The current global movement in the reform of education seems to focus on a number of issues that include standards, quality and teacher preparation. With regard to the latter, while teacher education curricula in most parts of the world attempt to strike a balance between content and professional training, the emerging scenario is that of training expert teachers. Three types of knowledge identified as necessary for expert teaching are content knowledge, pedagogical knowledge and pedagogical content knowledge. For Hong Kong to embark on a satisfactory and effective public education reform, it is essential that its most valuable human resource (i.e. teachers) must be comprehensively and adequately developed. Attention must be paid to both pre-service and in-service to raise an excellent quality-oriented teaching force. Teacher educators and researchers make important and well-informed decisions about what should be included in pre-service and in-service teacher development programmes. However, it is also important to take into account the teachers' own perceptions about the areas in which they feel confident and knowledgeable and those inwhich they do not. One practical avenue of sourcing such information is the teacher in training who is learning to acquire and display expertise. This paper reports on an investigation using a sample of 183 science and mathematics trainee teachers. A 60-item instrument, the Science and Mathematics Expert Teacher Preparation Survey (SMETPS),was developed to gather data on trainee teachers' perceptions of their current knowledge and what they think they need to know to become expert teachers. The data, analysed using both descriptive and inferential statistics, indicated some of the areas in which trainee teachers identified the need for future professional development that would contribute towards expert training. Several issues which emerged from the results are discussed, with reference to implications for current efforts in expert teacher

It has been observed that Asian, in particular Chinese students frequently outperform their Western counterparts in international academic comparisons. However, it is still open to doubt as to whether they actually possess a deeper conceptual understanding than their Western counterparts and as to whether they would perform as well in non-routine mathematical problems (such as open-ended problems). The reason for such queries owes as much to the students' as to teachers' conceptions of mathematics. When mathematics is regarded as an absolute truth or a set of rules governing symbols, students tend to consider doing mathematics as the memorisation of algorithms and learning mathematics as a process of transmission. We posed certain hypothetical situations to students in Hong Kong and China and found that they possess a relatively restricted conception of mathematics. Later, we investigated this phenomenon at greater depth by the use of open-ended problems. We found that students usually approached a mathematical problem by searching for a rule that identifies what is given, what is being asked and the category of topic for the problem. Evidence has also shown that this approach to mathematical problems is largely shaped by the way they experience learning, their response to task demands, and the classroom environment. In other words, such a restricted conception of mathematics which exists both within the students and in the classroom culture has led students to tackle mathematical problems by searching for rules rather than approaching them through a conceptual understanding of the context. It is well known that students' conception of mathematics is closely related to their problem-solving behaviour. This conception is shaped by a number of factors, in particular, by the space of learning in which they 'live'. Of particular significance is the finding that the teachers' conception of mathematics could contribute to the shaping of this 'lived space'. These inter-relationships