Constructivist theory of learning is employed in delivering mathematics methodology modules in the Two-year Full-time Certificate in Education (Secondary) Programme in the Hong Kong Institute of Education, where I am working. This paper aims to determine second year student mathematics teachers’ teaching strategies which they acquired after attending a Methods I module in their first year of study, and changes in their practices after attending a second methodology module (Methods II) in their second year. In their first year of study, Chinese student mathematics teachers had been taught in Methods I the various teaching models, for example, specific methods in concept and skill teaching, and the general discovery and expository strategies. Discussion and application of the models were further enhanced in the Methods II module in the second year of study. On the basis of these teaching models, a questionnaire of 64 items of specific teacher activities was designed. It was administered to the class of students at the start of the first semester in their second year of study. Students were asked to indicate the frequency of using each stated teacher activity on a 5-point frequency scale (from “almost never” to “almost always”). Methods II was then offered to these students. At the end of the module, the same questionnaire was administered again. A focus group meeting was also held at the same time. Results showed that student teachers very often tested their pupils’ prior knowledge at the start of the lesson, and they became more aware of building mathematics learning on pupils’ prior experience. Exposition of mathematics content was still preferred; some time was set aside during the lesson to offer guidance to their pupils. Nevertheless, they provided little opportunities for pupils to express themselves and to explore mathematics (e.g., in small-group discussion, in playing mathematical games, and in computer-assisted learning). In the focus group meeting, student teachers
