This paper arises from an attempt to survey professional educators to determine whether there is a common view of what constitutes quality teaching. Selected results from the survey are presented which highlight some apparent contradictions between commonly espoused views on learning and what experienced teacher educators believe about teaching. It is argued that if we are to accept that doing mathematics involves learners' activity we need to reconceptualise both teaching and mathematics education. The Interim Report of the Review of Educational Research in Australia listed seven priority areas. Teaching was not among them. This highlights a separation which has developed between research on learning and research on teaching; and there is also a distinct division apparent in the literature. The literature on learning is more coherent than the literature on teaching: there are emerging trends among views of educators about how children and adults learn, but less development of what this means for teaching. One view of learning which is gaining broad acceptance amongst educators is that of students constructing mathematical knowledge according to their personal experiences and prior understandings. This paper presents a discussion of some implications of this view for the teaching of mathematics, then relates these to the results of a survey of mathematics educators which was aimed at ascertaining if there is some agreement regarding the elements of quality teaching. There seem to be some incompatibilities between current, espoused views on learning and the perceptions mathematics educators have of quality teaching.