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<p>Professional noticing, encompassing attending to, interpreting, and responding to students’ understanding, is a vital skill for effective mathematics teaching. This study investigated how novice and expert primary school teachers developed instrumental relationships with fractions learning trajectory (LT) knowledge during professional noticing processes. Data were collected from 64 participants (30 novice teachers and 34 expert teachers) through tasks requiring them to analyse students’ fractional reasoning strategies and propose developmentally appropriate instructional activities. Results revealed that expert teachers exhibited significantly higher skills in interpreting and responding to students’ understanding compared to novice teachers, while showing minimal differences in attending capabilities. The study identified four levels of instrumental genesis—artifact role, using specific LT components, partial instrumentation, and full instrumentation—revealing that expert teachers consistently achieved higher levels of LT transformation from theoretical artifacts to practical instruments. Expert teachers demonstrated instrumental resilience, maintaining stable performance across varying cognitive demands, while novice teachers showed systematic regression as task complexity increased. These findings demonstrated that expertise enables robust instrumental relationships with theoretical frameworks, suggesting that teacher education programs must support systematic instrumental genesis rather than simple framework exposure to develop effective professional noticing capabilities.</p>

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Instrumental Genesis of Learning Trajectories in Professional Noticing: Comparing Expert and Novice Teachers’ Competencies in Fractions

  • 期刊论文

  • 发表日期：

    2026年7月16日

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  • Derya Can

摘要

Professional noticing, encompassing attending to, interpreting, and responding to students’ understanding, is a vital skill for effective mathematics teaching. This study investigated how novice and expert primary school teachers developed instrumental relationships with fractions learning trajectory (LT) knowledge during professional noticing processes. Data were collected from 64 participants (30 novice teachers and 34 expert teachers) through tasks requiring them to analyse students’ fractional reasoning strategies and propose developmentally appropriate instructional activities. Results revealed that expert teachers exhibited significantly higher skills in interpreting and responding to students’ understanding compared to novice teachers, while showing minimal differences in attending capabilities. The study identified four levels of instrumental genesis—artifact role, using specific LT components, partial instrumentation, and full instrumentation—revealing that expert teachers consistently achieved higher levels of LT transformation from theoretical artifacts to practical instruments. Expert teachers demonstrated instrumental resilience, maintaining stable performance across varying cognitive demands, while novice teachers showed systematic regression as task complexity increased. These findings demonstrated that expertise enables robust instrumental relationships with theoretical frameworks, suggesting that teacher education programs must support systematic instrumental genesis rather than simple framework exposure to develop effective professional noticing capabilities.