The semiotic potential of pseudo-random numbers for the idea of indeterminacy in algebra

This article is focused on the potential of spreadsheets to foster the transition from arithmetic to algebra in students who have not yet been exposed to formal algebra instruction. We study the potential of the pseudo-random number generator functionality of spreadsheets with the theory of semiotic mediation. Results are reported from a teaching sequence in which 6th-grade students (aged 11–12) are given tasks in spreadsheets incorporating this functionality. We analyze the artefact signs produced by a pair of students while solving the tasks, in terms of the processes pointed out by Radford as distinguishing features of algebraic thinking: addressing indeterminacy, denoting indeterminate numbers and operating on indeterminate numbers. In light of this analysis, we discuss the actual unfolding of the hypothesized semiotic potential of the pseudorandom number generator functionality, together with difficulties and cautions emerged, as well as possible refinements in the design of future iterations of the intervention.