An alternative instructional model, which due to the social reality created by the ongoing COVID-19 pandemic is gaining more and more popularity in the global educational community, is the so called “flipped classroom”. In this paper we give the details of a one-week qualitative research we conducted in order to explore the effectiveness of the flipped classroom model in an undergraduate “mathematics education” course in Greece. The study involved thirty third-year math students, whose achievements and perceptions were captured with the help of questionnaire, task, personal interviews, and open discussion in the class. The analysis of the research data indicated increased engagement of the students, development of positive attitudes about the learning, control of the learning pace, autonomy in managing the time required for study and relative improvement of students’ performance in problem solving and teamwork. At the same time, several challenges emerged. The main ones concerned the demand for frequent active students’ participation in the educational process, the management of queries during the homework, the doubts about the effectiveness of the method on difficult teaching subjects, as well as the time and skill requirements for preparing such a lesson.