The objective of this study was to characterise prospective kindergarten teachers’ development of noticing children’s thinking about length and its measurement. We used the concepts of instrumental genesis and learning trajectories to identify the ways in which prospective kindergarten teachers used a learning trajectory to learn to notice children’s mathematical thinking. Following a teaching experiment, we identified three ways in which prospective kindergarten teachers used the learning trajectory to notice children’s mathematical thinking. Two instrumented action schemes supported these ways of using the learning trajectory, namely, a scheme taking into account the mathematics learning progression to interpret children’s answers, and a scheme for proposing instructional tasks based on the interpretation of children’s mathematical thinking. Approaching the development of noticing as an appropriation process of a learning trajectory helps us to understand prospective teachers’ difficulties in endowing meaning to a learning trajectory’s conceptual structure. We suggest that these ways of using learning trajectory knowledge to interpret children’s mathematical thinking and to make instructional decisions can be understood as an instrumentation process that reveals how noticing skills develop.

这项研究的目的是表征未来的幼儿园教师在注意儿童的身长及其测量方法方面的发展。我们使用了工具起源和学习轨迹的概念来确定准幼儿园教师使用学习轨迹来学习注意儿童数学思维的方式。通过教学实验，我们确定了未来的幼儿园教师使用学习轨迹来注意儿童数学思维的三种方式。有两种工具化的行动方案支持使用学习轨迹的这些方式，即考虑数学学习进度来解释儿童答案的方案，以及根据儿童数学思维的解释提出教学任务的方案。将注意的发展作为学习轨迹的专用过程，可以帮助我们理解准老师在赋予学习轨迹概念结构意义上的困难。我们建议，使用学习轨迹知识来解释儿童的数学思维和做出教学决策的这些方式可以理解为一种揭示注意技能如何发展的过程。