Making sense of mathematical concepts and solving mathematical problems may demand different forms of reasoning. These could be either domain-based, such as algebraic, geometric or statistical reasoning, while others are more general such as inductive/deductive reasoning. This article aims at giving visibility to a particular form of reasoning which Piaget referred to as reversibility of thought or equivalently reversible reasoning. Reversible reasoning essentially involves reasoning from a given result to the source producing the result. Using examples from the school mathematics curriculum, this article illustrates how this mode of reasoning may be involved in the solution of mathematical problems. Further, it provides a strategy to foster reversible reasoning by formulating tasks in a primal and dual mode. Simultaneously, the article explains why such a mode of reasoning is essential in developing flexibility in thinking.