lee & Sarnecka, 2010), by analysing both the model fit and predictive error across seven Give-N datasets. Data were sourced from studies with French-, Hungarian-, and English-speaking children (N = 823) aged 24-86 months (M = 49.7). The model described most children’s number word acquisition with a high degree of confidence, and reported 29.6% of participants had applied the CP to their entire counting list (CP-knowers). Fits to data appeared to be reasonably good, but analyses revealed systematic error between model predictions and data. Most notably, predictions for children who had only applied the CP to a subset of their counting list (subset-knowers/N-knowers) were significantly higher than performance in trials for N + 1 and N + 2 (where N is the capacity of this subset). Additionally, performance error was reviewed for each knower-level individually. Ultimately, our results suggested that Lee and Sarnecka’s model did not accurately account for children’s behaviour on the Give-N task. Moreover, this highlights that the knower-level account of children’s number word acquisition may not effectively describe this process.