Air Miles and Financial Literacy

Progressive Differentiation and Integrative Reconciliation in Mathematics Education

Abstract

The article analyzes how progressive differentiation and integrative reconciliation—principles of the Theory of Meaningful Learning (TML) and the Theory of Critical Meaningful Learning (TCML)—can be observed in the process by which high school students come to understand airline miles during the implementation of a Potentially Meaningful Learning Unit (PSLU). The research employs a qualitative approach, designed as a case study, and was conducted with 16 second-year high school students in the Financial Mathematics course, part of the “Financial Education and Sustainable Development” track of the New High School curriculum. The pedagogical proposal was based on a PSLU, structured to integrate theory and practice, introducing students to concepts related to airline miles and promoting application activities in real-world financial decision-making contexts. The analysis was based on the students’ written work and photographic records of their activities. The results showed that students progressed from superficial conceptions to more structured understandings, demonstrating progressive differentiation, and began to critically integrate new knowledge with prior knowledge, reflecting integrative reconciliation. It is concluded that Financial Mathematics, combined with Financial Education, enables Meaningful and Critical Learning, in addition to preparing students for informed decisions in their daily lives. The topic of airline miles proved to be relevant and promising, albeit recent, planting a seed for future pedagogical practices focused on youth financial literacy.