This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused on what he calls the "unspoken curriculum": mathematical thinking. We consider the ways in which the TBL model promoted and enabled this in the light of literature on mathematical thinking, sense-making and behaviours, and strongly suggest that this approach warrants more attention from the mathematics teaching community. We also discuss shifts in the mathematician's thinking about task construction as he refined the tasks to encourage students to think and behave like mathematicians.