Formas de pensamiento algebraico temprano en alumnos de cuarto y quinto grados de educación básica primaria (9-10 años)

Abstract

The possibility of promoting the development of algebraic thinking in the early years of schooling is an issue that increasingly generates more interest for research in mathematics education. In particular, generalization of patterns is considered one of the most important ways of introducing algebra in school. However this necessarily demand develop an enlarged perspective on the nature of school algebra, consider a dialectical relationship between forms of algebraic thinking and ways of solving the problems of generalization pattern, which introduces a problem in terms of the constitution of algebraic thinking in young students. In this process of generalization of patterns we must consider that acts of knowledge by students include different sensory modalities, such as tactile, perceptual, the kinesthetic, etc., which become integral parts of cognitive processes. This is what has been called in the international context (Arzarello, 2006) the multimodal nature of human cognition. We are therefore faced with the need to recognize all those discursive situations (oral and written), gestural and procedural evidencing in student attempts to build explanations and arguments on general structures and mindsets, and their arguments and explanations are supported by individuals or situations into concrete actions. In epistemological terms, we are suggesting ways of conceptualizing, knowing and thinking can not be adequately described only in terms of discursive practices. It is important to consider the cognitive, physical and perceptual students mobilize resources when working with mathematical ideas. These resources or modalities include symbolic and oral communication as well as drawings, gestures, manipulation of artifacts and body movement (Arzarello, 2006; Radford, Edwards & Arzarello, 2009).