Fundamental Theorem of Calculus: Cognitive Demands and Learning Limitations on Mathematical Tasks

Abstract

Background: Mathematical tasks for university teaching are generally of great cognitive demand, without thinking about the limitations they imply for their students. Objectives: To develop a theoretical analysis of the teaching limitations and cognitive demand of four tasks proposed for teaching calculus, specifically, the Fundamental Theorem of Calculus. Design: Qualitative paradigm, with a descriptive-interpretive approach, according to the nature of the data collected. Setting and Participants: The study is framed in a Colombian University, in the subject “Calculus II” for second-semester engineering students, where a professor designs the tasks to be implemented in this course. Data collection and analysis: The data correspond to the professor's lesson plans the statements of the main mathematical tasks within them. These plans were chosen based on availability and accessibility. A content analysis was conducted, considering as units of analysis the paragraphs or sets of paragraphs of the statement of each school mathematics task. Results: Most of the proposed tasks correspond to high cognitive demand (procedures with connections and mathematical construction) and only one was of low demand (memorisation). Moreover, each of the tasks presents its own cognitive demand and several learning constraints that, some of them, agree with the exposed literature. Conclusions: The work aims to have implications for higher education, since to think of a didactic proposal for a better approach to teaching is necessary to configure lesson plans that mobilise the learning of mathematics in engineering, but from the use of tasks with different cognitive demands, in which will vary from less to more, and lead to meaningful learning for the approach of new tasks.