Extended theory of mathematical connections (ETC) and theory of mathematical argumentation (TMA) based on Toulmin’s (1984) model were articulated for the study of mathematical connections activated in the argumentation process. For this purpose, a “networking of theories” was made to obtain the complementarities between both theories. Then, a class episode was selected that dealt with the demonstration of the continuity theorem of functions of real variable “<i>if a function is derivable at a point then it is continuous at that point</i>”, made by an in-service mathematics teacher of differential calculus, who participated in a non-participant observation, where his classes were videotaped. The arguments of this episode were analyzed through with Toulmin’s (1984) model, after with thematic analysis method to identify mathematical connections, and, finally, the connections in the proof and mathematical argumentation were analyzed. The main result of the research reveals that the mathematical connections play a fundamental role in the argumentation process of the episode, given that, connection is important for the establishment and identification the argument and the warrant that supports it. In addition, complementarities were found between both theories, which makes this networking a useful tool for a better analysis of mathematical argumentation processes.
This paper describes a study of mathematical argumentation in primary school. The principal aim is to explore the nature of complex argumentation at a structural level. The context of the study was a teaching experiment involving nine tasks that promoted argumentation among fifth graders. We use the framework and method of reconstructing complex argumentation in the classroom proposed by Knipping (2008). The findings show that complex argumentation at a structural level in the context of refuting conclusions is characterized by a source-like structure with the addition of a new refutation argument element.Handle: http://hdl.handle.net/10481/57623Scopus record and citations
The purpose of this research is to promote the construction of mathematical proof from argumentation at the primary level. To show this is a viable instructional strategy at the primary level, we use a teaching experiment methodology and a task related to geometric proof in this research study. To model and analyze the collective argumentation that took place in the classroom, we reconstructed the discussion using the extended Toulmin model. Collective argumentation at the primary level is a valuable opportunity for primary students and their teachers to generate mathematical proof through collaboration. K E Y W O R D Sargumentation, primary school, proof, teaching experiment | 5 CERVANTES-BARRAZA ET Al.
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.
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