Exploring Young Children’s Number Order and Hierarchical Inclusion Concepts Through Modified Piagetian Tasks

This study examined children's comprehension of numerical concepts using Piagetian clinical methods with linguistically scaffolded questions to enhance clarity. Piaget theorized that number comprehension requires two key mental relationships: number order and hierarchical inclusion (Kamii). Number order involves establishing a mental sequence for counting without skipping or duplicating, while hierarchical inclusion refers to the ability to mentally integrate smaller quantities within larger ones. A total of 57 pre-kindergarten (n-18) and kindergarten (n-39) children from four U.S.A. early childhood settings participated in Piagetian tasks assessing these concepts. To address critiques of Piaget and Kamii's (2014a) findings-specifically, that children under six struggle with number concepts-this study refined Kamii's 'show me five' Piagetian task by incorporating clarifying questions to mitigate potential linguistic confusion. Results indicated that neither pre-k nor K students fully conceptualized hierarchical inclusion, with pre-k students demonstrating 0% success and K students achieving 41% success. However, K students showed strong proficiency in number order (95%), while pre-k students demonstrated 72% success, remaining below Piaget's 75% threshold for conceptual readiness. These findings underscore the need for refined assessment strategies to better support the development of early numerical comprehension and to ensure that instructional and assessment methods align with children's cognitive readiness.