Non-mathematics specialists' competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students with Mathematical Modeling (MM) activities, is one way to achieve this improvement. We examine the evolution of 12 first-semester biology students' mathematical discourse as they engage with such activities in four sessions which ran concurrently with their mandatory mathematics course and were taught by a mathematician with extensive experience with MM. The sessions involved brief introductions to different aspects of MM, followed by small-group work on tasks set in biological contexts. Our analyses use the "theory of commognition" to investigate the tensions between "ritualized and exploratory participation" in the students' MM activity. We focus particularly on a quintessential "routine" in MM, "assumption building": we trace attempts which start from ritualized engagement in the shape of "guesswork" and evolve into more productively exploratory formulations. We also identify signs of persistent "commognitive conflict" in the students' activity, both "intra-mathematical" (concerning what is meant by a "math task") and "extra-mathematical" (concerning what constitutes a plausible solution to the tasks in a biological sense). Our analyses show evidence of the fluid interplay between ritualized and exploratory engagement in the students' discursive activity and contribute towards what we see as a much needed distancing from operationalization of the commognitive constructs of ritual and exploration as an unhelpfully dichotomous binary.