Many engineering subjects rely on the interpretation of symbolic, numeric and graphic representations. Engineering students have challenges pertaining to their mathematical understanding of their actions with a computer algebra system (CAS). We investigated how a mathematical modelling task could mediate varied levels of mathematical understanding. When engineering students are exposed to a CAS environment, they habitually engage in programming activities without considering the computerised outputs. The purpose of this paper was to ascertain South African engineering students' actions that can mediate broader levels of mathematical understanding in a CAS by utilising the Pirie-Kieren model of growth in mathematical understanding. Thirteen participants agreed to engage collaboratively in a mathematical modelling task. The task was analysed by means of content analysis following a deductive research approach. The findings disclosed that engineering students interdepend on paper-and-pen, computerised and reflective actions in their growth of mathematical understanding. Engineering students can be assisted in mediated and folding-back actions in order to fluctuate back and forth on their way to a more sound mathematical understanding. Explicit planning and sequence of subtasks can support engineering students to merge new levels of mathematics understanding with past comprehensions. Thoroughly planned modelling tasks can mediate novel levels of mathematical understanding when engineering students learn with a CAS.