The Mathematical Association of America (MAA) maintains a list of several study away programs specifically devoted to mathematics.
The most famous study away program for mathematics, Budapest Semesters in Mathematics, is not affiliated with APU, but has been attended by multiple members of our department and is highly recommended. Hungary boasts a tradition that combines excellence in research with dedication to teaching and nurturing mathematical talent.
Students interested in teaching middle or high school math are encouraged to consider the Budapest Semesters in Mathematics Education program. Participants immerse themselves in mathematical exploration to experience firsthand learning in the Hungarian approach, then investigate how to bring this pedagogy into their own future classrooms. They observe Hungarian mathematics classrooms and have the opportunity to plan and teach their own lessons to Hungarian students (in English).