Argumentación matemática basada en refutaciones

Abstract

El estudio tiene como objetivo identificar las implicaciones de la refutación en argumentaciones con estudiantes de nivel primaria. Por lo que se presenta el análisis de los argumentos y refutaciones entre estudiantes de sexto grado de primaria en el contexto de la solución de tareas matemáticas relacionadas con la clasificación de triángulos según la medida de sus ángulos. Teóricamente el estudio se fundamenta sobre los conceptos base de la línea de investigación argumentación y prueba, de forma particular se abordan los conceptos de argumentación matemática, razonamiento y refutación. Los resultados del estudio documentan algunas implicaciones de la refutación de conclusiones en contextos de la resolución de tareas matemáticas a nivel primaria, y se reconoce que los estudiantes construyan argumentos mejoradas con base en características y propiedades de los triángulos.

Design of interactive mathematical tasks that make up the reasoning and the Ethnomathematics program

“…The tasks that belong to this first category involve questions with open or closed answers, without including a statement or initial information, however, Inprasitha, Changsri, and Boonsena (2020), note that through open questions it is possible to promote mathematical arguments. The different type of task designed in this study is established into categories C1, C2, C3, C4, C5, they are a synthesis of what a mathematics teacher are able to design by using the principles of argumentation and ethnomathematics, this is an opportunity to promote the learning of mathematics using and promoting mathematical competences like reasoning, connecting, refuting and representing (Cervantes- Barraza & Cabañas-Sánchez, 2022;Rumsey & Langrall, 2016;Yackel, 2002).…”

“…In the curricular of Mathematics Education, the relevance and pertinence of studies which encourage students' reasoning in classrooms are appreciated (e.g., Cervantes-Barraza & Cabañas-Sánchez, 2022;Cabañas-Sánchez & Cervantes-Barraza, 2019). Reasoning as a transversal competence in mathematics learning supports in the communicating answers by justifying conclusions, connecting previous concepts with new ones and the refutation, students' reasoning can be faced with the purpose of convincing others of the truthfulness of the conclusions presented in the collective (Cervantes-Barraza & Cabañas-Sánchez, 2022).…”

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.…”

Mathematical Argumentation in Higher Education: A Systematic Literature Review

“…In secondary and post-secondary education, constructing arguments is a well-researched and significant objective (Schwaighofer et al, 2015). This is because argumentation is recognized as a key element in teaching and learning mathematics (Cervantes-Barraza & Cabañas-Sánchez, 2022;Erkek & Isiksal-Bostan, 2019). Moreover, argumentation plays a crucial role in creating equitable learning opportunities in the classroom by shaping classroom discourse, which, in turn, influences students' understanding of mathematics (Francisco, 2022).…”