An approach to preschool task design: how narrative reveals the functionality of early math concepts.

Many preschoolers can count, yet formal mastery does not mean that counting is used meaningfully or embedded in other activities. Story-based tasks can reveal whether a child is acting formally, yet the literature lacks clear guidance on how such tasks should be designed. Drawing on CHAT, we identified five principles for constructing narrative-based tasks and developed a task battery designed to assess three levels of counting mastery: formal (targeting only operational mastery of counting), reasonable (addressing orientation to essential conditions of counting), and functional (capturing whether the child can use counting as a tool embedded in another activity). The battery was piloted on 56 older preschoolers (M = 68.9 months, SD = 3.86). To validate the battery, we assessed executive functions (working memory, inhibition, cognitive flexibility) using NEPSY-II and DCCS-expecting formal and reasonable levels to replicate known correlations with early mathematics, while the functional level might show a different pattern. The task battery successfully differentiated among the three levels of counting mastery: performance decreased systematically from formal to reasonable to functional (p < 0.001). Performance on tasks assessing formal and reasonable levels correlated with executive functions (Rs = 0.28-0.41, p < 0.05), whereas performance on tasks assessing the functional level showed no such correlations, suggesting that functional counting may rely on different mechanisms. The findings suggest that specially constructed story-based tasks may be necessary for assessing whether counting is used reasonably and embedded in another activity. The battery shows preliminary promise for distinguishing between formal and functional mathematical understanding in preschoolers, though further validation is needed.