The aim of this article is to comment on the ways in which beliefs and theories of learning affect the teaching and learning of mathematics. When mathematics is viewed as a static body of knowledge, a transmission style of teaching is often employed. In contrast, a radical constructivist view of learning suggests that mathematics could be a constructive and creative endeavour. We suggest that this perspective of mathematics aligns with the principles, values and key competencies in The New Zealand Curriculum (Ministry of Education, 2007). Examples relevant to the context of primary mathematics education are considered.