MA110-Mathematical Explorations-Spring 1997
Format and Grading of Problem Sets
In class we briefly discussed the nature of the final drafts of your solutions to the problem sets. This document explains in finer detail the format I would like your solutions to take as well as how these solutions will be graded. In particular, examples of appropriate solutions, grading categories and a grading checklist are given below.
Format
As stated in the course syllabus, class time will be devoted to group work on the assigned problems. In your groups you should develop solutions to each of the problems. Outside of class, on your own, you should write up final solutions to each of the problems. The final solutions you submit must be your own, and must be written in your own words. Solutions that I believe have been copied from others will result in failing grades for all parties involved, and will be considered violation of the college policy on academic honesty.
Context for the Solutions
If you find it helpful to have a context for your solutions, you can consider the following. At your job, a department outside of your own has submitted a formal, written collection of questions regarding a product that your department has developed. You must provide formal, written answers to these questions. These answers cannot be amended at a later time, this is to be a final report. Your report will be read and utilized by a variety of people in the corporation. It will be read by specialists interested in the details of the answers. Hence, answers need to be mathematically correct, stated precisely and unambiguously, and your reasoning for giving these answers must be carefully explained. Your report will be reviewed by your supervisor. Although he does not have time to carefully review every detail of the report, he will check to see that you have conveyed complete and coherent solutions, ones demonstrating that your department has a complete understanding of the nature of the issues at hand as well as solutions to these problems. Finally the department head will evaluate your report as evidence for future advancement and promotion questions. The department head is not a specialist in your area of work and has not read the other report. Hence, when she looks at your report she will evaluate it on issues such as organization, effort, completeness, and so on. In particular, because she has not read the other report, answers in your report should be readable without reference to the initial question.
The Solutions
Each of your solutions must be made up of complete sentences (unless the solution is simply a diagram). The solutions must be readable outside of the context of the original questions. They must precisely and completely present a correct mathematical solution to the problem at hand. You must justify your reasoning for the solutions that you present, and your solutions must demonstrate that you have a sufficient understand of both the problems at hand and the solutions you have proposed. Each of your solutions must be clear, coherent, and well organized. They should be grammatically correct and spelling should be correct. Lastly, your solutions should demonstrate that you have made a sufficient effort to understand and answer the questions at hand.
Examples
Here are some examples to indicate appropriate solutions.
Ch. 1, L. 1, S. I, #9,10. The ball will have the simplest path on table number 4, because on this table the ball travels directly from its initial position into the opposite corner pocket. This should happen on any square table.
Ch. 1, L. 2, S. I, #4. Our answers in questions 1-3 seem to support the claim that the ball will always end up in the upper-right corner on a table whose length is odd and width is 1.
Ch. 1, L. 3, S. I, #1. If the given pattern is continued, inductively one concludes that the next equation would be 1+3+5+7+9=5x5.
Ch. 1, L. 3, S. I, #2. The equation 1+3+5+7+9=5x5, given in the previous problem, is a true equation because 1+3+5+7+9=25 and 5x5=25 as well.
Ch. 1, L. 1, S. II, #3. The number of segments in the paths given in the table in problem 2 can be found by dividing the length of the table by the width of the table
Grading
At the end of each chapter you will hand in solutions to all of the lessons in that chapter that we have covered. I will choose between 5 and 15 problems from each lesson to grade. I will give detailed feedback in all areas. This feedback is meant to be constructive, and should be taken that way. You will spend a long time constructing and writing these solutions and I will spend a long time grading them; these efforts are designed, in both cases, to help you learn from this experience.
Areas Graded
For each lesson you will be graded in each of five areas. These areas are:
| Mathematical Correctness |
Have you presented a complete, legitimate mathematical solution to the problem at hand? |
| Depth of Understanding |
Does your solution demonstrate an understanding of both the problem at hand and your proposed solution? Are there important issues that you have neglected to consider? |
| Completeness |
Is your solution mathematically complete; fully answering the question as it was intended?
Have you completely answered all of the questions in this lesson? |
| Coherence and Clarity |
Is your solution coherent and readable? Has your answer clearly expressed the mathematical intent of your solution to the problem? Is the identity of objects you refer to clear? |
| Neatness, Organization, Grammar, Spelling, and Effort |
The presentation and mechanics of your solutions are important. It is also crucial that your solutions indicate that you have expended sufficient effort in solving and presenting the problems as described here. |
In each of these categories you will be awarded between 1 and 5 points on the following scale: 5-outstanding in every aspect of this category; 4-very good, but there is room for improvement in this category; 3-adequate, you have satisfied the requirements, but with substantial problems in this category; 2-marginal, you have serious problems that have adversely effected your solutions in this category; 1-unacceptable.
Notice, that within this grading scheme, approximately 60% of your grade is determined by purely mathematical issues. The other 40% is determined by issues related to your presentation of your mathematical solutions. If you do not make a contentious effort to express your solutions in the format described above, you can receive a failing grade even if your solutions are "correct" in a mathematical sense.
A Solution Checklist
As you are writing up solutions, the following checklist, which lists many of the common problem areas, might be useful.
1. Is my solution mathematically correct and does it completely answer the question asked?
2. Does my solution demonstrate a clear understanding of both the problem at hand and the solution being presented?
3. Have I given adequate justification in support of my solution to the problem?
4. Is my solution precise, coherent, well organized, and intelligible to somebody that has not read the problem at hand?
5. Are all quantities clearly identified; in particular, is the identity of all pronouns unambiguous?
6. Is my solution written in complete sentences that are grammatically correct?
J_FLERON@FOMA.WSC.MASS.EDU
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