Artificial Intelligence and its sub-disciplines are becoming increasingly relevant in numerous areas of academia as well as industry and can now be considered a core area of Computer Science [ 84 ]. The Higher Education sector are offering more courses in Machine Learning and Artificial Intelligence than ever before. However, there is a lack of research pertaining to best practices for teaching in this complex domain that heavily relies on both computing and mathematical knowledge. We conducted a literature review and qualitative study with students and Higher Education lecturers from a range of educational institutions, with an aim to determine what might constitute best practices in this area in Higher Education. We hypothesised that confidence, mathematics anxiety, and differences in student educational background were key factors here. We then investigated the issues surrounding these and whether they inhibit the acquisition of knowledge and skills pertaining to the theoretical basis of artificial intelligence and machine learning. This article shares the insights from both students and lecturers with experience in the field of AI and machine learning education, with the aim to inform prospective pedagogies and studies within this domain and move toward a framework for best practice in teaching and learning of these topics.