Recignising commonalities and reconciling differences in mathematics education

Data from a study of the practices of research mathematicians are used to highlight an exploration of commonalities across and differences between learners in mathematics classrooms. Such commonalities and differences are, it is claimed, central to a teacher's understandings of how to address her role and responsibilities. Commonalities discussed are those between learners,across mathematics and between communities of practice. Differences between syllabus and practice, between school mathematics,mathematics in the world, and academic mathematics and, finally, between members of the different communities of students,teachers of mathematics, mathematics educators, and mathematicians are explored. This revised version was published online in July 2006 with corrections to the Cover Date.