Professional noticing of children’s mathematical thinking (Jacobs et al. in J Res Math Educ 41(2):169–202, 2010) is a construct that is used frequently to understand the ways in which teachers attend to, interpret, and respond to children’s mathematical thinking. In this paper, we present our analysis of prospective elementary mathematics teachers’ (PTs’) responses to a pedagogical activity designed to engage them in an approximation (Grossman et al. in Teach Coll Rec 111(9): 2055–2100, 2009) of professional noticing of children’s mathematical thinking in the moment of teaching, with a focus on developing responses which extend the student’s thinking. PTs were provided two different examples of student work and a series of questions designed to elicit information about their ability to professionally notice student work. We present data and analysis of 73 PTs’ abilities to engage in the individual skills associated with noticing as well as their abilities to use the skills cohesively in concert. Our results demonstrate the type of representation used determined PTs’ success in all three facets of noticing, with a particular effect on interpreting. Further, our focus on a specific type of response move, along with the introduction of a scaffold for that response move, made a difference in PTs’ ability to successfully respond to student work when compared to a prior study with the same PTs (Tyminski et al. 2014). We unpack these results along with suggestions for pedagogical practice as well as directions for future research.

对儿童数学思维的专业注意（Jacobs 等人在 J Res Math Educ 41(2):169–202, 2010）是一种经常用于理解教师关注、解释和回应儿童数学思维方式的结构。数学思维。在本文中，我们分析了未来小学数学教师 (PT) 对旨在让他们参与近似的教学活动的反应（Grossman 等人在 Teach Coll Rec 111(9): 2055–2100, 2009 中）在教学过程中对孩子数学思维的专业注意，重点是发展反应，扩展学生的思维。向 PT 提供了两个不同的学生作业示例和一系列问题，旨在获取有关他们专业地注意学生作业的能力的信息。我们提供了 73 名 PT 参与与注意相关的个人技能的能力以及他们协同一致地使用这些技能的能力的数据和分析。我们的结果表明，所使用的表示类型决定了 PT 在注意的所有三个方面的成功，对解释有特殊影响。此外，与之前使用相同 PT 的研究相比，我们专注于特定类型的响应移动，以及为该响应移动引入支架，使得 PT 成功响应学生作业的能力有所不同（Tyminski 等2014 年）。我们将这些结果与教学实践的建议以及未来研究的方向一起解开。