Many children from low-income backgrounds worldwide fail to master school mathematics1; however, some children extensively use mental arithmetic outside school2,3. Here we surveyed children in Kolkata and Delhi, India, who work in markets (n = 1,436), to investigate whether maths skills acquired in real-world settings transfer to the classroom and vice versa. Nearly all these children used complex arithmetic calculations effectively at work. They were also proficient in solving hypothetical market maths problems and verbal maths problems that were anchored to concrete contexts. However, they were unable to solve arithmetic problems of equal or lesser complexity when presented in the abstract format typically used in school. The children’s performance in market maths problems was not explained by memorization, access to help, reduced stress with more familiar formats or high incentives for correct performance. By contrast, children with no market-selling experience (n = 471), enrolled in nearby schools, showed the opposite pattern. These children performed more accurately on simple abstract problems, but only 1% could correctly answer an applied market maths problem that more than one third of working children solved (β = 0.35, s.e.m. = 0.03; 95% confidence interval = 0.30–0.40, P < 0.001). School children used highly inefficient written calculations, could not combine different operations and arrived at answers too slowly to be useful in real-life or in higher maths. These findings highlight the importance of educational curricula that bridge the gap between intuitive and formal maths. Children who learn maths working in markets and children who learn maths only from school were both unable to transfer their skills to new contexts, highlighting a need to reconsider how maths is taught in school.