So far, my introduction to proofs class has met 5
times. We meet two times per week for
100 minutes, and I am continuing to use the flipped classroom model that I
started last semester. The big
difference is that this course is now a four-credit course and last semester it
was a three-credit course. So last
semester, we met two times per week for 75 minutes.

This is a great development but it has also created some
challenges. Our goal in increasing this
to a 4-credit course was not to add more content but to be able to spend more
time working with the students as they attempt to do proofs and to spend more
time on issues dealing with writing in mathematics. The basic model (times are approximate) for
the flipped classroom last semester was:

- A short period (about 5 minutes) for questions.
- A short quiz (10 minutes).
- Introduction to the problems for the day (5 minutes).
- Work on the problems in small groups (45 minutes).
- Summarize the day’s work and look ahead to the next class (10 minutes).

My basic approach for the 100-minute class has been to slightly
increase some of these times. In
particular, I thought the students could work on the problems for up to 60
minutes. After a few times of doing
this, I began to realize that this is just too long. As I walked around the room, I could tell the
discussions were “deteriorating” in that they were not really about the
problems or mathematics. So when I
walked into class on Wednesday, I decided to try something a bit different.

I usually give the students about 3 problems for the day,
have them work on them, and then collect one of the three problems to
grade. This is done to insure that they
will work seriously work on the problems and to make sure I do not have too
much to grade. What I decided to do was
to work on the problems one at a time and then discuss that problem as a class after
students have worked on it in groups for some time. I will have to make a judgment about when to
start the discussion. The idea is to
have the same amount of total time students work on problems but to have it
divided up into smaller chunks of time.
This will hopefully keep the student discussions from deteriorating
after a long time working on problems. I
will still have to decide which problem to collect and I am not yet sure how I
will do that. One option is to have one
of the problems be collected before the discussion for that problem. Another option is to let the teams decide
which problem they want to submit. We
will see what happens.

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