Connecting Anticipation to Noticing in Technology-Enhanced Mathematical Tasks: A Comparison of Preservice and In-Service Secondary Mathematics Teachers

Abstract

This study explored the potential connections between secondary in-service (ISTs) and preservice (PSTs) mathematics teachers’ anticipations and their noticing of student thinking in technology-mediated learning environments, a topic with limited prior research. Specifically, the study examined how teachers (ISTs and PSTs) anticipate student thinking while engaging with technology-enhanced mathematical tasks and notice student thinking while students are engaging with the same tasks, with the aim to describe their knowledge for teaching mathematics with technology—Technological Pedagogical Content Knowledge (TPACK). Using a descriptive embedded multiple-case study design, the study involved two groups of participants: ISTs (N=3) and PSTs (N=2), who had completed a technology-focused methods class. Using statistics and algebra task, data were collected through video-recorded task-based interviews focusing on how teachers anticipate and accompanying written noticing assessments focusing on how they notice student thinking. Key findings revealed that neither group initially anticipated student challenges before being prompted. When they did, the ISTs focused more on task-related difficulties, whereas the PSTs considered potential difficulties related to both task representation and underlying concepts. The ISTs and PSTs also exhibited differences in how they engaged with tasks and anticipated student thinking. The ISTs tended to explore tasks sequentially, separating their exploration from anticipation, while the PSTs simultaneously engaged in both processes. When noticing student thinking, the ISTs attended more to students’ verbal and written responses, while the PSTs attended more to students’ technology engagement. When interpreting, both groups showed similar patterns: On the statistics task, they interpreted the students’ understanding but also interpreted what students did not yet understand regarding the concept. On the algebra task, they interpreted the students’ current understanding by focusing only on the aspects with evidence in the students’ work. When deciding how to respond, both groups aligned their questioning strategies with performance goals and prioritized learning goals in their next task decisions. Additionally, the examination of potential connections between the teachers’ anticipations and noticing revealed that they possibly leveraged their anticipations when noticing key aspects of student thinking, with ISTs relying more on their anticipations. This study addresses gaps in the literature regarding teachers’ anticipation and noticing practices in technology-enhanced tasks, offering insight into how these practices develop in both PSTs and ISTs. The findings may contribute to teacher education by informing the design of programs that support teachers in developing the knowledge and skills necessary to effectively teach mathematics with technology.