A major challenge for practitioners in adult mathematics education is to achieve effective learning outcomes in the face of prevailing negative attitudes in their students, often present as a consequence of unsatisfactory early mathematics learning experience and flowing from the wellestablished connection between adult innumeracy and mathematics anxiety. Whether in nonspecialist mathematics teaching in diverse disciplines such as economics, nursing, and teacher education, or in adult numeracy teaching, the issues are essentially the same: traditional approaches to mathematics teaching, including constructivism, do not work for math-averse students. The need to find new ways to tackle old problems is further fuelled by the impact of the digital age, with mounting evidence that many aspects of accepted teaching and learning practices are being generally undermined by learners' exposure to technology. Consideration of some stereotypes of traditional methodologies in the context of behavioural and cognitive characteristics common among math-averse and math-anxious students motivates a re-framing of the practitioner's approach and outlines strategies for effective practice that find alignment with connectivist approaches to learning, which is a more flexible approach than the constructivism currently favoured as a positive way of presenting mathematics to learners.