Initiation to Differential Calculus: Teaching Practices of Portuguese Secondary School Teachers

Abstract

Context: The study of teaching practice is an emerging topic of research and is directly linked to the importance of improving the teaching and learning of Mathematics. Goals: To understand the core aspects of how secondary school teachers teach Differential Calculus. Design: The study uses a qualitative methodology, based on an interpretative paradigm, and is carried out by means of three case studies. Environment and participants: Three Portuguese secondary school teachers who teach Mathematics A took part in the study. Data collection and analysis: The data were collected through direct observation of lessons and semi-structured interviews. The data analysis gave rise to two dimensions: (i) general aspects, and (ii) specific aspects of didactic exploration. The general aspects are split into three subcategories: (i) lesson structure; (ii) interactions in the lessons; and (iii) working with the tasks. The specific aspects were also split into three subcategories: (i) connecting concepts; (ii) time for the students to elaborate and present their reasoning; and (iii) interaction between the graphical and algebraic aspects. Results: The results of the study point to the almost exclusive use of textbooks without using other tasks. Conclusions: The conclusions point to a significant emphasis by the teachers on the connection between the different concepts involved. The approach adopted seems to be more focused on conceptual questions than procedural techniques.