In some situations, memorisation is useful, even necessary. It can give students enough concrete facts on which to reflect; it can limit anxiety by reducing mathematics to a set of simple facts, rules and procedures; and it can help to develop fluency with numbers early in a child's development, before the child is asked to tackle more complex problems. But to perform at the very top, 15-year-olds need to learn mathematics in a more reflective, ambitious and creative way--one that involves exploring alternative ways of finding solutions, making connections, adopting different perspectives and looking for meaning. Fewer 15-year-olds in East Asian countries reported that they use memorisation than did 15-year-olds in some of the English-speaking countries to whom they are often compared. In no PISA-participating education system did boys report more intensive use of memorisation than girls when learning mathematics. Memorisation as a learning strategy may work with easy problems, but it is unlikely to be effective if it is the only strategy used when confronted with complex mathematics problems.