Using a Theory of Learning in College Mathematics Courses

Suppose you were teaching a mathematics course that included the topic of coset of a group. More specifically you might want your students to understand what a coset is to be able to find examples and non-examples to establish some properties such as the lemmas leading up to Lagrange’s theorem as well as the theorem itself together with its applications. You might even want your students to be able to construct examples of quotient groups and prove theorems relating properties of a quotient group to properties of the original group.