Forms of early algebraic thinking in students in fourth and fifth grades of elementary school education (9-10 years)

This report is part of a doctoral research aims to analyze forms of algebraic thinking in students of 9-10 years. From a microgenetic approach (Vygotsk), 1978) and a multimodal perspective of human cognition (Radford, Edwards & Arzarello, 2009) that considers the multi-semiotic dimension is analyzed mathematical activity a student of 10 years when it faces a patterns of generalization task. Preliminary analysis suggests that there are some connections between the syntax of the "algebraic" student and mobilized semiotic means of objectification. In addition, through one of its pronouncements, may be evidenced how the rhythm, which emerges as a means of semiotic objectification, is embedded in the algebraic syntax.