Influences of a Virtual Manipulatives Context on Argumentation About Integers

Abstract

This article presents a case study of two Grade 5 boys’ argumentation concerning addition and subtraction of negative numbers while using an interactive tablet-based application simulating positive and negative tiles. We examine the properties of integers they conjectured, and the kinds of evidence and arguments they used to support their conjectures. The proof-based teaching theory used to develop the tasks, and the features of the virtual manipulative environment, are described. The results show that the tasks, in combination with the virtual manipulative environment, allowed the boys to perform calculations that they had not been able to perform previously, that in one instance one boy used a deductive argument to explain a conjecture they had made, and that a known weakness of the counterbalance model of integers that was used was not a problem in this case.