Argumentos de estudiantes de primaria en el contexto del álgebra temprana

Abstract

Objetivo: caracterizar los argumentos emergentes en estudiantes de cuarto grado de primaria al resolver tareas en el contexto del álgebra temprana. Método: Se implementó el estudio de casos para recolectar evidencia empírica de los argumentos y los niveles de algebrización de estudiantes de cuarto grado de primaria. Para reconstruir y analizar los argumentos se utilizó el modelo Toulmin junto con los niveles de algebrización. Resultados: Los resultados reportan los argumentos construidos por estudiantes de cuarto grado de primaria en la solución de tareas del álgebra temprana, en este contexto se reconoce que los estudiantes y profesores manifiestan dificultad en el proceso de argumentar desde la matemática. Discución y conclusión: Se considera que la integración de tareas que buscan promover la argumentación y el álgebra temprana favorece el desarrollo de habilidades como: razonar, justificar y comprender conceptos matemáticas.

Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories

“…Considering argumentation from Toulmin's (1984) perspective allow us to highlight the function of the warrant in the context of mathematical proof, this element supports the conclusion based on mathematical axioms, definitions, or theorems (Pedemonte & Balacheff, 2016) and provides an idea about the type of reasoning adopted by the arguer (Cervantes- Barraza et al, 2020Barraza et al, , 2022Conner et al, 2014). In this paper, the (Toulmin, 2003) warrants play an important role because their content evidence the different mathematical connection that a student or teacher make in order to justify the linking of the initial data or hypothesis with the conclusion.…”

“…Unlike, TMA has adopted a particular method from philosophical field, Toulmin's (2003) model was designed under informal logic perspective allow researches in adapting this model & analyze mathematical argumentation in classroom (Boero et al, 2010;Conner et al, 2014), also is a methodological tool that allows to reconstruct the meaning of the classroom talk (Krummheuer, 1995(Krummheuer, , 2015, it has been modified in order to reconstruct complex argumentation occurred in mathematics class (Knipping & Reid, 2015;Cervantes-Barraza et al, 2019, 2020. It is for this reason that this research connects theories, but it also analyzes an empirical phenomenon that deals with the mathematical connections that a teacher established when performing the proof of the theorem of the continuity of a function at a point.…”

“…Studies on mathematical connections have focused mainly on identifying the connections made by high school students, undergraduate students in mathematics, pre-service mathematics teachers and inservice mathematics teachers (García-García & Dolores-Flores, 20182020;Rodríguez-Nieto et al, 2021a, 2022a, 2021b, 2021c, worrying about answering questions aimed at the meaning of mathematical objects, what are the representations of mathematical objects, logical relationships of implication and part-whole, features of the concepts, but have not focused on the reasons, arguments, justifications that support a connection. It is important to mention that, in Rodríguez-Nieto et al (2021d) the mathematical connections were detailed in terms of OSA, without deeply emphasizing the arguments that a subject construct.…”