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As a core practice, teacher noticing of students' mathematical thinking is foundational to other teaching practices. Yet, this practice is difficult for preservice teachers (PSTs), particularly the component of interpreting students' thinking (e.g., Teuscher et al., 2017). We report on a study of our design of a specific approximation of teacher noticing task with the overarching goal of conceptualizing how to design approximations of practice that support PSTs' learning to notice student thinking in technology-mediated environments with a specific focus on interpreting students' mathematical thinking. Drawing on Grossman et al.'s (2009) Framework for Teaching Practice (i.e., pedagogies of practice), we provided decomposed opportunities for PSTs to engage with the practice of teacher noticing. We analyzed how our design choices led to different evidence of the PSTs' interpretations through professional development design study methods. Findings indicate that the PSTs frequently interpret what students understood. Yet, they were more challenged by interpreting what students did not yet understand. Furthermore, we found that providing lesson goals and asking the PSTs to respond to a prompt of deciding how to respond had the potential to elicit PSTs' interpretations of what the students did not yet understand. The study highlights the interplay between task design, prompt wording, and PSTs' interpretations, which emphasizes the complexity of developing teacher noticing