The purpose of this section is to give a brief overview of how the course runs from day to day. This section can be seen as trying to give a context to the snapshots, for those who would like to see how they fit into a larger scheme of things.
Roughly speaking, I view the content of the course as answering the question: Why do we have all these numbers anyway? Layered on top of this content, are several basic themes:
What we do in individual class days varies depending on what is being covered. Roughly 70% of the class days are spent in lecture, 5% of them are spent in whole class discussions, and the remaining 25% involve having the students doing small group work on assignments. Almost no class time is directly devoted to the student projects. Rather, they are expected to meet with me during my office hours throughout the term. In many respects,the different things that go on in my classroom correspond to dance instruction (see Magdalene Lampert's article): sometimes I show the students the dance steps, sometimes they practice with each other, and sometimes they get to dance with the expert. Each piece of this puzzle fits together to (I hope) teach the students how to dance mathematically.
The grading in the class is reflected in the syllabus. Students turn in roughly 10 homework sets during the term, have a midterm and a final, and they write up their project paper.
Below I have given details about some sample class days.