Central to the didactical contract (Brousseau 1997) are the implicit rules that teachers develop in their interactions with their students on a day-to-day basis. This article will examine the role that teachers play, in classrooms viewed as activity systems, in developing the degree to which students are enabled to develop agency in their learning and use of mathematics. Building on the work of Swan (2006) we developed a uni-dimensional scale that identified the degree to which teachers’ interactions with their students might be considered to range between transmissionist and connectionist. In general we found much mathematics teaching of post-16 students might be characterised as transmissionist with, as our case-study work found, students passively ‘engaging’ in learning. In the relatively few cases where we identified strong connectionist teaching we noted that the teacher plays a crucial role in orchestrating both mathematics and social engagement in ways that encourage students to develop agency. In this article, drawing on classroom observations and student and teacher interviews, we consider in some detail how connectionist teaching of this type requires a teacher to pay particular attention to both the students’ mathematical and social development.