Longitudinal changes in young children’s 0–100 to 0–1000 number-line error signatures

We use a latent difference score (LDS) model to examine changes in young children's number-line (NL) error signatures (errors marking numbers on a NL) over 18 months. A LDS model (1) overcomes some of the inference limitations of analytic models used in previous research, and in particular (2) provides a more reliable test of hypotheses about the meaning and significance of changes in NL error signatures over time and task. The NL error signatures of 217 6-year-olds' (on test occasion one) were assessed three times over 18 months, along with their math ability on two occasions. On the first occasion (T1) children completed a 0-100 NL task; on the second (T2) a 0-100 NL and a 0-1000 NL task; on the third (T3) occasion a 0-1000 NL task. On the third and fourth occasions (T3 and T4), children completed mental calculation tasks. Although NL error signatures changed over time, these were predictable from other NL task error signatures, and predicted calculation accuracy at T3, as well as changes in calculation between T3 and T4. Multiple indirect effects (change parameters) showed that associations between initial NL error signatures (0-100 NL) and later mental calculation ability were mediated by error signatures on the 0-1000 NL task. The pattern of findings from the LDS model highlight the value of identifying direct and indirect effects in characterizing changing relationships in cognitive representations over task and time. Substantively, they support the claim that children's NL error signatures generalize over task and time and thus can be used to predict math ability.