Procesos de razonamiento y argumentación en el aprendizaje de números fraccionarios

Abstract

The present research project aims to identify factors for incorporating argumentation and mathematical reasoning processes into hypothetical learning trajectories for fractional numbers for learners between the ages of 7 and 12. Fractions have been identified as one of the most complex and difficult concepts to master in mathematics, both for students and teachers (Behr et al., 1992; Bezuk & Cramer, 1989; Moss & Case, 1999). The results of assessments such as NAEP and PISA reveal low performance in fraction management, highlighting the need to address this problem from a more argumentative and conceptual perspective (Mullis et al., 1991; Kloosterman & Lester, 2004). The study uses the design of Hypothetical Learning Paths (HLPs) as a framework for structuring the teaching process, drawing on the approaches of Clements and Samara (2016). These learning trajectories guide the development of students' mathematical reasoning through the formulation and evaluation of conjectures (Perelman & Olbrechts-Tyteca, 1989; León, 2005). Using a qualitative approach and a case study, students at different levels (from third to seventh grade) will be observed in activities involving the use of fractions, in order to compare actual learning trajectories (ARP) with the hypothetical ones designed. The expected results include the identification of skills or processes by students, taking into account learning indicators related to fractions from the part-whole relationship, based on argumentation and reasoning, and the design of a series of activities that promote the levels of understanding of fractional numbers. This project hopes to contribute to the improvement of the argumentative environment in classrooms, as recommended by the Ministry of National Education (MEN, 2006), thus allowing students to develop critical and reflective mathematical skills (Obando, 2003).