The objectives of this study were to identify exemplary school programmes with well‐developed independent study programmes in mathematics and to isolate the key ingredients of such programmes. The first objective involved analysing data from 509 schools. Four stringent criteria were applied to isolate the top 2% of the schools and these were labelled exemplary schools. Each of the exemplary schools had developed viable independent research programmes in mathematics. The key ingredients that were isolated included the following: dynamic research‐oriented mathematics teachers, establishing problem‐centred courses which used no text or tests, securing administrative support, active student recruiting, and making contact with nearby universities. None of the schools had above average facilities or extensive computer resources.