Problem-solving (PS) is taught and practised in many higher education institutions across various disciplines. However, there is a lack of understanding of how to teach PS in a way that aligns with the specific principles and methods associated with its pedagogy. This study aimed to understand how tutors of Problem-Based Learning (PBL), a problem-centered instructional practice, conceptualize teaching problem-solving (CoTPS). Through qualitative interviews followed by phenomenographic analysis, we developed a model of CoTPS, which analyses how PBL tutors conceive problems in instruction, the process of problem-solving, and their role in tutorial groups. The categories of description, forming a hierarchy of inclusivity, enabled us to identify the least and most complex conceptions of teaching problem-solving. This model allows PBL tutors and, more broadly, higher education teachers to reflect on their conceptions and enables academic developers to create programs that enhance both conceptual understanding and practical application of problem-centred instruction.