Grading Policy

Grading Scale

I use a four-point scale for grading all regular (non-bonus) problems in my courses, including homework, quiz and test problems. My grading scale is achievement-based and additive like a video game score as opposed to subtractive like many grading systems. In my system, you don't start with an assumed perfect score and take off points for mistakes; rather, you start with zero and earn points for various correct aspects of your solution. Here's how it works:

0 points -- This is the base score. To earn more than zero points, a solution must meet one or more of the below criteria.

1 point -- To earn one or more points, a presented solution must demonstrate an accurate understanding of what the question is asking and include some progress toward a solution.

2 points -- To earn two or more points, a presented solution must be complete (i.e., the question or questions asked must all be answered) and must demonstrate understanding of all concepts involved in the problem. Incomplete solutions and solutions demonstrating conceptual misunderstandings cannot earn more than one point.

3 points -- To earn three or more points, a presented solution must be complete, demonstrate correct understanding of all concepts involved, and have correct reasoning and logic. Solutions demonstrating incorrect reasoning cannot earn more than two points.

4 points -- To earn four or more points, a presented solution must be complete, demonstrate correct understanding of all concepts and employ correct logic and reasoning, and must have correct computation. Solutions with incorrect computations, including sign errors, cannot earn more than three points.

5 points -- It's possible to recieve a fifth point, provided that the presented solution is exceptionally clear and well-written in addition to being technically correct regarding concepts, reasoning and computation. The difference between a four-point solution and a five-point solution: someone who already knows how to do the problem can follow a four-point solution, but reading a five-point solution is enough to teach the solution to a fellow student who didn't already know how to do the problem.

The final letter grades will then be determined numerically using the scale in the syllabus. The numbers roughly correspond to letter grades, with 0=F, 1=D, 2=C, 3=B, 4=A and 5 points representing a "super-A". CMC awards final grades on a 12-point scale, with the possible grades being F, D-, D, D+, C-, C, C+, B-, B, B+, A-, and A (note that there is no A+ at CMC, so the ordinary A is the highest possible and thus hardest to achieve grade). To compute your current grade, divide your total number of points earned by the number of points you'd have if you scored 4 points on every problem, then multiply that number by the "A" cutoff as listed on your syllabus. Alternatively, you can email me for your current grade at any time.

This grading system is designed to be simple, straightforward, and to ensure that students who learn the concepts of the course receive passing grades while those who do not, do not. Moreover, minimally passing the class only requires getting the concepts of the course right on average, while getting an A requires a much higher standard of consistent excellence. Note that this scale is not a percentage-based scale; getting a score of 1/4 does not mean the offered solution was 25% correct.

Bonus problems on exams are 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.

"Curving"

Part of my job as a professor is to evaluate honestly, to the best of my abilities, how much of the course material my students have learned, and to report this in the form of grades. I want all of my students to be successful at learning the course material; however, a teacher can only lead students to knowledge, not force them to learn. Learning mathematics, or any subject, is ultimately something that is done by the learner, not the instructor. Students are not computers to be programmed!

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.

Typo Bounty

During tests, the first student (and only the first, since I will then put up the correction on the board) to bring any typo or misprint on the test to my attention will get bonus points. Thus, it pays to read the test problems very carefully. This rule applies even to minor typos such as spelling or punctuation errors, though of course the goal is to catch any more serious typos which alter the mathematics of the problem. Note that grammatical quibbles do not count as typos, nor do deviations from some standard (MLA, APA, etc.) style guide -- we mathematicians have our own style, thank you very much. Also, the typo bounty policy only applies to tests and the final, not to practice tests, syllabi or other course materials. Aside from the bonus problems, the typo bounty is the only extra credit available in my courses.

Make-up

Homework assignments have a due date listed in bold at the top of the page. Once I have collected a given assignment, I will post the solutions to your class' page. Once the solutions have been posted, obviously, I cannot accept late homeworks.

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.

Attendance

Though students are encouraged to attend every lecture, I do not keep track of attendance. Because I do not require attendance in class, when you show up for a lecture I expect you to pay attention to the lecture and to be respectful both to me and to your fellow students. This is not high school; those who would rather talk or sleep than pay attention are encouraged to do it somewhere else, rather than distracting their classmates who are trying to get the education they're paying for. You are not directly penalized for missing lectures, though of course you pay indirectly by missing the content of the lectures (but hey, it's your tuition money), so there is no reason to show up to the lectures if you are not going to pay attention and be a serious student.

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.

Academic Dishonesty

Cheating in any form will not be tolerated. If I catch a student in the act of cheating on a test or quiz or if I suspect that a particular test, quiz or homework problem is the result of cheating, (including copying from another student, using unauthorized notes on a test, etc.), the student will receive a zero on the homework, test or quiz in question. Repeated incidents may lead to further disciplinary action consistent with Claremont McKenna College policy.

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.

Copyright © 2003-2012 Sam Nelson