Attention is focused on one particular aim of mathematics education: the fostering of an appreciation of the unified and integrated nature of mathematics. To clarify this aim the concepts of the integrated nature of mathematics and its appreciation are analysed in some detail. Appreciation of the unity of mathematics is understood to combine knowledge of integration within mathematics and the possession of a particular problem‐solving ability: integrative skill. A definition of an integrative problem or task is proposed. Subsequently integrative skill is defined in terms of success at integrative tasks.