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
