There are many recent studies which have explored the notion of high quality or effective mathematics teaching but relatively few have sought the views of students. Student perspectives regarding effective teaching are important for many reasons, and are arguably particularly significant in mathematics given the international trends of declining engagement and participation in this curriculum area. Studies that have asked students to identify reasons for their disengagement from mathematics have found a lack of confidence with mathematics, a lack of understanding of mathematics, a lack of enjoyment of mathematics, and/or dissatisfaction with mathematics teaching to be major factors. Research that has directly considered students' perspectives about effective mathematics teaching has yielded valuable insights. This study explores the concept of a "good" mathematics teacher from an important perspective: that of the learner. A total of 90 students from Years 10 and 11 participated in the study. They were from two comprehensive public secondary schools in regional towns in New South Wales. Participants indicated the centrality of teachers to their learning of mathematics. Further, they appeared to place responsibility with teachers to a large extent: they considered that good teachers should have the skills to explain concepts well and ensure that students understand them, and to provide expert individualised help. However, most participants did not expect to be passive recipients of teacher expertise. They expressed the view that good mathematics teachers create classroom environments wherein students feel comfortable to actively seek help and enhance their own learning. Further research exploring how students see teachers and their own roles and responsibilities in the learning process in mathematics would be of value. (Contains 2 tables.)