We propose a methodology for studying the processes of learning and teaching mathematics. We will argue that this methodology carries many of the advantages of qualitative approaches while still keeping the main advantage of quantitative research methodology, which is the potential to produce findings that could be generalized. At the heart of this methodology is a research tool that quantifies learning processes and enables visualization of the learning paths. This is achieved by means of a comprehensive graphical profile of the processes. This graphical profile of an individual learner lends itself to detailed analysis and offers new kinds of insights into the learning/teaching processes. It is unique in the kind of conclusions it suggests and in the scope of the conclusions it allows one to make. (Contains 5 figures.) [For complete proceedings, see ED489597.]