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:
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.
a.
Summary: Include brief summary of the problem, highlighting the parts that
you felt were most interesting or surprising. Compare your
"gutfeeling", 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.
Grading:
All projects will be graded using the
following rubric:

Limited Proficiency 
Some Proficiency
(.25.5) 
Proficient
(.5.75) 
Highly Proficient
(.751) 
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 