One of the major benefits of the face-to-face teaching environment is that social interaction opportunities are a natural part of the course: Learners meet in the same room for the same allotted period of time each week. This social opportunity is not organic to online courses; therefore, to have this social interaction as a part of online classes…

Responding to students' questions is a critical part of teaching mathematics. A particular response may either stifle a student's inquiry or, ideally, stimulate his or her interest in mathematics. Although formulating responses that have the potential to engage students in developing new mathematical insights is challenging, the authors believe…