This paper reports observations and reflections from a pedagogic intervention intended to enhance mathematics students' learning of course content in a course in multivariable calculus. The intervention design required students to structure, practice, and deliver an oral presentation that was a synthesis of the teacher's weekly lectures, for the benefit of themselves and their peers. The intervention appears to have incentivized students to engage with and learn mathematics contents in an effective way, and it also helped the mathematics teacher to reflect on, adapt, and develop his teaching strategies. To conclude, it would seem that both students and teachers in mathematics have much to gain from giving students opportunities to develop their own voice in learning contexts otherwise relying on books and lectures.