Summary: This paper outlines phenomenographic research carried out at the outset of Initial Teacher Training with a group of UK student primary teachers to determine the range of variation in their perceptions of mathematics. The resulting outcome space indicates four qualitatively differentiated hierarchical categories of ways of perceiving mathematics, forming a potential framework for reflection. It is posited that beliefs about mathematics result from prior experiences which in turn affect subsequent learning and teaching. As such, the framework of mathematical perceptions is intended to provide a means for student primary teachers to make conscious their own experiences and perceptions, through comparison with those of others in terms of resonance with their own relationship with mathematics and to use in setting goals for their future learning in ITT and teaching of mathematics.