This paper presents a case study of two prospective teachers' perturbations and professional development during lesson demonstrations which focused on technology-rich mathematics teaching and learning by analyzing a series of individual and collaborative video-based reflections to support the prospective teachers' learning. Drawing on the construct of hiccups in technology-rich mathematics teaching, our analysis highlights the different types of hiccups the prospective teachers noticed in their lesson demonstrations; how they responded to the hiccups they identified; their professional learning from these experiences; and the differences in the prospective teachers' noticing from the perspectives of the lesson teacher and the student audiences. Results highlight the strengths and limitations of prospective mathematics teachers' noticing during technology-rich teaching and learning; for example, prospective teachers taking the role of student audiences during lesson demonstrations allows for different and additional in-the-moment noticing compared to them taking the role of teachers. Results also suggest the need for multiple reflection opportunities to help prospective mathematics teachers develop their noticing skills in technology-rich classroom contexts.