Using teaching representations is one of the common means for preparing pre-service mathematics teachers (PSTs) to learn how to teach mathematics meaningfully. However, turning PSTs’ attention to the mathematical objects that students engage with during the lesson is a challenging pursuit. This paper suggests using the Realization Tree Mediator (RTM) as a visual teaching representation for PST learning to implement cognitively demanding tasks in their classrooms. The RTM depicts the mathematical object at the core of a task and its different realizations while illustrating imaginary classroom discussions in which different realizations and the links between them are produced. By analyzing PSTs’ conversations around RTM images, we show how contrasting pairs of RTMs can be used for eliciting conversations about various aspects of cognitively demanding instruction. We discuss the affordances of the RTM as a teaching representation and how it can assist in making the mathematical content and meanings visible, public, and communicable among teachers and teacher educators.

使用教学表征是让职前数学教师 (PST) 学习如何有意义地教授数学的常用方法之一。然而，将 PST 的注意力转向学生在课堂上接触的数学对象是一项具有挑战性的追求。本文建议使用实现树中介器 (RTM) 作为 PST 学习的视觉教学表示，以在课堂上实施认知要求较高的任务。RTM 描述了任务核心的数学对象及其不同的实现，同时说明了想象中的课堂讨论，其中产生了不同的实现及其之间的联系。通过分析 PST 围绕 RTM 图像的对话，我们展示了如何使用对比的 RTM 对来引发有关认知要求教学的各个方面的对话。我们讨论了 RTM 作为教学表征的可供性，以及它如何帮助使数学内容和意义在教师和教师教育者之间变得可见、公开和可交流。