Contribution: This article proposes and applies a new systemic 3-D model and a methodology for empathy awareness and development, integrating different partial approaches found in the literature for developing empathy as a transversal competence. Background: Empathy is a competence linked to collaboration and teamwork. Perspective taking (PT) is an important component of empathy and it is key for professionals today. Even though empathy is valued in computer science engineering (CSE) courses, it is not yet fully addressed as an integral part of the training process. Intended Outcomes: Both the model and the methodology are put into practice with a group of first-year CSE students, highlighting the possibilities of the proposal for this course of studies. The experience presented here is an example of a classroom activity in which awareness and PT are addressed, as key components, in relation to the collaborative work toward achieving empathy. Application Design: The methodological proposal is applied to guide educators' decisions so that they can work on empathy in the classroom. Responses to several standardized and ad-hoc questionnaires by students from two universities are analyzed. Findings: The results revealed low to medium empathy levels in participating students, but a higher perception of their own empathic ability. The proposed methodology allows students to become aware of and develop some initial changes in relation to empathy, particularly in its PT component, through classroom work.