This resarch identified K-6 children's (N=1202) and teachers' (N=54) perceptions of what constitutes doing or using mathematics. Perceptions were documented by a questionnaire which included items reflecting the six major strands of the K-6 syllabi and explicit and implicit use of numbers and operations as both facilitating and distracting elements. Children were given a situation and asked whether the person in the situation was doing or using mathematics. Teachers' perceptions were identified through discussions of questionnaire content and results and taping of classroom discussions with students. The results showed that children's perceptions of the domain of mathematics, although constrained by an emphasis on topics of arithmetic, were reasonably amorphous and fluid and were influenced by developmental factors, explicit numbers and operations, perceived difficulty and activity level of the situation, linguistic factors and experience. (Author)