Transparent Objects and Processes in Learning Mathematics

This paper examines the notion of transparency in learn-ing and understanding mathematics. The notion of transparency may be associated with mathematical objects as well as thought processes. It carries two re-lated meanings: Seeing-through and being visible. It has been addressed with respect to learning mathematics in a number of different contexts. In dealing with the roles and nature of mathematical examples, Mason & Pimm (1982) discuss the idea of a generic example, which basically is a specific example that conveys a more general case. That is, a generic example is trans-parent to a general case. The authors (ibid) suggest that often students fail to see in an example what the teacher had in mind. In particular, a generic example that is meant to demonstrate a general case or princi