One hundred and ninety-four first-year sixth-form college pupils completed a questionnaire in which they were asked to rate 38 teacher characteristics according to the extent to which they perceived each of the characteristics to be associated with the effective teacher of mathematics at 'O' level. A specific criterion of teacher effectiveness was employed: pupil success at 'O' level. The characteristics with the highest mean ratings were 'explains points clearly and at pupils' level', 'is confident and at ease when teaching' and 'pays attention to revision and examination technique'. A principal components analysis of the ratings identified five factors which were labelled: 'positive rapport ', 'monitoring progress', 'aloof discipline', 'exam oriented' and 'enthusiast'. The similarities and differences of the findings here with those reported in earlier studies using the same questionnaire with heads of mathematics departments in secondary schools and PGCE students are discussed, and the relationship between these findings and research elsewhere is explored.