MA110-Mathematical Explorations-Spring 1998
Format and Grading of Solutions
In class we briefly discussed my expectations in regard to written solution sets and solution set quizzes. This document explains in finer detail the format I would like all of 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. All of your work on these problems must be recorded in your notebook. These answers will serve as rough drafts for final solutions. Final drafts of these solutions will be submitted either as part of a solution set for an entire lesson or as specific answers on quizzes. You should be sure to include in your notebooks sufficient detail and justification that you can formulate appropriate final solutions when it is necessary.
The Solutions
Each of your final 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 provide reasoning that justifies the solutions that you present, and your solutions must demonstrate that you have a sufficient understanding 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 all words should be spelled correctly. Your solutions should be neat, clearly written and well organized. 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.
From Chapter 1, Lesson 1, Set 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.
From Chapter 1, Lesson 2, Set I:
#4. Our answers to questions 1-3 of this section 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.
From Chapter 1, Lesson 3, Set I:
#1. If the given pattern is continued, inductively one concludes that the next equation would be 1+3+5+7+9 = 5x5.
From Chapter 1, Lesson 3, Set I:
#2. The equation 1+3+5+7+9 = 5x5, given in the previous problem, is a valid equation because 1+3+5+7+9=25 and 5x5=25 as well.
From Chapter 1, Lesson 1, Set II:
#3. The number of segments in each of 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
For each lesson we cover I will choose several problems to grade -- generally 3 to 5 from each set from each lesson. I will give detailed feedback in all areas. This feedback is meant to be constructive, and should be taken that way. Your work on these problems represents the majority of your efforts in this class. This is a great deal of work on your part, and grading them will be a great deal of work for me. In either case, these efforts are designed 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 complete, legitimate mathematical solutions to the problems at hand? |
| Depth of Understanding |
Do your solutions demonstrate an understanding of both the problems at hand and your proposed solutions? Are there important issues that you have neglected to consider? |
| Completeness |
Are your solutions mathematically complete, fully answering the questions as they were intended? |
| Coherence and Clarity |
Are your solutions coherent and readable? Have your answers clearly expressed the mathematical intent of your solutions 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 the problems and presenting the solutions as described here. |
In each of these categories you will be awarded between 0 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; 0 - essentially no work completed in this area. Missing solutions will count negatively against your scores in all of these areas.
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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