Rhythm and the grasping of the general

In this paper we deal with the genesis of students’ algebraic generalization of patterns. Our aim is to better understand the way students attend to the perceptually given (e.g. the three first elements of a geometric or numeric sequence) and start moving beyond it in their attempt to grasp a possible general mathematical structure. We provide a multi-semiotic microanalysis of the work done by one Grade 9 student and her small-group mates and show how rhythm accounts for a subtle semiotic device which helps the students project −at the aural, kinesthetic and visual levels− a regularity which proved to be crucial in conveying a sensuous meaning of mathematical generality.