Understanding by Design (UbD) is a well-known curricular methodology aiming at leading students to develop deep understanding of the arguments proposed by teachers. Through a path including stimulating questions, student motivation, deepening of the argument, reflection, design and assessment of authentic performances, the students develop a broad understanding of the learned argument. While there is plenty of articles describing various experiences in classrooms and schools showing the benefits of UbD, rarely this methodology has been the object of experimental or quasi-experimental studies. A research conforming to quasi-experimental criteria has been performed in a Swiss vocational school, where three groups of students have been submitted to teaching based on UbD principles (the first two) and to a more traditional teaching approach (the remaining one). The argument was the study of mathematical Relations and Functions. The results, collected during one school year, showed that the first two groups outperformed the third one and that the effect lasted at least for one school year. Since the teacher remained the same, it is likely that the outcome can be attributed to the use of the methodology.