There were fourteen students in the class in the fall term of 2000 at Michigan State University. One other student attended the course for one week before dropping the course. Of the fourteen students, thirteen were intending to be secondary mathematics teachers. All took the course to fulfill the capstone requirement of the mathematics major at Michigan State University. The first homework assignment was for the students to write a mathematical biography and to give short answers to several questions. Students generally reported that we study mathematics to learn how to solve problems and because it was useful. However, few could give applications of any higher level algebra skills. Some reported having had relatively bad experiences in advanced mathematics courses. Most of these involved poor grades. At least two students reported needing a sufficiently high grade in the class to be allowed to continue on in their teacher education program. (The program at MSU requires at least a 2.5 gpa in the student's major.)
As part of a research study analyzing what the students considered interesting mathematics questions, students were asked what was the most interesting mathematics problem they had ever worked on, and what features make a mathematics problem interesting. The answers to this question showed that students, in general, believed that applications were what made problems interesting, although these applications could either be real-world, or could be to teach the students more about a concept that they had studied.
The names below (and throughout) are all pseudonyms.
Here I have gathered a spreadsheet of the previous courses each of these students had taken.