All three research papers of this volume deal with secondary (student) teachers’ professional development. However, they differ considerably concerning research contexts, research questions, kind and number of involved participants, methodologies, and results. The first research paper of Cecilia Agudelo-Valderrama, Alan J. Bishop and Barbara Clarke builds on previous research in Colombia which revealed an unsatisfactory situation concerning the teaching of algebra: ‘‘The teachers emphasised the great difficulties and the low motivation that their pupils showed in the learning of algebra. However, most teachers showed very low interest in participating in professional development, despite their awareness of the high rates of mathematics failure, and despite the support offered by their head teachers for their participating in the programme offered to them. The emphasis placed in central policy on teachers becoming continuous constructors of the curriculum did not seem to represent a call for change in their teaching approaches.’’ Based on these findings, the reported research project asks the questions: ‘‘Can the perspectives of teachers about their own contextual teaching situations tell us something about the difficulties of teacher change?... How do teachers see the relationship between their conceptions of mathematics and their conceptions of their own teaching practices ...?’’ Taking a case study approach the paper gives insight into five secondary mathematics teachers’ conceptions of the crucial determinants of their teaching practices of beginning algebra. The study reveals interesting differences in teachers’ conceptions and explains them in a theoretical model. Among others, the study shows that the teachers did not see their conceptions of mathematics as the crucial determinant of their teaching practices: ‘‘Instead they saw factors belonging to the social/institutional context of their teaching as the main reasons for what took place in their classrooms and for the difficulties of introducing change in their teaching. Even Pablo, the only teacher who showed great awareness of the impact of this knowledge and dispositions on his teaching practice, joined