A recent investigation of primary teachers' epistemological beliefs concerning the teaching and learning of mathematics discovered that teachers' beliefs cannot be said to form neat world views. Teachers' hybrid world views often included epistemological beliefs that supported teaching approaches which evidence suggests leads to greater conceptual understanding of mathematics. Classroom observations and semi-structured interviews with primary teachers suggested that although there is a desire to adopt an investigative approach, this is perceived to be largely incompatible with some of the requirements of the UK National Curriculum. Common potential barriers identified by teachers included: the volume of curriculum content they are required to cover, the limited time available to cover it, some working practices perceived to be associated with the current emphasis on teacher accountability and the current method of assessment by Standard Assessment Task tests (SATs). The findings are discussed in relation to challenges facing UK policy-makers if an approach to teaching primary mathematics, which is known to support conceptual understanding, is to flourish. (Contains 2 notes.)