In this paper we explore two conceptions of mathematics that are evident in literature. Mathematics as a static body of knowledge is one conception, and another is of mathematics being an endeavour that is constructive and creative. With the release of The New Zealand Curriculum (Ministry of Education, 2007), we formalised our ongoing debates about these conceptions by constructing and using metaphors to explore and refine our ideas. In some parts of the curriculum document, there is juxtaposition with a conception of mathematics being social, constructive and creative. However, other aspects of the document appear to reflect the conception of mathematics as a body of knowledge. We express a concern that this latter conception of mathematics may become privileged over other possibilities. We therefore explore what constructive, creative mathematics might look like in a classroom.