The Structure Beneath the Symbols: How Children Develop an Understanding of Place Value

Abstract

The place-value concept is fundamental to understanding the symbolic number system. It dictates that the value of a digit in a number is based on its position or place within the number (e.g., the “5” in “510” is five units of 100, whereas the “5” in “51” is five units of 10). Place value is central to understanding multidigit numbers, performing arithmetic, and learning more complex math. Despite its significance, relatively little research has systematically examined the developmental trajectory and cognitive underpinnings of the place-value concept. In this article, we synthesize prior findings and propose a conceptual framework that delineates the core properties of the place-value concept and characterizes its developmental trajectory. We also identify key cognitive factors that may underpin individual differences in its acquisition. This framework can guide future research to understand how children acquire the place-value concept and how best to support this learning. It also has broad implications for understanding the cognitive architecture of human compositional symbol systems.