This paper develops a method for the construction and evaluation of cognitive models to support students in their problem-solving skills during robotics in school, aiming to build a basis for an implementation of a tutoring system in the future. Two Wizard-of-Oz studies were conducted, one in the classroom and one in the lab. Based on the cognitive model, the human wizards gave support to 20 students working in pairs. The studies were video recorded and a qualitative analysis was conducted. This qualitative research approach is described in detail. The evaluation of the studies showed that students reacted mostly positively to the wizards. We also uncovered ways in which students' problem-solving skills could be improved. Based on the evaluation and observations of the Wizard-of-Oz studies, the paper proposes a design for a future robotics skills tutoring system.