Dialogue on mathematics education: Two points of view on the state of the art

On many fronts, the field of mathematics education does not speak with a single voice. There appears to be no firm consensus regarding the scientific character of mathematics education, the research methodologies it deems legitimate, the kinds of questions it addresses, the appropriate preparation for its practitioners, and its relationship with other disciplines, including, ironically, mathematics itself. Our field seems to be going through a new phase of self-definition, a crisis from which we shall have to decide who we are and what direction we are going. The authors of the present paper themselves tend towards different positions on these questions. The paper, then, takes the form of a letter in which one of us raises issues about the current state of mathematics education and the other responds. We see this as an attempt to initiate a dialogue on our field, which we consider urgently needed.