The use of the graduate teaching assistant (GTA) to support the teaching activities of higher education institutions has been growing over the years and it is now a well-established practice. Conventionally training sessions, consisting usually of workshops, remain general and overemphasise policies, not providing sufficient preparation for in-service teaching. This study proposes to overcome these shortcomings by introducing a new methodology that is based on the use of peer teaching and self-reflection and that is both continuous and discipline-specific. The analysis of the feedback, collected from GTAs' teaching practical engineering sessions during a full academic year, shows that by engaging with the training, each GTA developed their reflective practice and their student-centred teaching. Interestingly, results also show that some GTA underwent a regression phase during the second semester. It is expected that only a training method that continuously supports their pedagogical development can lead these GTAs towards a recovery phase.