Fostering pre-service teachers’ attention to mathematical objects: The realization tree mediator as a teaching representation

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.