Many countries face mathematics and science teacher shortages. There is a need for greater knowledge about eligible individuals' potential interest to teach and career motivations. We explored career motivations and interest in a teaching career, among 470 tertiary mathematics and science students from four Australian universities. Students with high interest in teaching were distinguished from those with low interest, by high 'altruistic' motives, positive prior experiences, career progression prospects, family flexibility and working in a team. They also held more positive perceptions of the status, salary and expertise of teaching. Policy initiatives likely to attract them into teaching were identified, of which those most endorsed were jobs combining teaching with other work, increased permanency and salary, and paid study leave.