Proximities when actuating epistemic-cognitive mathematics. prelude that springs from testimonies of novice and expert mathematicians. an exploratory study

Abstract

In this article we present some results, reflections and contributions of a research work (Sánchez, 2018) whose central problem is directed to study the epistemic and cognitive actions that activate the novice and expert mathematicians when developing mathematical knowledge and offer the didactic new clues on how it is possible to learn to think and generate mathematically. We set ourselves two great intentions: (1) to study how, cognitively, the expert or novice mathematician recognizes a problem and certain possibilities, structures new conjectures, to lead to a formal proof and thus generate contributions to mathematics, and (2) propose a theoretical and conceptual approach to the job of the teacher and student of mathematics in light of the contributions recorded by the epistemic and cognitive actions of the professional mathematician. In this manuscript we only show part of the first purpose. Conceptually, the research focuses on the cognitive domain of the so-called Advanced Mathematical Thought. Methodologically we adhere to the perspective of qualitative research. The analysis of these records focused on a process of description, categorization and interpretation, with the support of systemic networks, where categories and/or attributes emerged led us to characterize the actions of novice and expert mathematicians in solving mathematical problems