Around the time of the last picture, the students worked through two homework sets on the algebraic numbers. I have chosen these sets in part because they show a different student from what we saw at the beginning of the course, although not a perfect student by any means. Also, at the end of the second set was a problem in which the students were to read through the NCTM Standards (NCTM 2000) and comment on various aspects of the number thread.
This last question shows the value of collaborations between mathematics education faculty and mathematics faculty, as the last question (and indeed, much of the set) was written by my colleague David Meel. David developed this second homework in part to get the students to see that a deep understanding of the real numbers was required to teach high school in the way the standards recommend, and so that the students could see that even higher level mathematics topics that they did not consider important for high school came up as part of the standards. In fact to see that the standards actually recommends studying some of these topics in high school today.