Course Projects:

Students will hand in a detailed typed report for each project. In this course you should not confuse the written project with "showing your work".  Instead your written work should indicate to the reader how well you understand the mathematical concepts you have used in your solution.  A list of calculations without reasoning is not mathematics.  When writing each project your goal will be to communicate your solutions to another person rather than to show you've completed the assignment.

Students will be expected to write clearly and carefully.  There is no required length or word count.  Each project write up should be exactly as long as it needs to be to convey the required ideas.  Hence you will not feel pressure to omit required details or add padding to meet an arbitrary length requirement.

With this in mind each write up must include the following:

1. Introduction:  A brief description of the central problem. Do not simply recopy the problem.  Rather, describe the problem in enough detail that another student not in the class could understand the main problem and its importance.  Also give a brief description of how you plan on solving the problem.

2. Results: This section is comprised of 3 sub-sections:

a.       Exploration give a brief description of the explorations you performed and explain how they were used to arrive at your conjecture.  Include several specific examples that will help the reader understand both the problem and your solution.  You must describe how your examples helped you to generate a conjecture. If you used a computer program to generate examples attach a copy of the code and/or output.

b.      Conjecture: After your exploration, you will be ready to make a conjecture about the problem.  The conjecture for each part of your project should be clearly stated and labeled.

c.       Proof: Provide a complete and rigorous mathematical proof.  There should be no gaps in your explanation. Clearly define each mathematical term and variable in the problem.  Other than results from high school algebra, include the full statement of any theorem that was needed to solve the problem.  Results from high school algebra should be labeled HSA.

1. Conclusion:  This section has 2 sub-sections:

a.       Summary: Include brief summary of the problem, highlighting the parts that you felt were most interesting or surprising.  Compare your "gut-feeling", if you had one, to your actual solution explaining any differences.

b.      Further Work: Finally, state at least 3 new problems that are related to the original problem that you would like to investigate in the future.  These problems should be individually numbered and should be a clearly and carefully (with all the detail) stated in the same fashion as the original problem. The reader should not need to know the original problem to understand the new problems.

Limited Proficiency
(0-.25)

Some Proficiency        (.25-.5)

Proficient                 (.5-.75)

Highly Proficient          (.75-1)

### Inquiry

Included new problems but were either too few or in appropriate

Included too few problems that were clearly worded

Included 3 new problems but not completely clear

Included 3 clearly worded new problems

Exploration

Misunderstood question or did inappropriate exploration

Exploration was included but not clearly defined

Exploration was included but how it was used was not made clear

Exploration included and was clearly explained

Conjecture

Incorrect conjecture included.

Correct conjecture included but explanation was ambiguous

Correct conjecture included but not clearly stated

Correct conjecture included and clearly stated.

Proof

Incorrect reasoning provided

Reasoning provided with weak explanation or correlation to exploration.

Reasoning provided appropriately tied to exploration but not clearly or fully explained

Accurate proof included