Points of connection to secondary teaching in undergraduate mathematics courses

Prospective secondary mathematics teachers frequently take as many (or more) mathematics courses from a mathematics department as they do methods courses from an education department. Sadly, however, prospective secondary teachers frequently view their mathematical experiences in such courses as unrelated to their future teaching (e.g., Zazkis & Leikin, 2010). Yet there is some optimism that having instructors alter their instructional approaches in such mathematics courses can enhance such experiences to be a positive part of their preparation for teaching. This theoretical report elaborates on four points of connection to secondary teaching that can be made in undergraduate mathematics courses, illustrated via examples from abstract algebra, and organized along a spectrum of intended implications on secondary teaching. The purpose is to provide a theoretical bridging between instructional approaches in undergraduate mathematics and aspects of secondary teaching practice.