The theoretical origins of the study lie in the realisation that an educational reform regarding mathematics teaching cannot take place in the absence of an awareness of the learner's thought processes. Coupled with the intrinsically idiosyncratic epistemological complexity of mathematics, the cognitive dimension of didactics arises as particularly significant.

With regard to learning advanced mathematics this study originates in the assumption, grounded on the relevant literature, that a novice mathematician faces a series of cognitive difficulties in the encounter with mathematical abstraction. Abstraction is meant both from a psychological perspective i.e. that the advanced mathematics learner has to build up knowledge in an axiomatic way and learn how to reason deductively; and from an epistemological perspective, i.e. that the nature of the objects of advanced mathematical learning can extend beyond the physical or the numerical.

In the above, learning is not seen as isolated in a cognitive vacuum but embedded in a sociocultural context. Therefore, in a constructivist strand of thinking, the learner's cognition, while being personal and individually interesting, is also emphatically seen as taking place in a learning environment.

If, as R.B.Davis contends (1989), 'theory building is the trademark of science' then this study of the learner's difficulties ought to be carried out in such a way that it leads to the enhancement of theory in the field of Didactics of Mathematics. This study seeks to construct a psychological profile of the novices' difficulties in their encounter with mathematical abstraction by probing into their expressions of learning. It is assumed here that the phenomena of cognition, an inaccessible and esoteric process, can only become visible and accessible through the learners' oral and written (in this study: oral) articulations of their mathematical thinking. In effect of the above in Chapter 2 the study is presented as a phenomenological study of advanced mathematical cognition.