To bring educational robots to classrooms, we need to consider teachers' self-efficacy and challenges in managing a robot-mediated classroom, and how to support them in overcoming these challenges. Orchestration tools are designed to support teachers by providing real-time information on the students' actions and progress within the activity, at various levels of detail and scope, as well as levers to control the flow of the activity. In order for orchestration tools to be effective and useful, their features should be designed according to the needs of the teachers in each specific classroom context. This thesis starts by investigating the orchestration practices enacted by teachers in authentic robot-mediated classrooms, i.e. during classroom activities in which students, individually or in groups, are envisioned to interact with educational robots, and find the teachers' needs that can be supported by orchestration technologies. Building on the results of such classroom observations, the thesis then discusses the design and classroom evaluation of orchestration tools for robot-mediated classrooms. Concretely, this thesis makes three contributions. 1) It provides an overview of the challenges that teachers face in their practice, when orchestrating robot-mediated math activities and specifically to the purpose of orchestrating math class discussion to be productive. The results are based on more than twenty hours of in-session analysis of teachers' behaviour and class discourse in eight math sessions. 2) It analyses the results of how teachers orchestrate robot-mediated math activities and evaluate whether orchestration tools can improve their orchestration practices. I design, develop and study the usage, usability and usefulness of a novel orchestration tool, called CelloRoom, in the context of a series of robot-mediated activities aiming to teach the mathematics concepts of coordinate system and line slope in in-person classrooms to children aged 7-14 years old. Across two design iterations, eleven teachers in different primary/secondary schools across Switzerland adopted the mathematical robot-mediated activities in their classrooms, using two versions of CelloRoom for a total of 14 sessions and more than 200 students. The findings emphasize the importance of investigating teachers' orchestration practices by analysing class audio/video recording, to evaluate the usefulness of orchestration tools in class time. 3) It proposes a set of novel quantitative measures to describe and assess how teachers perform the practices of orchestrating productive math discussions, defined by stein2008orchestrating, namely monitoring students' mathematical thinking, selecting and sequencing students' solutions in class to emerge mathematical ideas and connecting these ideas to the underlying learning goal of the activity. These measures were used the evaluate the usefulness of CelloRoom 2.0 in supporting teachers' orchestration of productive math discussions. Our findings highlight the benefits that orchestration tools can bring for the orchestration of robot-mediated classroom activities by teachers: the teachers involved in our studies could get aware of robot failures in the class quickly and reliably, could adapt the activity sequence on the fly and found students' data visualization helpful to create discussion in the classroom, especially for selecting and sequencing students' solutions