Researchers examining elementary teachers’ mathematical teaching expertise—that is, teachers’ knowledge both of mathematics and of how to effectively teach mathematics—have linked such expertise to student outcomes. But, given the increasing use of classroom observations for teacher evaluation in the USA, this study considers whether and how upper elementary teachers’ mathematical teaching expertise is observable in everyday classroom observations. Using classroom observation data collected with the widely used CLASS observation instrument, this study examines relationships among observation data, student outcome data, and data on opportunities for professional learning from 298 upper elementary teachers in four urban school districts in the USA. Using principal components analysis, this study isolates an observable dimension of mathematical teaching expertise. Regression analyses then identify statistically significant relationships among observed mathematical teaching expertise and multiple student outcomes, including mathematics learning and self-efficacy, as well as teacher professional learning through collaboration with mathematics coaches. Our findings inform strategies for observing mathematical teaching expertise, strengthening the practices of upper elementary teachers, and improving student experiences in the upper elementary grades.

中文翻译：

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高阶基础教师中可观察到的数学教学专业知识：与学生体验和专业学习的联系

研究基础老师的数学教学专门知识（即老师对数学以及如何有效教授数学的知识）的研究人员已将此类专业知识与学生的学习成果联系起来。但是，鉴于美国越来越多地将课堂观察用于教师评估，本研究考虑了在日常课堂观察中是否以及如何观察到高级基础教师的数学教学专长。本研究使用广泛使用的CLASS观测仪器收集的课堂观测数据，研究了观测数据，学生结果数据以及来自美国四个城市学区的298位高级基础教师的专业学习机会数据之间的关系。使用主成分分析，这项研究隔离了数学教学专业知识的一个可观察的维度。回归分析然后确定观察到的数学教学专业知识与多个学生成果之间的统计学显着关系，包括数学学习和自我效能感以及通过与数学教练的协作进行教师专业学习。我们的发现为观察数学教学专业知识，加强高级基础老师的实践以及改善高年级学生的学习经验提供了策略。以及通过与数学教练的合作来进行教师专业学习。我们的发现为观察数学教学专业知识，加强高级基础老师的实践以及改善高年级学生的学习经验提供了策略。以及通过与数学教练的合作来进行教师专业学习。我们的发现为观察数学教学专业知识，加强高级基础老师的实践以及改善高年级学生的学习经验提供了策略。