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AbstractA key question in early number development is how 4‐ and 5‐year‐olds learn the roles that counting and cardinal numbers play when comparing quantities. Children who wrongly used length to identify numerosity were assigned to five experimental groups and trained to judge whether a puppet – who sometimes miscounted – created equivalent sets. Over three training sessions, children who were asked to compare sets after they were counted learned to base their judgments on cardinal numbers when the puppet counted accurately by being given feedback. However, only the groups who were also asked to explain either their own or the experimenter's reasoning made progress in identifying the puppet's miscounts. This ability to recognize the importance of counting accuracy for quantitative comparisons predicted whether children would spontaneously count to compare sets on a post‐test. The importance of asking children to identify miscounts is discussed alongside the social factors that influence children's recognition of the relationship between procedural counting, cardinality and relative number.

AbstractThe study of nineteenth‐century infant mortality in Britain has neglected the rural dimension to a surprising degree. This article maps the change in infant mortality rate (IMR) between the 1850s and the 1900s at registration district (RD) level. Latent trajectory analysis, a longitudinal model‐based clustering method, is used to identify the clusters into which rural RDs fell, based on their IMR trajectories. Relationships between IMR and population density, fertility, female tuberculosis mortality, female illiteracy, male agricultural wages, and distance from London are examined in a longitudinal study. The tuberculosis (maternal health), illiteracy (education), and distance variables had the most effect. IMR responded most strongly to improving health and education in the east, less in the central area, and least in the north and west. The eastern zone's higher‐than‐average mid‐century infant mortality therefore declined faster than the national average. A central and southern zone had slightly lower IMR in mid‐century but did not keep up with the rate of decline in the east. The peripheral north and west had the lowest mid‐century rates but their decline was overtaken by the other zones. The interpretation of these findings and their relevance to the wider study of infant mortality are discussed.