Final Comments
What Was Accomplished

In looking at the class as a whole, we first must ask what was accomplished: did students reach the desired outcomes, did the outcomes change for the class, and what unexpected outcomes (both good and bad) came about. We begin by looking at the original outcomes.

The positive outcomes that I added in the class were two regarding student use of technology for investigation, which the entire class did. Most project groups needed to use technology to get started, and the first homework set certainly added on to this. Finally, if one looks at the spirals project, one can explicitly see technology playing a major role. The other outcome dealt with understanding how math is done. Again, this became a central tenet of the projects, and Alan upon being asked what relationship he saw between the class and the projects, quickly responded:

They were both about how mathematics is done.

Other students didn't recognize this, but allowed that they did learn that from the class.

In addition to evaluating the outcomes that I was after, it is useful to look at other outcomes, some negative, some positive. One negative outcome, was that two students left feeling quite negative towards group work. Jill, felt this way previous to the class, but Mary did not. Other negative effects of the class, include leaving three students (Ron, Ellen, and Teri) apparently convinced that they could not really do mathematics. In all three cases, I saw capability at doing a research project, but in each of these cases, the stronger students in the groups left these students feeling slightly out of place.

On the other hand, there were other interesting positive outcomes. Ron stated near the end of the interview

That's it! That is what I finally learned from the class that I did differently, I learned to talk more. Cause after 496, I am in 425 right now, I don't have anyone except the professor, which is limited hours to talk with. With Neal I did that in 496 and I was really good, help me learn, I realized verbal discourse helps me retain more of the knowledge.

Brad's comment was:

That's what I meant, that made me feel good, like we could actually come up with something, be creative, with something like that and you know gonna be a teacher trained at getting the kids to see all these different ways you can do it, why things happen, why you do it this way, and stuff like that is really important, I got that from this course.

Namely, he saw the importance of teaching that allows for different ways of doing things. In some ways, this outcome while not specific to the goals of the course is the kind of thing I hope for a teacher to do when they are in the classroom.

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