ABSTRACT Using multiple representations and changing between them is at the heart of the mathematics classroom; unconnected changes can, however, be obstructive for students’ learning. In order to support students’ learning with multiple representations, teachers have to link observed situation aspects with relevant professional knowledge, a competence we described as teachers’ analysing of classroom situations in prior research. Although teachers’ professional knowledge plays a critical role in such competence, empirical evidence regarding different facets of such knowledge and their interplay is still scarce. This study investigates different facets of teachers’ knowledge of using multiple representations in the context of learning fractions and their role for teachers’ corresponding competence of analysing. We asked N = 298 teachers at different levels of expertise to analyse six classroom situations presented as text, comic or video. Our findings indicate that knowledge facets related to mathematical content are significant predictors for teachers’ competence of analysing.

中文翻译：

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专业知识在教师使用多重表征分析课堂情境中的作用

摘要 使用多种表示并在它们之间进行转换是数学课堂的核心；然而，不相关的变化可能会阻碍学生的学习。为了支持学生多方面的学习，教师必须将观察到的情境方面与相关专业知识联系起来，我们在先前的研究中将这种能力描述为教师对课堂情境的分析。尽管教师的专业知识在这种能力中起着至关重要的作用，但关于这种知识的不同方面及其相互作用的经验证据仍然很少。本研究调查了教师在学习分数的背景下使用多重表征的知识的不同方面及其对教师相应分析能力的作用。我们要求 N = 298 名不同专业水平的教师分析以文本、漫画或视频形式呈现的六种课堂情况。我们的研究结果表明，与数学内容相关的知识面是教师分析能力的重要预测因素。