Uso de representaciones y patrones por alumnos de quinto de educación primaria en una tarea de generalización

Abstract

En este artículo presentamos parte de los resultados de una investigación más amplia cuyo principal objetivo es indagar sobre las estrategias y representaciones que utilizan alumnos de quinto de educación primaria cuando abordan una tarea de generalización basada en un ejemplo genérico. Recogimos información en el aula habitual de un grupo de 20 alumnos del citado curso, mediante una tarea escrita constituida por diez cuestiones que involucran relaciones funcionales entre dos variables. En este artículo mostramos el análisis y resultados de las respuestas a cuatro de esas cuestiones. Destacamos la diversidad de representaciones utilizadas, el uso de diferentes patrones como estrategia más frecuente, y las evidencias obtenidas de la capacidad de generalización de los escolares de quinto de educación primaria.

Strategies Employing Prospective Primary Education Teachers in a Functional Relationship Task

“…In this article, we focus on external representations, which refer to "symbolic or graphic notations, specific to each notion, through which mathematical concepts and procedures are expressed, as well as their most relevant characteristics and properties" (Castro & Castro, 1997, p. 96). We considered those representations because they allow us to evidence the subjects' productions when solving mathematical tasks (Merino et al, 2013).…”

“…Pictorial representations allude to visual resources, such as drawings, that allow mathematical relationships to be expressed and are paramount because they are own and original representations of the subjects who solve mathematical tasks (Blanton et al, 2011;Cañadas & Figueiras, 2011). Numerical representations use numbers and operations expressed by mathematical language (Merino et al, 2013). The symbolic representation is alphanumeric, the syntax of which is described by a series of rules and procedures (Rico, 2009).…”

“…A strategy is understood as a "procedure or rule of action that allows us to obtain a conclusion or answer a question using relationships and concepts, general or specific to a certain conceptual structure" (Rico, 1997, p. 31). Several authors highlight the need to investigate problem solving strategies in the functional context, given that, in that context, students manifest various difficulties in finding an appropriate strategy (e.g., Amit & Neria, 2008;Merino et al, 2013;Moss & Beatty, 2006). Considering the above definition, we assume that functional relationships can be seen as resolution strategies when someone faces a task involving covariable amounts.…”

“…It is used to solve problems and allows students to identify patterns and represent and generalise relationships between quantities . The reasons above are enough for this thinking to be considered a disciplinary goal in the teaching of mathematics (Rico, 2006), and for countries such as Australia, Canada, China, Chile, Korea, United States, Japan, Portugal, and Spain to incorporate it in their curricula (Merino et al, 2013; Ministerio de Educación de Chile [MINEDUC], 2012a).…”

Working With Patterns Through Chess-Based Problems. Strategies and Reasoning Levels of Primary School Students.

“…These relationships allow this topic to permeate the entire school mathematics curriculum, both to prepare students for further learning and to develop problem solving and communication skills (Vale, 2009). In particular, there are previous studies about the levels of reasoning of primary school students (Zapatera, 2018), strategies when solving pattern problems (Merino, 2013), and the presence of reasoning and strategies in the case of visual patterns (Barbosa & Vale, 2015).…”