How big is many? Development of spatial and numerical magnitude understanding

This chapter proposes that children's spatial and mathematical development are deeply interconnected because both domains involve magnitude processing. Magnitude can be conceptualized as applying to continuous quantities or collections of discrete entities, and can also be treated either intensively (relative) or extensively (absolute). We suggest that young children may show an extensitivity bias due to a focus on extensive quantity as they learn about numbers and counting. Discrete presentation may prompt extensive thinking even when it is inappropriate. Here, we connect five domains of developmental research that have traditionally been treated as separate: spatial estimation, spatial scaling, using number lines to represent integers, proportional reasoning, and fraction understanding. We discuss how children's difficulties with coordinating intensive and extensive information may explain recurring response biases in these domains. In the last section, we consider how this theoretical framework sheds light on overall relations between spatial and mathematical thinking, and how it may suggest new avenues for research.