Summary: This article analyzes the possibilities of three ways of representing knowledge ‒ verbal, diagrammatic and formal ‒ for solving problems in the mathematics domain, and specifically in the integers domain. It deals with the capabilities introduced by digital environments to handle these representation modalities. The state of the art draws differences among these tools related to information value and usefulness for activating reasoning. Studies from the cognitive psychology domain and from Artificial Intelligence provide the support for understanding the abstraction, transfer, and contextualizing of the learning process. Diagrammatic reasoning has been a strong research line for the last decade whose results will influence the study of mathematics learning.