5 points -- ``Perfect'', meaning complete and correct work which implies the correct answer, written correctly.

4 points -- The only mistakes present are notational. The student has a correct solution and correct logic but has written it incorrectly.

3 points -- The solution contains careless computational errors, arithmetic mistakes or small oversights which do not show misunderstanding of the course's techniques or concepts. This includes the case of a miscopied but otherwise correctly solved problem.

2 points -- The solution contains conceptual errors, but the core technique or concept being tested is displayed correctly. That is, to receive two points on a problem, a student's work must demonstrate that the student understands the main idea of the problem and its solution.

1 point -- Any solution where the student shows a misunderstanding of the techniques and concepts being tested. Even if the rest of the work is impeccable, if the student misses the point of the problem, then no more than one point is appropriate. Any solution where an answer is given without work when work is expected should receive no more than one point. If a correct beginning is present but the solution is incomplete, 1 point is also appropriate.

0 points -- Any solution left blank, or any solution which does not contain at least a correct beginning. Also, if a correct answer with no work mysteriously appears as if by technology-indistinguishable-from-magic, zero points may be appropriate, though certainly no more than 1 point may be given in this case.

The final letter grades will then be awarded numerically -- scores between 4 and 5 are As, scores between 3 and 4 are Bs, etc. This scale is designed to be fair and objective, and to ensure that students who learn the concepts of the course receive passing grades while those who do not, do not.

One caveat -- this scale is not a percentage-based scale; getting a score of 1/5 does not mean the offered solution was 20% correct. To find your letter grade on a given assignment or exam, just multiply the 5-point scale by the number of problems. For example, if an exam has 12 problems, then 12 points is the cutoff for a D, so 0-11 is an F, 12-23 is a D, 24-35 is a C, etc.

Bonus problems on exams will be graded on a 0-2 point scale, with 2 points for a completely correct solution, 1 point for a partly correct solution, and 0 points for a completely incorrect solution.

By "curved grades" I mean grades awarded on a relative scale, one that depends on the overall performance of the class. Rating performance on a relative scale makes sense in some areas of life, e.g. in sports, where "success" mean "doing better than the other team". Mathematics, however, is not a sport, and knowing more than the other students does not mean that you understand the subject. The content of a math course consists of a set of concepts and problem-solving techniques to be mastered, and grading a student's performance in a math course is about evaluating the degree to which the student has demonstrated her/his knowledge of and ability to use these concepts and techniques. To grade mathematics on a curve, therefore, is to inaccurately report how much of the course material a student has learned.

It is important to understand that a student's grade in a mathematics class is not a measure of the student's personal worth, nor is it a measure of how much the teacher likes the student, or how smart, talented, or otherwise good the student is. A student's grade in a particular math class is not even necessarily a measure of how hard the student tried to learn the material. Indeed, this misconception is part of the motivation for curving grades: a student might think "as long as I honestly try, I deserve a passing grade." The expression "A for effort" indicates a common belief that "level of effort" should contribute explicitly to one's final grade, not just in the obvious way that higher effort is likely to result in better performance, but that even effort that does not result in better performance is worthy of points toward a passing grade simply for being effort. Some students think there is some maximum percentage of the class that can receive a failing grade, e.g., "you can't fail us all!" Nevertheless, if the entire class fails to learn the material, it would still be dishonest to pretend that some students did learn the material.

Another rationale commonly given for curving grades is that the class average reflects the quality of teaching, and that curving adjusts the grades to account for possible poor teaching. However, this kind of thinking misses the point that regardless of the quality of teaching, to award a passing grade to a student who can't solve the problems and doesn't understand the concepts is to lie about whether the student has successfully learned the course material. This kind of reasoning would suggest that bad teaching plus dishonesty is somehow better than just bad teaching, though it should be clear that these two wrongs do not make a right.

Though many students might view curved grading as a favor from the teacher, it's not hard to see that it's nothing of the sort, as becomes obvious as soon as the student needs to use the course content. Should someone who can't pass a driving test be awarded a driver's license and allowed to drive anyway because the teacher was bad? Does an incompetent pilot deserve a license to fly just because his classmates or instructor were even more incompetent?

This kind of dishonesty is not just ethically questionable, it's dangerous. If I'm entrusting my health to a surgeon, for example, I don't care how well she did in comparison to the rest of her class, I wanna know that she really knows what she's doing! "But my classmates did even worse" is not a valid excuse for medical malpractice. If I'm driving over a bridge, it's not good enough that the designer "did his best" or "did better than the others in his class"; I want to know that the bridge is actually stable. College and University courses are intended to prepare you for the real world, and while high school-style "social promotion" may be considered excusable by some, it is certainly not acceptable in higher education, and I won't be a part of it.

In summary, I do not "curve" grades. My students earn the grades they get in my classes by demonstrating to me how much of the course material they've learned by providing answers with complete work on tests, homework, quizzes and the final exam. Passing my classes means proving that one understands the concepts and can solve problems successfully; failure to do so results in failure in the class.

A word of clarification: some students interpret "curving" to mean any scale other than the percentage-based 10-point scale; since my scale is not a ten-point percentage-based scale, then by that definition my grades are "curved". Nevertheless, my grading scale is not relative and does not depend on student performance.

If a student must miss a test or the final, it is that student's responsibility to get in contact with me as soon as possible. The dates of the exams and in particular the date and time of the final exam are announced on the first day of class and are recorded in the syllabus; it is a student's responsibility to be there on the day and time listed, and in particular, to see to it that travel plans do not conflict with the final exam.

In particular, talking during the lecture should be limited to whispers, and should be restricted to the course subject matter, e.g., telling someone which page we are on, interpreting my handwriting on the board, or asking questions (though if you're asking me a question, please do so in a regular voice). Extraneous conversation and other types of disruptive behavior are not permitted. If you arrive late, please come in and sit down quietly.

A word about collaboration: mathematics as a whole is a collaborative effort, and I'm just as happy for my students to learn mathematics from each other as from me or from the book. Thus, working together to solve problems and teach each other is great. However, students still need to write their own solutions in their own words, since I am trying to assess how well each student understands the material. In particular, if a student just copies someone else's solution, even if the copying student helped the other student figure it out, it still counts as cheating. The only exception will be if I explicitly assign group work, in which case each collaborator must write some portion of the finished assignment.