The role of intuition in the process of objectification of mathematical phenomena from a Husserlian perspective: a case study

摘要

The research is a study of the Husserlian approach to intuition, informed by Merleau-Ponty's theory of perception, in the case of a prospective teacher of mathematics. It explores the two major stages-categories of intuition, the essential relations between them, and their vital role in the emergence of empirical and abstract mathematical objects, as they are used by the student in order to conceptualise mathematical phenomena. The student's activity is analysed to its intuitive origins, and an intuition of essences manifests its significance for generalisations and insights for mathematical proofs. Through an in depth phenomenological data analysis, intuition is delineated as an essential mediator between the learner's world-as-lived and her objectification process. Finally, some implications for teaching and learning are suggested.