School mathematics leaders have an important role supporting teachers to improve student-learning outcomes, yet little is known about their professional goals or the challenges they face. The study reported in this paper examined school mathematics leaders' views by analysing the qualitative responses of 193 primary and secondary leaders to two online questionnaire items. Participants described the goals they held and challenges they perceived when improving mathematics teaching and learning in their schools. Data were coded to categorise responses and examine patterns in the findings. Leaders had clearly defined goals focused on improving teaching and learning, which described their visions, their aspirations for teacher collaboration, and practical actions they intended to implement. Leaders recognised the importance of teachers' knowledge, teachers' mathematical dispositions, and teachers' preparedness to change, in the achievement of their goals. Other goals concerned conditions in schools including the need to: prioritise mathematics improvement; provide time for mathematics leadership; and manage school structures to support teachers' collaborative learning.