A Bit More on Mathematics in Decision Making

[Originally Posted 12-19-2011]

I mentioned before that a typical class meeting in my IBL liberal arts math class will have 35 minutes of “stuff” and 15 minutes of presentation and discussion. What will fill the 35 minutes?

At least at the beginning, the students will be working through a set of carefully chosen problems that aim at the distinction between countable and uncountable sets. The trick is to have the following things occur simultaneously in each days’ problem set:

  • There are more problems than can be done in a single meeting.
  • There are not so many problems that a hard-working student cannot complete the rest of the problems before the next class meeting.
  • At least some problems are pretty easy and can be dispatched quickly to build confidence.
  • Some problems are more challenging and require more thought.
  • The problems are sequenced in such a way as to build confidence and understanding.
  • The problems are sequenced to avoid having the simpler ones all in class and the hard ones all for homework.

A big part of the challenge for me is that I have not taught this class (hence this audience) before. It is important to pitch the challenges at the proper level, and I won’t really know what that is the first week. This means that I have to have a really good plan A, and good versions of plan B and plan C ready to go when I find out that I missed my mark.

I envision the material on comparing large sets will take three or four weeks of class, and I am going to try for a list of seven or eight problems for each day. That means |\mathbb{N}| \neq |\mathbb{R}| should be broken into 11\times 7 \approx 80 very small pieces.

I’ll post my working version of the problem sequence when I get it rolling.