Introduction
In Chapters 6-9, the themes, outlined in the Interlude and related to the novice mathematician's cognition, were elaborated within the four mathematical areas of Introductory Analysis, Calculus, Linear Algebra and Group Theory. In Part III of each one of these chapters the paradigmatically problematic concepts within each area (supremum and infimum, limit, spanning set and coset ) provided the contextual basis for a micro-discourse on the novice mathematician's cognition. In this final chapter the focus is on a macro-discourse, a cross-topical synthesis of the observations made in Chapters 6-9. In Part I the novice mathematician is described as an individual learner struggling to come to terms with the intellectual demands of mathematical formalism, whereas in Part II the novice's encounter with mathematical abstraction is described as an enculturation process which takes place through the mediation of an expert, the tutor. So in a sense the perspectives in Parts I and II reflect the distinction of perspectives, made in Chapter 1, between learning as a cognitive process and learning as a sociocultural process. By implication — if Parts I and II form a coherent discourse on the novice mathematician's cognition — the approach taken in this study gives evidence that a description of learning cannot take place in the absence of either of the two perspectives and that, in fact, the dissection of the two perspectives is dubious and unnatural.
In Parts I and II the novices' cognition is explored from a learning point of view. A brief and general reference to issues from a teaching point of view is the focus of Part III. Part IV contains a few methodological observations, made in the light of the experience from this study. The chapter closes with a short statement (Part V) about how the synthesis of the findings in this Chapter is embedded in the research reviewed in Chapter 1 and about possible extensions of the study in the future.