Abstract

RIVERA-FIGUEROA, Antonio  and  BRAVO-DIAZ, Ernesto. How does the shape of conics vary when their eccentricity tends to one or zero? An exploratory study with high school teachers from a Mexican university. Educ. mat. [online]. 2023, vol.35, n.3, pp.209-236.  Epub Mar 19, 2024. ISSN 2448-8089.  https://doi.org/10.24844/em3503.07.

Abstract: This work is part of a more extensive investigation in which we investigate the knowledge that high school teachers from a Mexican university have regarding the eccentricity of the conics. Here, we report the knowledge that the participants showed concerning the behavior of the conics when the eccentricity approaches zero or one. Derived from the statements that some authors of analytic geometry textbooks usually make about the tendency of the shape of conics when the eccentricity tends to zero or one, or when from the appearance of a conic they deduce estimates about the values of eccentricity, we consider it pertinent to find out if teachers understand the authors' statements. The study’s theoretical basis is the Mathematical Knowledge for Teaching (MKT) model by Ball, Thames, and Phelps (2008). We identified teachers’ knowledge in their responses to questionnaires before and after an activity in which participants interacted with applets and in their responses to unstructured interviews.

Keywords : Shape and Eccentricity of the conics; Mathematical Knowledge for Teaching; Common Content Knowledge; Specialized Content Knowledge.

        · abstract in Spanish     · text in Spanish     · Spanish ( pdf )