This paper advocates using large language models (LLMs) to enhance students' open-ended mathematical problem-solving skills. The literature review reveals that using large language models (LLMs) in educational settings is an emerging field with limited research evidence. Much of the existing literature focuses on the perceptions of educators and other stakeholders and evaluations of LLM model accuracy rather than their potentially transformative impact on educational outcomes or personalised learning in mathematics. This paper reports on the ongoing development of a study to provide such evidence. It presents expected results derived from our preliminary development work, which suggests that teaching students to utilise LLMs like ChatGPT effectively can enhance their critical thinking and analytical skills in mathematical problem-solving. Initial observations and iterative refinements inform these anticipated outcomes during the pilot phase of our research.