In this paper I shall discuss data from a study on Colombian mathematics teachers' conceptions of their own teaching practices of beginning algebra, which led to the development of a theoretical model of teachers' thought structures designed as a thinking tool at the initial stage of the study. With a focus on the perspectives of teachers, the study investigated the relationship between the teachers' conceptions of beginning algebra and their conceptions of their own teaching practices, with a view to unravelling their conceptions of change in their practices. Significant findings which threw light on the aforementioned relationship have been presented in Agudelo-Valderrama, Clarke and Bishop (2007), highlighting a direct association between a teacher's conceptions of the nature of beginning algebra, the crucial determinants of her/his teaching practice, and her/his attitude to change. After an overview of the study, this paper focuses on specific evidence which clearly shows that in contrast to the strong relationship between a teacher's conceptions of mathematics and her/his teaching practice, assumed in the theoretical model of teachers' thought structures, the teachers see a strong relationship between their conceptions of social/institutional factors of teaching and what they do in their teaching. Implications of the findings for teacher education in Colombia are identified.