This article is based on research conducted as part of a broader study, the Teacher Education and Development Study in Mathematics (TEDS-M), which was sponsored by the International Association for the Evaluation of Educational Achievement (IEA).  TEDS-M compared the ways in which 17 countries prepared teachers of mathematics and the knowledge their future teachers had of mathematics and mathematics pedagogy near graduation.  The study included teachers being prepared for teaching at the primary and lower secondary levels.  TEDS-M also gathered data about policies and practices at the national level to assure the quality of graduates from the teacher education system, the focus of this article.  A consistent association was found between the strength of a country’s quality assurance arrangements and graduates' knowledge of mathematics and mathematics pedagogy.  Countries with strong quality assurance policies and practices were also found to be amongst the strongest performers on international tests of mathematics achievement.