Software engineering (SE) teaching uses learning strategies to promote the acquisition of technical and social capabilities; typical strategies are project-based learning, collaborative learning, and problem-based learning. SE teachers need to compare, evaluate, and select strategies and practices for specific courses, but they are usually described in imprecise and subjective manners. This paper describes SETMAT (Software Engineering Teaching Method and Theory), a descriptive theory of SE teaching with a common conceptual framework for describing teaching strategies and practices, combining concepts and relationships of SE. SETMAT has been used in a pilot study by teachers of Colombia, Chile, and Mexico to represent their SE teaching practices. SETMAT adoption would allow to represent, compare, compose and transfer SE teaching practices and strategies. © 2019, Associacao Iberica de Sistemas e Tecnologias de Informacao. All rights reserved.