This homework set naturally leads off of the previous set. It also sets up the students for seeing new and different proofs of irrationality of numbers, which they need to be ready for the proof that pi is irrational. It also helped the class in that we can discuss the use of non-constructive proofs early on with a context for the discussion. Since such proofs may well be part of what they need for the projects, this is important. Also, they got a chance to see a strange number that we came back to later in the course.
The other two problems also seemed to have done what I wanted them to do for the students. On the third page, however, I think I might do better to give them more structure with which to answer the last questions. Several students did not spend much time answering the questions. I found that the longer responses helped me to frame future issues in the classroom better and with more knowledge of where the students were coming from. For the most part, however, I would stick with this setup on the second homework set.
One important unexpected part of the second set was that the set helped to start the process of building cohesion among the project groups. I suspect that if I had been smarter about intervening in these groups, I might have done a better job with getting the ineffective project groups working in a good way.
Return to First Two Assignments