Two sort of important questions:

My colleague suggested that this course sounded like " A Conversation with Smyth". I like that idea - but maybe as a conversation among all of us. To start it off think about this:
We are math teachers. Consider these questions:

What is mathematics?
What does it mean to know mathematics?

Please respond to this post with a tentative answer to these questions - not as a mathematician, but as a math teacher. We will revisit these responses at the end of the course.