During the past decade three different bridging mathematics courses have been offered at the University of Auckland. A case study approach was used to investigate the effectiveness of these courses: two larger courses and one individual study programme. A different teaching approach, by committed experienced teachers, was used in each course. The focus of this research is on affective change in the students, relating this to their achievement. This paper discusses some of the main findings of this large study. Important themes which emerged from the data analysis were the importance of teachers' acknowledgement of students' past experiences and current feelings about mathematics, dealing effectively with students' differing background knowledge of mathematics, as well as the effective use of contexts in non-routine problems. Interviews showed the variation of student reactions in the less successful demographic groups. The two approaches, which presented mathematics in a new way, had the effect of changing students' views of the nature of mathematics. (Contains 2 tables.)