Values are taught in every lesson. However in mathematics classes, the teaching of values seems to be implicit rather than explicit. One challenge in this context is how does a teacher and a researcher recognise the values that the teacher is teaching? One crucial area that has emerged during the progress of the Values and Mathematics Project* is in trying to find a common language for teachers and researchers. What is an appropriate language for the ideas that we as a research team are forming, reforming and refining, which will communicate with our teacher colleagues? In turn the teachers also have difficulties in articulating their ideas. This issue appears to be so new to teachers that they do not have common expressions in their vocabulary which come easily to mind. In this paper we also compare this Australian project with a parallel project colleagues in Taiwan are conducting. A heightened challenge for us that has come from the Taiwan group is to look more closely for the influence of teachers? personal value systems when they are teaching mathematics. We conclude that instead of trying to minimise or ignore the effects of such an influence, we need to find ways to recognise such influences and take seriously how teachers respond to them.