The development of structural analogy in number-line estimation

Recent studies have revealed that making number-line estimates requires not only number knowledge but also a host of other cognitive skills. Here, we argue that a fundamental component of number-line estimation is the act of relating the target number being estimated to another numerical reference point (e.g., a previous estimate, the endpoint of the line) and then extending this relation to the spatial domain-in other words, that children recruit analogical reasoning skills when estimating. Because such analogical comparisons require both the selection of a numerical reference point and the comparison of that reference point with the target number, we aimed to understand which reference points children use and how they use them. To this end, we tested whether and how 5-, 6-, and 7-year-olds used their previous estimates to constrain subsequent estimates. We found that children used their previous estimates as reference points, that older children used reference points differently than younger children, and that the ability to access previous estimates limited our youngest participants' ability to perform well on our number-line estimation task. We conclude that the analogical reasoning component of number-line estimation is substantial and shapes children's earliest estimation performance.