Creativity is generally considered to be something to encourage in young children. It is, however, popularly associated more with the arts than with the sciences. This study used phenomenographic analysis to identify some primary school student teachers' conceptions of creativity in school science lessons (a class of 16 final year students on a degree course leading to qualified teacher status in the UK). Their conceptions were narrow, focused mainly on practical investigations of matters of fact, and included misconceptions. Teacher trainers are advised that student teachers' conceptions of creativity can be grossly inadequate in several ways and they may omit significant opportunities for creativity involving, for example, the imaginative processing of scientific information and the construction and testing of explanations. As conceptions may be shaped by creativity in the arts, it is suggested that science educators might loosen the connection by introducing students to the broader term of "productive thought", i.e. a combination of creativity and critical thought which is particularly relevant in science.