Parts I-IV are a synthesis of the findings as these were presented elaborately in the analysis in Chapters 6-9. The analysis as well as the topical and cross-topical syntheses were strongly data-driven processes, simultaneously informed by the theoretical framework of the study as outlined in Chapter 1.

As emphasised in the Introduction, the structure of this Chapter reflects the juxtaposition of perspectives on learning presented in Chapter 1. The psychology of the individual learner is clearly influenced by the Piagetian ideas on how the transition to abstract forms of thinking takes place (mostly the notion of Reflective Abstraction as specifically transformed for the needs of Advanced Mathematics by the PME-AMT theories outlined in Chapter 1, concept-image and metaphor construction being the dominant ones). The Vygotskian impact can be seen in the recognition of the strong interdependence between formal reasoning/thought and formal language in the presentation of the findings. The Lacanian psychoanalytical approach has influenced the part of the analytical discourse in this study with relation to the role of the unconscious in learning and its control by the learner as a means for conceptualising and overcoming Epistemological Obstacles. The novice's induction to Mathematical Abstraction has been described as a process of conceptualisation and confrontation of Epistemological Obstacles as well as an enculturation process. The perspective on the novice's learning as an enculturation process was generally drawn from Hall's (transition from informal to technical level) and Foucault's (from the rules of sense to the rules of rationality) archaeologies of knowledge. The perspective on this enculturation as a learning process built upon a didactical contract — the clarification of the conditions of this contract are described here as the ultimate task of the tutor-enculturator — is drawn from the eponymous theory of Guy Brousseau.

The broadness of the theoretical influences of the study — as recapitulated briefly in the above and reviewed in Chapter 1 — as well as its wide scope — as evident in the presentation of the findings, the analysis and the syntheses — allow a range of possible extensions: