Curriculum reforms in the teaching of mathematics have encouraged a move away from sole memorisation of facts to the construction of deeper levels of understanding. With this reform, teachers of mathematics are called to act as facilitators of the construction of mathematical knowledge. However, some research suggests that students believe that their teacher's role is one that would be more aligned with the transmission of knowledge. This paper reports an aspect of a small-scale pilot study that sought to illuminate the beliefs that students hold about their preferred mathematics learning environments. It also highlights the role that "concept cartoons" played in making known these beliefs. (Contains 2 figures and 1 table.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]