Background: ChatGPT, an AI-based chatbot, supports learning by accurately interpreting and responding to user inputs. Despite its potential, few empirical studies have examined its influence on college students' mathematical problem-solving processes. Objectives: This study aimed to introduce a ChatGPT-facilitated scaffolding to investigate its impact on students' mathematical problem-solving behaviours, performance and perceptions. Methods: Twenty-nine undergraduates participated in this study, engaging in mathematical problem-solving tasks using the scaffolding. A mixed-method approach was employed, incorporating performance data, interaction analysis and self-reported surveys to assess both quantitative and qualitative aspects of students' experiences. In particular, lag sequential analysis was applied to explore the undergraduates' problem-solving behavioural patterns. Results and Conclusions: Results demonstrated that the ChatGPT-facilitated scaffolding significantly improved students' mathematical problem-solving performance. The high-performance group (HPG) exhibited a greater frequency of interpretive and evaluative activities, transitioning from factual to metacognitive representations, while the low-performance group (LPG) primarily transitioned from prompt selection to procedural representations. Additionally, most participants expressed positive perceptions of the scaffolding experience and reported an improvement in their problem-solving skills. Major Takeaways: These findings offer valuable insights for the design and implementation of AI-facilitated learning activities in mathematical problem-solving contexts.