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.