The objective of the study was to characterise how pre-service kindergarten teachers used a Hypothetical Learning Trajectory on length and its measurement to notice children’s mathematical thinking. A total of 64 pre-service kindergarten teachers enrolled in an Early Years Education mathematics teaching course were asked to notice teaching situations focusing on kindergarten children’s learning of length. On the one hand, three profiles of pre-service kindergarten teachers were found according to the use they made of the Hypothetical Learning Trajectory. These profiles were characterised by three ways of learning to use the Hypothetical Learning Trajectory based on the type of mathematical elements they identified: only mathematical elements related to the magnitude; only mathematical elements related to the measurement of length; or both magnitude and measurement elements. On the other hand, when considering the three skills of professional noticing, by identifying the mathematical elements required to solve the proposed task, a group of pre-service kindergarten teachers within each profile were able to notice the thinking of these elements by children and to suggest activities. Our findings provide learning opportunities to pre-service kindergarten teachers who use a Hypothetical Learning Trajectory. It provides them with ‘check-points’ to answer the proposed questions, in order to learn the specialised knowledge for teaching length and its measurement as well as to develop the skill of noticing student’s mathematical thinking.

这项研究的目的是描述学前班教师如何使用假想学习轨迹的长度及其测量方法来注意儿童的数学思维。总共邀请了64位参加“早教”数学教学课程的学前班幼儿园教师注意以幼儿园儿童的身长学习为重点的教学情况。一方面，根据他们对假设学习轨迹的使用情况，发现了三种职前幼儿园教师的概况。这些配置文件的特征在于，根据识别出的数学元素的类型，通过三种学习方法来使用假设学习轨迹：仅与幅度有关的数学元素；仅与长度测量有关的数学元素；或两者兼有。另一方面，当考虑专业提示的三种技巧时，通过确定解决拟议任务所需的数学要素，每个档案中的一组职前幼儿园教师能够注意到孩子对这些要素的思考，并建议活动。我们的发现为使用假设学习轨迹的职前幼儿园教师提供了学习机会。它为他们提供了“检查点”来回答所提出的问题，以便学习有关教学时长及其测量方法的专门知识，并发展注意到学生数学思维的技能。通过确定解决拟议任务所需的数学要素，每个档案中的一组职前幼儿园教师能够注意到儿童对这些要素的思考并提出活动建议。我们的发现为使用假设学习轨迹的职前幼儿园教师提供了学习机会。它为他们提供了“检查点”来回答所提出的问题，以便学习有关教学时长及其测量方法的专门知识，并发展注意到学生数学思维的技能。通过确定解决拟议任务所需的数学要素，每个档案中的一组职前幼儿园教师能够注意到儿童对这些要素的思考并提出活动建议。我们的发现为使用假设学习轨迹的职前幼儿园教师提供了学习机会。它为他们提供了“检查点”来回答所提出的问题，以便学习有关教学时长及其测量方法的专门知识，并发展注意到学生数学思维的技能。我们的发现为使用假设学习轨迹的职前幼儿园教师提供了学习机会。它为他们提供了“检查点”来回答所提出的问题，以便学习有关教学时长及其测量方法的专门知识，并发展注意到学生数学思维的技能。我们的发现为使用假设学习轨迹的职前幼儿园教师提供了学习机会。它为他们提供了“检查点”来回答所提出的问题，以便学习有关教学时长及其测量方法的专门知识，并发展注意到学生数学思维的技能。