Components and Subcomponents of the Slope used by High School Mathematics Teachers

Abstract

The present study aims to identify and describe the components and subcomponents of the slope used by a group of seven high school mathematics teachers to solve tasks involving it. Its importance is due to the unquestionable role of the teacher as promoter of the learning of his students, since he considers and transforms his knowledge about a content to put it into play in his teaching practice. Data were collected through a Task-Based Interview, whose protocol consisted of six tasks (two situations with real-life context and four questions associated with teaching and learning the concept). Data analysis was code-bycode using the statements and procedures used by the teachers and the framework of the components and subcomponents of the slope. The findings of this exploratory study showed that teachers have conceptualized the concept in the Trigonometric Conception and Constant Ratio components, mainly in the visualprocedural and non-visual-procedural approaches. On the other hand, their interpretation of the concept makes it difficult to establish its relationship with real-world situations that allude to variational ideas. These results suggest the implementation of professional development courses to broaden their understanding and interpretation of the slope in authentic and realistic scenarios involving geometric and variational notions.