How much do you spend on your cell phone? An experiment with the study of multivariable functions

Abstract

The present work aims to report an experience lived by third-year students of the Mathematics Licentiate Program at the State University of Paraná – Paranavaí Campus (UNESPAR) with the study of functions of several variables, involving the analysis of a mobile phone plan in the course of Multivariable Calculus. The class was based on Mathematical Modeling as a teaching and learning strategy, understood as a practice that consists of converting real-world problems into mathematical problems, whose solutions are later interpreted in the language of the original context (Bassanezi, 2013). It is characterized as a dynamic process, which integrates theoretical and practical aspects, with the purpose of making trend predictions, based on the development and validation of mathematical models. With this approach, the class was structured around a problem situation, which consisted of analyzing the daily cost of a mobile phone plan. The objective of the class was to understand the concept of functions of several variables based on a topic related to the students’ daily lives. For this, as an introduction to the proposed theme, the teacher presented two news reports. The first, published by the G1 portal in 2022, showed a survey in which Brazilians were pointed out as the users who spend the most time on their phones. The second, published by Teletime in 2018, pointed out Brazilian mobile service as one of the cheapest in the world. Based on these references, the teacher encouraged the students to reflect on their own consumption habits, asking them about monthly expenses on mobile phone services and the types of services included in their respective plans. After each one reported on their phone plan, the teacher presented a task, adapted from Tatsch, Rachelli, and Bisognin (2016), which requested the analysis of a plan called Daily Prepaid Plan from a mobile operator, valid in 2015, which offered the user the possibility of paying a fixed amount for a package of services only on the days of use, and with the possibility of paying additional fees for certain services exceeding the package. Three questions were proposed, which essentially consisted of: (i) calculating the daily cost of services used in different situations; (ii) constructing a mathematical expression that generalized the amount spent when the user exceeded the benefits of the package; and (iii) reflecting on the ideal consumer profile for this plan. The task was carried out in groups of two or three students and the different solutions were shared with the class. At the end of the activity, the teacher systematized the concept of functions of several variables based on the discussions held and the students’ responses. The experience with this task allowed the students to mobilize the concept of a function (of one or more variables), applying it in a situation of their daily life, developing skills in mathematical modeling, algebraic reasoning, critical analysis of situations, and decision-making based on the development and validation of mathematical models.