Critical Moments in Generalizations Tasks. Building Algebraic Rules in a Digital Sign System
We report findings of research that deals with secondary students’ interaction with a digital microworld, eXpresser. eXpresser is designed to support students in constructing general figural patterns of square tiles and expressing the algebraic rules that underlie them. Our focus is on the sense production that emerges as students use eXpresser. In order to analyze student productions, we adopt a semiotic perspective based on a broad notion of mathematical sign systems. We identify in the analysis, critical moments that illustrate the emergence of algebraic expression in eXpresser’s alternative sign system. These moments are constituent elements of the process of deriving a general rule and support the evelopment of the notions of dependent and independent variable.