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
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
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.
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.
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.
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.
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
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
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