Children can map precise number words to approximate arithmetic prior to formal instruction.

Abstract

Humans possess an intuitive number sense that can both represent and arithmetically transform visually presented collections of objects (e.g., allowing children to determine that two collections of 10 dots added together are less than 30 dots). This competency, however, is distinct from problem-solving in school-taught mathematics, where children must determine one precise number as the correct answer. Here, we show that once children have mapped number words to their intuitive number sense, they can perform approximate arithmetic estimation: that is, they can attach precise number words to approximate division operations. Forty-five 5- to 8-year-olds completed an approximate division task in which they were given a unit of one, three, or five objects and had to then estimate between five and 110 briefly presented dots. Children provided highly accurate estimates and flexibly switched their responses according to the divisor provided. We further show that they did so without relying on various possible "cheats" and discuss three possible mechanisms for this competency. These findings highlight how the interface between number words and intuitive numerical capacities can support rich mathematical reasoning, including helping children arrive at a single approximate answer despite the inherent uncertainty of the underlying representations. (PsycInfo Database Record (c) 2025 APA, all rights reserved).