KNOWLEDGE OF THE MATHEMATICAL HORIZON IN THE PRINCIPLE OF MATHEMATICAL INDUCTION IN A HIGHER-LEVEL CONTEXT; [EL CONOCIMIENTO DEL HORIZONTE MATEMÁTICO EN EL PRINCIPIO DE INDUCCIÓN MATEMÁTICA EN UN CONTEXTO DE NIVEL SUPERIOR]
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abstract
This research presents a theoretical problem that refers to the recognition of a theoretical model that describes the mathematical connections that are executed in the principle of mathematical induction. The purpose of this article is to highlight the connections from the subdomain of Horizon Content Knowledge (HCK) from the Mathematical Knowledge for Teaching (MKT) model. The methodology proposed is an intrinsic case study, where two higher-level teachers in the area of mathematics are selected; and an interpretation and triangulation of data where recorded classes are examined, semi-structured interviews are applied and field notes are evidenced. Among the actions for the assessment of the research, the analysis of the HCK subdomain is deepened in its three dimensions (practices, themes and values), as well as the design of conceptual maps in the three types of connections of the HCK (intraconceptual, interconceptual and temporary). Among the main results, a large number of HCK indicators are presented that the teachers demonstrate in the principle of mathematical induction, which reflect the impact on the curricular contents in the area of science, which from the perspective of teacher training is relevant for the exercise of qualitative analysis placed in a mathematical context.
