Preservice secondary mathematics teachers (PSMTs) need exposure to noticing students' mathematical thinking when students are engaged with technological tasks. In this paper, we share results from a study in which PSMTs first watched videos of students engaged with a technological mathematical task focused on the concept of function and after watching the videos, were asked to predict the students' technological mathematical thinking as they continued to interact within the technological environment. Results showed that it was difficult for the PSMTs to coordinate the students' mathematical thinking with the students' engagement with the technology. However, for PSMTs who did coordinate both the students' thinking and their engagement with the technology, we identified two components of their predictions that seemed to provide specific insight into the PSMTs' overall noticing of the students' thinking. These were (1) predicting cognitive dissonance or lack thereof, and (2) predicting how the students would interact with each other and with the technology. These results provide mathematics teacher educators with specific additions to potential noticing prompts for PSMTs to express their interpretation of students' technological mathematical thinking when predicting what students may do next when working in a technology-mediated environment.