This study contributes to the growing body of research that highlights the usefulness of professional noticing of children’s mathematical thinking for understanding the complexity and variability in teaching expertise. We explored the noticing expertise of 72 upper elementary school teachers engaged in multi-year professional development focused on children’s fraction thinking. Our assessment addressed the three component skills of professional noticing of children’s mathematical thinking: (a) attending to children’s strategy details, (b) interpreting children’s understandings, and (c) deciding how to respond on the basis of children’s understandings. We used a latent class analysis to empirically identify three distinct “profiles” of noticing expertise—subgroups of teachers who responded similarly to each other and differently from teachers in other profiles. The profiles differed in their overall noticing expertise as well as their patterns of strengths and areas for growth across the component skills. Thus, the profiles provide a concise, multi-dimensional characterization of noticing expertise that integrates expertise in each of the component skills. The profiles also provide tools for differentiating learning opportunities for teachers in professional development. In addition, our design allowed us to compare teachers’ expertise in two common forms of deciding how to respond: deciding on follow-up questions and deciding on next problems. In all three profiles, teachers demonstrated more expertise when deciding on follow-up questions than when deciding on next problems, suggesting not only a starting point for teacher learning but also the need for a line of research focused on different forms of this component skill.

这项研究有助于越来越多的研究强调专业关注儿童数学思维对于理解教学专业知识的复杂性和可变性的有用性。我们探索了 72 名从事多年专业发展的小学教师的注意专长，重点是儿童分数思维。我们的评估涉及专业关注儿童数学思维的三个组成技能：(a) 关注儿童的策略细节，(b) 解释儿童的理解，以及 (c) 决定如何根据儿童的理解做出反应。我们使用潜在类别分析来凭经验确定三个不同的注意专长“配置文件”——教师的亚组，他们对彼此的反应相似，但与其他配置文件中的教师不同。这些概况在他们的整体注意专业知识以及他们的优势模式和组件技能的增长领域方面有所不同。因此，这些概况提供了一个简洁的、多维的注意专业知识的特征，它整合了每个组件技能的专业知识。这些概况还提供了区分教师专业发展学习机会的工具。此外，我们的设计允许我们比较教师在决定如何回答的两种常见形式方面的专业知识：决定后续问题和决定下一个问题。在所有三个配置文件中，