Pólya’s Methodology for Strengthening Problem-Solving Skills in Differential Equations: A Case Study in Colombia

Abstract

The formation of students is integral to education. Strengthening critical thinking and reasoning are essential for the professionals that today’s world needs. For this reason, the authors of this article applied Pólya’s methodology, an initiative based on observing students’ difficulties when facing mathematical problems. The present study is part of the qualitative and quantitative research paradigm and the action research methodology. In this study, the inquiry process was inductive, the sample is non-probabilistic, and the data interpretation strategy is descriptive. As a case study, six students were enrolled onto a differential equations course at the Universidad Autónoma de Bucaramanga. A didactic process was designed using information and communication technologies (ICTs) in five sequences that address first-order differential equation applications. As a result of the pedagogical intervention, problem-solving skills were strengthened. All this was based on asking the right questions, repeated reading, identifying and defining variables, mathematization, communication, and decomposing the problem into subproblems. This research study seeks to set a precedent in the Latin American region that will be the basis for future studies.