  Robust preparation of future secondary mathematics teachers requires
attention to the acquisition of mathematical knowledge for teaching. Many
future teachers learn mathematics content primarily through mathematics major
courses that are taught by mathematicians who do not specialize in teacher
preparation. How can mathematics education researchers assist mathematicians in
making explicit connections between the content of undergraduate mathematics
courses and the content of secondary mathematics? We present an articulation of
five types of connections that can be used in secondary mathematics teacher
preparation and give examples of question prompts that mathematicians can use
as applications of teaching secondary mathematics in undergraduate mathematics
courses.
