The movement of the variable in one-sided limits as resource for teaching differential calculus

Abstract

Introduction: Understanding the movement of the variable in the concept of functional limit constitutes a challenge for students beginning the study of differential and integral calculus. This difficulty is related to the multiple meanings of mathematical infinity, which transcends the everyday notion of magnitude.

Objective: To describe the behaviour of the variable in irrational functions to develop students' skills in variable movement analysis. Additionally, to offer didactic resources that allow teachers to address lateral limits from a conceptual and procedural perspective.

Methods: A descriptive-didactic analysis was carried out by solving cases of irrational functions of the form  (with n even and  polynomial). It was complemented with a quasi-experiment involving two engineering student groups: one received explicit instruction on variable movement and the other followed a traditional approach.

Results: The group that received instruction focused on variable movement analysis outperformed the control group in all assessed items, with pass rate differences ranging from 4 to 10 percentage points, depending on the complexity of the case studied.

Conclusion: Explicit teaching of variable movement in irrational functions, supported by the use of multiple registers of semiotic representation, significantly contributes to a more solid understanding of the limit concept and reduces common procedural errors.