The teaching practice of noticing students' thinking includes both attention to students' mathematical strategies and interpretation of their mathematical understanding. This practice is further complicated when students are engaged with mathematical action technologies while learning mathematics content because, in these contexts, teachers must also notice how the students' engaged with the technology to develop their mathematical understanding. For this crossinstitutional study, we focus on how preservice secondary mathematics teachers (PSMTs) coordinated their noticing of students' mathematical thinking and engagement in a technology-mediated environment. The PSMTs viewed artefacts of high school students working with a Desmos task focused on rational functions, specifically locating vertical asymptotes, and noticed the students' mathematical thinking. Results showed it was easier for PSMTs to attend to and interpret the students' spoken and written responses than for them to attend to and interpret the students' engagement with the technology. Further, it was even more difficult for the PSMTs to coordinate the students' spoken and written responses with their technology engagement.