Teacher education is of vital importance for what teachers are capable to do for their pupils, but little is known about student teachers' pedagogical knowledge. The "Didaktik" and the curriculum traditions are two main education approaches underpinning formal schooling and teacher education programmes (TEPs) in the Western world. The main difference between the two traditions lies in the content and objectives of teacher education, which are either theoretical or action-oriented. Two questions are addressed quantitatively: How do teacher education programmes and their outcomes vary across "Didaktik" and curriculum traditions? How do opportunities to learn and beliefs about teaching methods affect mathematical content knowledge (MCK) and mathematical pedagogical content knowledge (MPCK) scores? Empirical data from the Teacher Education and Development Study in Mathematics (TEDS-M) are used, with samples from Norway, Germany, Switzerland, and the US. The study offers alternative explanations for variations of TEPs' outcomes within the Western world.