We present the results of a study investigating the potential role of the generative AI GPT-4 in scaffolding students' metacognitive activities during problem-solving. The theoretical framework according to which students' interactions with GPT-4 are analysed is based on three main components: the notion of utilisation scheme within the frame of instrumental genesis, the construct of metacognitive activity, and the construct of Model of Aware and Effective Attitudes and Behaviours. The developed analysis characterises ChatGPT's tutoring approach in supporting students' metacognitive processes and shows how students have used ChatGPT to carry out problem-solving processes by developing specific initial utilisation schemes. This study has both practical and theoretical implications. On the one hand, identifying categories of students' approaches to using ChatGPT's scaffolding of metacognitive processes in problem solving could help in the design of teaching interventions to support the development of critical and reflective mathematical thinking. On the other hand, this study points to the need to refine the model for analysing interactions between human users and digital environments to take into account the complexity introduced by generative AI technologies.