Tuesday, July 11, 2006

A is for Artificial

The extra credit hoax

I hate messages like this:
Dear Dr. Z,

I am wondering if there are any extra credit or make up exam I can do to improve my grade to an A? This is very important to me to get an A at this class, please let me know.

Thank you.
Would you consider coming to class on time? Or coming to my office hour for assistance? You were half an hour late to the last two class sessions and you have never sought help during the hour I'm in my office right after class.

Actually, I didn't say that to her. I tried to be more subtle:
Thanks for your message. There is very little extra credit in a calculus class like ours. (I give a few extra points to students who put solutions up on the board.) A good grade depends mostly on doing well on exams. You should focus on being prepared for those. It would also be a good idea to earn all the points possible on quizzes, even though they're not worth as much as exams, so attending class regularly and on time (so you don't miss the ones at the beginning of the period) is also a priority.

The main reason I don't give much extra credit or make-up work is because an A should reflect mastery of the subject, not the amount of extra work one does.

Be ready for tomorrow's exam and do the best you can. You are doing rather well in the class and can be confident of at least a B for the course. An A is more difficult, but within reach if you earn excellent scores on the remaining two chapter tests and the final.

As you may have noted from my response, the “I need an A” message arrived the day before an exam. That's never a good sign. It smacks of grasping for straws after a frustrating study session.

I tried to be reasonably encouraging. The student has been earning a middling B in the course, but after looking over the most recent exam I can see why her concerns are mounting. She may be one of those “one-shot” students—those who cram facts and examples into their heads just before a test and lose it all the moment they walk out the door afterward. That is, of course, the kiss of death in a math course, or any other course where cumulative knowledge is at a premium. Today's exam was about optimization techniques, but it requires everything the students learned in preparation for the exam on differentiation methods. While she passed the differentiation exam (squeaking out a B with a score of 80%), since then she's gotten a little unclear on the power and product rules. This is not good. Her B is weakening and can't withstand a continued slide in her performance.

You'll note that I also gently prodded my student about coming to school on time, since she has missed quizzes that were held at the start of class. The day after I sent her the gentle reminder, she strolled in thirty minutes late. Apparently she did not feel any need to attend the in-class review session that I conducted just before administering the exam. The preliminary indications suggest her need was greater than she realized.

Learned behavior

A colleague and I discussed the situation in which my student finds herself. My colleague suggested that the “extra credit” approach might have worked for her in the past, especially in classes other than math. If it's worked before, one can hardly blame her for trying again. I just regret that she's seized on it as a panacea for her predicament.

But what does “extra credit” signify? Bonus points might increase a student's grade, but they say nothing about whether a student actually learned anything. I suppose I could devise extra-credit projects that would entail solving actual mathematical problems, but that's what homework is for. If you're still unclear on the concept after doing the homework, then it's time to see the teacher (I should think). Or raise questions during the homework review session in class (which the student in question never does).

The clear impression I received from my student (and others like her in past years) is that “extra credit” is the magical solution that permits any diligent student to rack up the points necessary for a target grade—entirely independent of mastery or comprehension. Understanding stuff is challenging, but earning a grade via the extra-credit route merely requires a willingness to grind away at point-earning projects. Frankly, I think grades earned that way are bogus grades. They may look great on a transcript, but they mislead you about the student's accomplishments. They mislead the student, too. Witness the example of my student, who struggles with the product rule for derivatives yet thinks she could reasonably hope for an A in calculus.

I'm afraid one of her biggest lessons this summer session will not be mathematical.

Update: The exam results are in. My “needs an A” student managed a score of only 64%. Her course average drops from a lower-middle B to a high C. The trend line is not encouraging. The evidence now suggests she would have to work diligently to demonstrate that she is a good calculus student—let alone excellent.


Mamacita said...

This is the best article about extra credit that I've ever read. Thank you VERY much for sharing.

I agree with you 100%, but you have put it into words as no one else ever has.

Well done, indeed.

Anonymous said...

Going through college, I never asked for extra-credit. That was my mistake. What I learned too late is the credo "nothing ventured, nothing gained." While I was playing by the overt rules, many a student was succesfully needling the professor for extra-time or extra-credit. My grades suffered and, on the strength of my LSAT, I was lucky to make it into Duke Law.

The point is... maybe your student isn't lacking in ANYTHING... Maybe she's just got moxie. And if I could go back and choose between an A in calculus through hard-work or an extra dash of futile moxie... I'd say a pinch of moxie would have served me better in life.

Anonymous said...

Giving extra credit for solving nontrivial problems doesn't seem unjustified to me, so long as they are significantly more difficult than the norm. A student who can succesfully solve such exercises might be demonstrating genuine understanding and not just mindlessly accumulating points. Moreover I think students should have the opportunity to "make up for" a poor showing on mid-term exams and homework if they genuinely improve their understanding of the subject matter. To be honest, I don't even know of many good reasons for setting _mandatory_ exams before the end of a course.

Of course your students might well just be after easy points.

John said...

My son starts college next month, I just sent him a link to your post. Thanks for the insight.

Zeno said...

Of course your students might well just be after easy points.

Yeah, they're after easy points. I have yet to have a student ask me to challenge them with non-trivial problems so that they can prove to me they really understand the material. No, they just ask for "extra credit" because they "need more points."

