Predictors of early numeracy: Is there a place for mistakes when learning about number?

It is one thing to be able to count and share items proficiently, but it is another thing to know how counting and sharing establish and identify quantity. The aim of the study was to identify which measures of numerical knowledge predict children's success on simple number problems, where counting and set equivalence are at issue. Seventy-two 5-year-olds were given a battery of nine tasks on each of three sessions (at 3-monthly intervals). Tasks measured procedural proficiency, conceptual understanding (using an error-detection paradigm) and the ability to compare sets using number knowledge. Procedural skills remained fairly stable over the 6-month period, and preceded children's ability to detect another's violations to those procedures. Regression analysis revealed that children who are sensitive to procedural errors in another's counting and sharing are more likely to recognize the significance of cardinal numbers for set comparisons. We suggest that although children's conceptual understanding of well-rehearsed routines is often limited, conceptual insight might be achieved by setting tasks that require reflection rather than practice.