SCI 360, Spring 2006
Final Project
Projects will be chosen from those at the end of each chapter, in consultation
with the instructor. I prefer that you work with a partner on your project (since
more learning occurs when people communicate about mathematics than when a person
works alone), but you may choose to work alone if you wish. You and your partner
should choose a project by March 22. After your project has
been completed, you will write a paper and make a presentation in class. Both
of these should be joint efforts. And yes, I do know that collaborative writing
is difficult! It's a great professional skill, though: you'll likely write papers
for teaching journals and grant proposals with colleagues.
Paper
For your project, you will turn in a 5-7 page paper. The paper will include
the following sections:
- Introduction: Explain the problem in terms understandable by a peer. Why
is this problem interesting to you? Why is it important?
- Background: What did you know about this problem before you began trying
to solve it? What mathematical topics are involved in understanding the statement
of the problem? Give a brief history of the problem, if applicable. Introduce
any definitions or terms here, if necessary. Please refer to our course readings,
if possible.
- Methods: Describe the methods you used to solve the problem. What strategies
did you try that didn’t work, but that gave you some insight into the
problem?
- Results: Describe your solution to the problem, giving as much detail as
possible. This should be an expository paper, not merely a list of equations.
Emphasize why your solution makes sense.
- Discussion/Conclusions: How could you extend your solution, or adapt your
methods to solving other problems? What new concepts or strategies did you
learn or discover while solving this problem? What are the applications of
this problem, and how does your solution deepen your understanding of those
applications?
- Implications for teaching: What have you, as a future high school teacher,
learned from this problem that will be useful to you in the high school classroom?
Could you adapt this problem for use in your classroom? Explain. How has your
solution of this problem deepened your understanding of the related mathematical
concepts?
Class Presentation
You will have 15 minutes to present the results of your project in class on
May 3. This presentation should summarize and present your
paper in the form of a PowerPoint presentation. It should be interesting and
informative! Rather than spending a lot of time on the mechanics of how you
solved the problem, highlight what is important about the solution.