Teacher orchestration of technology-enhanced learning (TEL) processes plays a major role in students' outcomes, especially in face-to-face classrooms. However, few studies look into the fine-grained details of how such orchestration unfolds, the challenges and cognitive overload that using technologies at a classroom level pose for teachers. This paper proposes a mixed-method approach to the study of orchestration cognitive load, combining physio-behavioural (eye-tracking) and subjective measurements (questionnaires, stimulated recall interviews). We illustrate the approach by applying it to study the orchestration of two technology-enhanced geometry lessons, by a secondary school teacher. The results of our mixed-method analyses highlight the difficulty of classroom-level (as opposed to individual- or group-level) interactions, especially in modelling students' progress and understanding. Such insights can be useful in the design of new classroom technologies, and to focus researchers' attention on critical orchestration episodes during their evaluation.