This paper applies the well-known cognitive bias of loss aversion from behavioural economics to student decisions over engagement with mathematically demanding coursework. This bias is shown to predict behaviour that is consistent with mathematics anxiety in a dynamic model of student engagement. It is shown that these forces can imply polarization in student outcomes with some students chronically disengaged in a low-attainment equilibrium, in the absence of any countervailing pedagogic interventions. However, the model illustrates that chronic disengagement is not necessarily equivalent to chronic apathy. Rather, students for whom the short-term cost of failure looms large are shown to be at heightened risk of disengagement. The model is used to understand and evaluate various elements of the mathematics anxiety literature including the role of formative assessment, the fixed and growth mindset models, the efficacy of task-oriented achievement goals, the cognitive interference and motivation enhancement models of test anxiety, the provision of remedial classes and technology-enhanced solutions to learning and assessment.