Hong Kong teachers' views of effective mathematics teaching and learning

Twelve experienced mathematics teachers in Hong Kong were invited to face-to-face semi-structured interviews to express their views about mathematics, about mathematics learning and about the teacher and teaching. Mathematics was generally regarded as a subject that is practical, logical, useful and involves thinking. In view of the abstract nature of the subject, the teachers took abstract thinking as the goal of mathematics learning. They reflected that it is not just a matter of "how'' and "when'', but one should build a path so that students can proceed from the concrete to the abstract. Their conceptions of mathematics understanding were tapped. Furthermore, the roles of memorisation, practices and concrete experiences were discussed, in relation with understanding. Teaching for understanding is unanimously supported and along this line, the characteristics of an effective mathematics lesson and of an effective mathematics teacher were discussed. Though many of the participants realize that there is no fixed rule for good practices, some of the indicators were put forth. To arrive at an effective mathematics lesson, good preparation, basic teaching skills and good relationship with the students are prerequisite.