This research develops and evaluates a pedagogical intervention for teaching Machine Translation Quality Assessment (MTQA) to postgraduate students in Natural Language Processing (NLP). While Translation Studies (TS) has a long tradition of exploring MTQA, MTQA pedagogy is underdeveloped in NLP education. In both academic and industry contexts, MTQA is most commonly carried out using Automatic Evaluation Metrics (AEMs). These metrics are valued for their speed, low cost, and scalability, but they fail to capture important linguistic, contextual, and ethical aspects of translation quality. Human Evaluation (HE), while capable of providing more reliable and nuanced insights, is underused because it is complex, resource-intensive, and time-consuming. As Neural Machine Translation (NMT) continues to produce mistranslations, omissions, and biases, and Large Language Models (LLMs) raise new risks such as hallucinations and instability across system updates, the need for rigorous evaluation practices becomes even more critical. To address this imbalance, this study draws on the ADDIE instructional design framework and Freirean critical pedagogy to structure a training course on MTQA. A systematic review of literature and a survey of educators identified gaps in how MTQA is taught and reported. Based on these findings, a syllabus and course were designed, combining theoretical foundations with hands-on practice in HE, AEMs, evaluation design, and ethics. The course was implemented with postgraduate NLP students, who participated in lectures, lab-based evaluation tasks, and critical reflection on the methodological and ethical dimensions of MTQA. Effectiveness was assessed through a mixed-methods design, including pre-, midand post-tests analysed with Bayesian linear mixed modelling, classroom observation, and thematic analysis of student reflections. The results show that the students increased their confidence in conducting HE, developed a greater critical awareness of the the strengths and weaknesses of each type of evaluation, and demonstrated the ability to apply rigorous evaluation practices to MT systems. By designing, delivering, and evaluating this course, the study demonstrates that critical MTQA training is both feasible and effective. It contributes a structured pedagogical model for embedding responsible and transparent evaluation practices into NLP curricula, promoting more human-centred and accountable approaches to the development of systems focused on AI-driven translation.