Argumentaciones De Estudiantes De Primaria Sobre Representaciones Externas De Datos: Componentes Lógicas, Numéricas Y Geométricas

Abstract

Argumentar y representar son habilidades promovidas en los currículos escolares de muchos países. En este estudio, se presentan las argumentaciones sostenidas por seis estudiantes de grados distintos, desde primero a cuarto, sobre representaciones externas construidas por ellos. Se analizó la estructura de su argumentación respecto a algunas componentes presentes en estas representaciones mediante el modelo simple de Toulmin, realizando una interpretación de las argumentaciones e integrando la representación construida con la argumentación. Los elementos argumentativos verbales y gestuales parecen verse influidos por habilidades de expresión oral, conocimientos numéricos y geométricos de los estudiantes. Los argumentos sobre la componente lógica, variable, y la componente numérica, frecuencia, fueron verbalizados por los estudiantes, mientras que las componentes geométricas, base - lineal y linealidad - gráfica, fueron argumentados mediante el lenguaje oral, el gesto y la metaforización.

Statistical knowledge of primary schoolchildren: An overview of study approaches

“…As mentioned in the introduction, this paper addresses the analytical approaches of students' knowledge described in the different studies found on the issue. It focuses particularly on TM, which integrates representations with argumentation, highlighting the verbal and gesture elements originating from the oral, numerical and geometrical skills of the students (Estrella et al, 2017;Toulmin, 1958); SMWS, which provides an analytical approach from a theoretical and methodological point of view for studying the work carried out by students when confronting a mathematical activity, in this case in terms of statistical knowledge and related cognitive skills possessed by a student when carrying out a statistical task (Vidal-Szabó et al, 2020); SOLO taxonomy of Biggs and Collis (1982), which aims to characterize the answers, which arise in the process of interaction; and CGRL (Curcio, 1987;Friel et al, 2001), which consider elements such as the words, which make up the title, the labels of the axes and scales on statistical graphs, the implicit mathematical content represented therein and the symbology used in their creation. Such components provide the keys to understanding the context of the data, the variables, and their relationships (Díaz-Levicoy et al, 2019a).…”

“…In other words, students draw conclusions based on their representations of data and there should be a guarantee to support these conclusions. This approach takes into consideration three elements, which play a role in argumentation: the conclusions, which are the statements used by the subjects of the study with the aim of achieving the acceptation of their ideas; the data, which are the elements, which justify and ground the conclusions; and the warrants, which are the processes, which validate the conclusions based on the data (Estrella et al, 2017). In order to clarify the difference between data and warrant, it can be said that the former obeys the explicit manifestation of the ideas, whereas the latter occurs in a more hidden way.…”

“…As far as the TA is concerned, Estrella et al (2017) explore and characterize the structure of arguments regarding the external representation built by three children of eight and nine years old, via organizational tasks with manipulative material (colored tokens) and the implementation of a semi-structured interview including additional tasks associated with the logical, numerical and geometrical components of the representation created by the students. In this analysis, the elements of TM (Toulmin, 1958) are presented and justified by way of the arguments provided by the students when asked how they had organized the data and about certain components of the representation of the data, which they had built.…”

“…They also analyze the students' construction of arguments as a fundamental part of the comprehension of different statistical concepts. In this sense, the authors consider it to be of vital importance to reflect on such knowledge when designing and constructing curricular materials and guidelines for statistical literacy (Estrella et al, 2017).…”

Representaciones de datos en estadística: de listas a tablas

“…Si bien las tablas y gráficos ocupan un papel central en la práctica científica y se usan ampliamente en las aulas y en textos escolares de diversas materias, su construcción e interpretación no es fácil, y la adquisición de la habilidad de representar posee ciertas complejidades (Estrella, Olfos, Morales y Vidal-Szabó, 2017;Estrella, Olfos, Vidal-Szabó, Morales y Estrella, 2018). Investigaciones previas han señalado la especificidad de las tablas y la forma en que tanto estudiantes como profesores las comprenden (Brizuela y Alvarado, 2010;Brizuela y Lara-Roth, 2002;dibble, 1997;duval, 2003;Estrella, Mena-Lorca y Olfos, 2017;Friel, Curcio y Bright, 2001;Gabucio, Martí, Enfedaque, Gilabert y Konstantinidou, 2010;Martí, García-Mila, Gabucio y Konstantinidou, 2010; Martí, Pérez y de la Cerda, 2010; Martínez y Brizuela, 2006;Wu y Krajcik, 2006).…”