This study used the Teacher Education and Development Study in Mathematics (TEDS-M) to examine the differences in opportunities to learn to teach elementary school mathematics and the learning outcomes of final year pre-service elementary teachers in seventeen countries. The study also examined the influence of the pedagogical approaches used in the preparation of final year elementary pre-service teachers' knowledge for teaching and beliefs about learning mathematics in three countries: Poland, Russia, and the United States using a multi-level modeling approach. The study found that there were significant differences in pre-service teachers' knowledge for teaching, beliefs about learning mathematics and opportunities to learn to teach mathematics.Most of the pre-service teachers from the participating European countries and Chinese Taipei experienced lecture presentations often, while most of the pre-service teachers from the American geographical region and Singapore experienced group work often during their mathematics methods courses. The analysis of teaching and learning mathematics through video analysis, readings and live classrooms was not a common practice across most of the participating countries. Nonetheless, pre-service teachers in Botswana, Russia, Thailand, and the United States experienced this pedagogical practice occasionally. The opportunities to learn how to plan mathematics instruction for conceptual understanding that include the analysis of learning goals, introductions to standards-based curriculum, and learning meaningful learning experiences were often experienced by the pre-service teachers in the Philippines, Singapore, Russia, and the United States. The opportunities to learn mathematics instruction for conceptual understanding were mostly experienced by countries in the American region and those countries whose elementary teachers are prepared as mathematics specialists (e.g. Thailand and Malaysia).The opportunities to learn to teach mathematics that made a difference in the pre-service teachers knowledge and beliefs in the three selected countries showed similarities in the three countries. Notably, experiencing models of reform-oriented instruction had a positive within-institution influence on pre-service teachers inquiry beliefs about learning mathematics. Additionally, opportunities to learn how to plan mathematics instruction for conceptual understanding that include analysis of learning goals and introductions to standards-based curriculum had a positive within-institution influence on pre-service teachers' inquiry beliefs about learning mathematics. The opportunities to learn mathematic instruction for conceptual understanding that include learning to show why mathematics procedures work had a positive within-institution influence on pre-service teachers' inquiry beliefs about learning mathematics in the generalist programs in the three countries. Some differences were found across the three countries. In the East Asian countries, opportunities to ask questions and engage in whole group discussion during their mathematics-related courses had a positive within-institution influence on pre-service teachers' pedagogical content knowledge. Also, opportunities to learn to teach mathematics by teaching using methods demonstrated by instructors had a positive within-institution influence on PSTs inquiry beliefs. Lecture presentations had a negative within and between-institution influence on PSTs' knowledge for teaching mathematics in the United States.These findings suggest the need for pre-service teachers to take more active roles in their learning to teach mathematics during their teacher preparation
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