How Does the Accuracy of Children's Number Representations Influence the Accuracy of Their Numerical Predictions?

Predictions begin with an extrapolation of the properties of their underlying representations to forecast a future state not presently in evidence. For numerical predictions, sets of numbers are summarized and the result forms the basis of and constrains numerical predictions. One open question is how the accuracy of underlying representations influences predictions, particularly numerical predictions. It is possible that inaccuracies in individual number representations are randomly distributed and averaged over during summarization (e.g., wisdom of crowds). It is also possible that inaccuracies are not random and lead to errors in predictions. We investigated this question by measuring the accuracy of individual number representations of 279 children ages 8-12 years, using a 0-1,000 number line, and numerical predictions, measured using a home run derby task. Consistent with prior research, our results from mixed random effects models evaluating percent absolute error (PAE; prediction error) demonstrated that third graders' representations of individual numbers were less accurate, characterized by overestimation errors, and were associated with overpredictions (i.e., predictions above the set mean). Older children had more accurate individual number representations and a slight tendency to underpredict (i.e., predictions below the set mean). The results suggest that large, systematic inaccuracies appear to skew predictions while small, random errors appear to be averaged over during summarization. These findings add to our understanding of summarization and its role in numerical predictions.