Positives About Negatives: A Case Study of an Intermediate Model for Signed Numbers

In this article, we present a study using an intermediate abstraction as a model for the acquisition of the concept of negative numbers. The intermediate abstraction is a computerized environment based on a detailed epistemological analysis of negative numbers. Four children participated in activities with the intermediate abstraction during eleven 30-min training sessions. This article outlines the development of the children's representations of negative numbers during the experiment. We analyzed how students used their representations as problem models in transfer tasks with several different referents. The results obtained in the experiment support the use of certain environments for the acquisition of higher level mathematical concepts that cannot be learned informally.