TEMPORAL DEVELOPMENT OF PRESERVICE MATHEMATICS TEACHERS' PRODUCTIVE NOTICING DURING A SEMESTER-LONG PRACTICUM: A FOCUS-ALIGNMENT TRAJECTORY STUDY

초록

Extended school-based practica are expected to help pre-service teachers connect university coursework with classroom practice, yet little is known about how their mathematics-specific noticing develops week by week. This longitudinal multiple-case study traced three preservice mathematics teachers (PST1-PST3) during a semester-long practicum. The data comprised 108 dated practicum journal episodes written by the participants from Weeks 2-15, supplemented by mentor/supervisor feedback, lesson artifacts, and research-lesson transcripts for contextual and process-tracing purposes. Using the FOCUS framework, each episode was coded for the degree of alignment among mathematical key ideas, anticipated or observed student difficulties, and pedagogical responses (A0-A2), with the final code based on the preservice teacher's own written reflection. Findings show that robust alignment was not a simple linear outcome of time in school. Rather, A2 episodes appeared unevenly when preservice teachers explicitly connected mathematical key ideas, student difficulties, and pedagogical responses in their own journal texts. Early peaks occurred during the assisting and co-teaching stage for PST2 and PST3, while selected responsibility and closure episodes also showed robust alignment. The study shows how practicum-semester designs can cultivate productive noticing when feedback and teaching experiences are taken up in preservice teachers' reflections as an explicit connection among mathematics, student thinking, and instructional response.

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