For the last couple of days, I’ve been blogging the grading of a calculus homework assignment that has yielded a lot of ~~headaches~~ interesting results. Readers will remember that calculus homework is worth 10 points. If a student fails to make significant progress on any part of any exercise — including leaving the question blank or putting down an answer without an attempt at justification — the entire assignment gets a 1 out of 10. If a student violates a formatting rule, the entire assignment gets a 1 out of 10. Here’s the breakdown:

*Number of students who got 1/10 due to formatting violations*: Section A — 1; Section B — 0.
*Number of students who got 1/10 due to putting down answers without justifying work**: Section A — 7; Section B — 5.
*Number of students who got 1/10 due to leaving part of an exercise blank***: Section A — 6; Section B — 5.
*Average of grades which were not 1/10*: Section A — 8.36; Section B — 8.58.

* This includes failing to explain the meaning of an answer if the problem says “State such-and-such quantity and explain its meaning.”

**This includes failing to turn the problem in on time (i.e. the rest of the assignment was turned on on time but that problem was late) and doing the wrong problem.

This amounts to between 1/3 and 1/2 of each class getting an automatic 1/10 because of “significant progress” violations. That may seem excessive, but I don’t think so. Those rules have been spelled out in multiple formats over multiple days in class and reiterated countless times. If a student still insists on writing down an answer without justifying where it came from, or refusing/neglecting to explain the meaning of an answer when asked to do so, then I want the message to get sent loud and clear that college-level work requires more than that.

I won’t be a popular guy when I hand these back tomorrow, though. (Good thing it’s not my job to be popular.)

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Unless you think people are cheating, i disagree with this:

“f a student still insists on writing down an answer without justifying where it came from….then I want the message to get sent loud and clear that college-level work requires more than that.”

It’s MATH. If you don’t do it right, you don’t get the right result. If you get the right result, you did it right. Collega (and professional leval) work privileges results.

As someone who used to be able to do pretty complex equations in my head, I’ll say what I said to my teachers then:

You have the moral right to make me do neat organized busy work showing you exactly how I reached all my results in only two instances:

1) You think I’m cheating; or

2) I’m not getting 100% of the homework right.

Other than that, why possible reason could there be?

Note that I’m not protesting this: “refusing/neglecting to explain the meaning of an answer when asked to do so” which is an entirely different thing.

“It’s MATH. If you don’t do it right, you don’t get the right result. If you get the right result, you did it right.”

In my classes, the process is what I grade, not the answer. I am assessing whether students have internalized and mastered the concepts of calculus — not whether they can produce a correct number or formula regardless of technique. And there are a lot of ways an answer can be right in calculus but the process be completely off the mark. For instance, cheating; for more instances:

(1) They got the correct formula for f'(x) but they used shortcut methods when the question asked them to use the definition of the derivative.

(2) Vice versa.

(3) They got the correct answer for f'(3) but they used graphical estimation when the question asked them to use algebra.

(4) Vice versa.

(5) Similarly, except there was a table of data involved.

(6) They were working an optimization problem that involves not only an answer but an entire process of setting up a diagram, deriving a formula, getting the answer through proper derivative techniques (see above), and then checking the answer using the First or Second Derivative Tests.

And so on. Math is way more than just getting answers. Students are usually working a problem to demonstrate their mastery of a particular process or concept; an answer by itself conveys no information about that.

I recognize this is quite a while after this entry’s publication, but the rule about 1/10 for failure to follow formatting rules or for skipping any part of an assignment seems very odd. Perhaps I misunderstand, but it seems that the message of the formatting rules is that presentation is more important than knowledge. Furthermore, do you really assign the same points for doing 9/10 of the assignment correctly and rigorously while skipping 1/10 as for simply scribbling down some made-up numbers? Of course you don’t want to give credit for un-justified answers, but it sounds like you also take away the credit for all the other parts of the assignment.

Lisa – It’s not so much that presentation is more important than knowledge (certainly I don’t believe that) but that college-level work has to meet certain minimal standards of quality before I can accept it. Those standards are pretty simple: students have to make a good-faith effort on each exercise (i.e. they can’t pick and choose), it must be legibly written up, and it has to be somewhat professionally put together.

People teaching composition do this all the time. If there are a number of spelling errors past a certain established number, or if the paper is not typed, etc. then the work is simply not graded. The reason is that college-level work is supposed to reflect the actions of a serious student who is attempting to learn something. Also, my hope is that a seriously costly penalty — losing all but one point regardless of what else happens — will act as a deterrent, making students less likely to make these mistakes (incl. not showing work) than just a point here and a point there.

For what it’s worth, here at semester’s end and after 12 exercise sets handed in, I think I only gave one 1/10 for violating these guidelines in the last 7 assignments after giving lots of them in the first 5. So I think students got the picture, and their work has been much better in terms of basic quality than I’ve seen in past classes.

Thanks for responding – what you’ve said makes a lot of sense. Honestly, I can see why this sort of rule would be necessary – there’s no way I would ever accept an assignment written in pastel gel-pen, for example. There are some basic rules of professionalism that can’t be ignored, and that do reflect the real world (if they write their resumes in crayon..). I was somewhat disconcerted to read it the first time, though, since it called up memories of a high school teacher I had who demanded not only coloring but

shadingon our geography assignments. Glad to be able to putthatimage to rest.