The purpose of this study has been to compare teachers' differing methods of teaching mathematics and their perspectives on the learning process in a municipal school to a Waldorf school. The study has examined which approach best promotes student engagement and learning in mathematics in the first three years of schooling. The study is based on four interviews. The informants’ accounts are interpreted using theories from previous research. The study shows that the municipal schools and Waldorf schools use different methods in mathematics teaching. In the public school, the focus is mostly on the students achieving curriculum goals and passing the national tests in the third year of primary school. "Silent counting" and  individualized education” are methods that teachers in the municipal school make use of in mathematics teaching. In the Waldorf school students make their own textbooks, and through longer periods of teaching the teachers are aiming for deeper understanding of mathematics and its relations to the world around. The study favors the approach to teaching used in the Waldorf school in primary schools. It is assumed that students in a Waldorf school masters and have a deeper understanding of mathematics, than students in the municipal school where they work with pre-written math books.