I'm not looking to give anyone a bad grade, so I give my students lots of opportunities to practice the material. The homework and frequent quizzes are not heavily weighted in the grading, so they provide a low-impact environment in which to make mistakes and learn the ropes. The quizzes also telegraph very clearly (if they're paying attention) what I'm going to put on the exams, so the exams are a recapitulation of our classroom practice rather than any kind of surprise or ambush. (In classes with several exams, I also drop the lowest one before averaging.)

I do see a good reason for mandatory exams before the end of the course: They break the material up into manageable chunks and give me the opportunity to evaluate and monitor student progress during a long semester. One of my colleagues used to give his students the option of wagering the entire grade on the final exam, but for many students this was an irresistible "sucker bet". The best way to prepare for a final exam was to take the chapter exams seriously. Instead my colleague always had a few students who would just say, "I'm going to do really well on the final." While I agree that ultimate responsibility for learning lies with the student, I'm unwilling to set them up for a catastrophic one-point failure like an all-or-nothing final exam.

Dan Greene said...

My experience with extra credit is that, if the problem is a genuinely challenging problem, the only students who can or will do it are the students who don't need any extra credit.

Regardless, my students love extra credit. I think that it has been a learned behavior for many students over the years that extra credit is the ticket to passing. If I tell them there is a 100 point exam coming up, it makes less of an impression than if I offer a 5 point extra credit assignment. For these reasons, it is very rare that I offer extra credit - and it's usually only a few points for doing something well in class, or winning a team review game, or something like that.

How about this as a grading philosophy: students don't earn any points at all - they all get a 0. However, all assignments (homework, quizzes, tests) are worth extra credit, at exactly the same value they would have been given for regular credit. Can you imagine the pure student joy? Every single assignment is extra credit! Every student will be inspired to earn an A!

eProf2 said...

Professor Z:

Good for you for sticking to your guns and not giving an individual student extra credit because she asked for it. Maybe, she was begging a little, too.

It always bugged me when I was a student to discover that one or more of my classmates received extra credit or extra credit assignments that were not made available to the entire class. I worked 48 hours a week on rotating shifts while an undergraduate and, quite simply, I had to really manage my time to work, go to school, and raise a family. Those students who asked for and received extra credit usually didn't have the same kinds of time management issues working students struggled to meet.

So, when I started my community college teaching career I made a hard and fast rule: no extra credit unless the entire class knew about it up front and published in my syllabus. I did offer "Push Grade" assignments for the entire class worth one percent so that if a student was border line between and two grades they had an opportunity to earn the additional one percent. But, the whole class knew about it at the beginning of the course.

Nicely done post.

Zeno said...

Dan, I fear to think how many students would be delighted with your ploy.

eProf2, thanks for the real-life example. As noted in one of the anonymous comments, squeaky wheels get greased often enough that students with less "moxie" (as the commenter noted) get screwed by sticking to the given standards. I think it's a simple matter of student equity that any option or appropriate accommodation be uniformly available to all students. I'm not inclined to help students game the system.

A little night musing said...

I was intending to write pretty much what Dan Greene did, only not so well. So I'll just say: you tell 'em, brother!

I have at times given tough problems as extra credit in calculus courses, figuring that to do those problems they would have to show some mastery of the material. This also let me assign problems that were so challenging that if I had given them as regular homework problems, no matter with how many warnings about their challenging nature, the students would have whined about them. (I find that high-performing students have the expectation that they will always be able to do every problem set before them without any significant difficulty, leading me to believe that they are never challenged to do anything but routine problems in their courses prior to mine.) So calling the problems "extra credit" is the only way to sneak them onto the students' plates without it hurting their eventual evaluations. (Another way the excessive attention paid to poorly-written student evaluation instruments can warp teaching, BTW.)

We had a saying one place I taught that you can get students to do anything by calling it extra credit. I kept thinking I would ask them to prove Goldbach's conjecture. Hey, if you don't tell them it's an unsolved problem. . .

A little night musing said...

Oh, also, to second what eprof2 said and take it a little further: I think it is rather unethical to make a method of improving a grade available to some student(s) and not to others. I've had to explain this to students who asked for special considerations. (For example, they want the opportunity to retake a test [!] but not that the whole class should be given that opportunity. "Is there something extra I can do to pull up my grade" usually falls under this heading as well, as upon questioning the student turns out in fact to be asking, inevitably, for something that is not part of the stated grading procedure.)

I don't think the students are really thinking the issue through when they ask for "extra credit." As several have said, it's probably a strategy that has worked for them at least once in the past so they reckon there is no harm in asking. They are not thinking of the consequences or the ramifications or the extra time the teacher might have to take or the potential unfairness, or much of anything except their felt need to get a good grade at any cost (apart from that of actually mastering the material).

To pick up another thread:

Students are often under incredble pressure to get grades which may be unrealistic for them given their current state of preparedness and organization and maturity. Some of this pressure may be self-generated, but a lot comes from outside. I had a student break down into tears on two separate occasions in my office begging for extra credit opportunities, because she "needed" to get a B in the course for her program, and her level of understanding was such that even a C would have been a stretch for her. Perhaps in another term she could have brought herself up to the B level or higher, but her program would not allow her that luxury. In her eyes, getting less than a B was the end of the world, and in a certain real sense she was right.

It's easy to say that she didn't belong in that program, but having got to know her I wouldn't say that. Very frustrating, and I don't have any good idea what to do in those situations.

disturbingtheuniverse said...

My standard response to extra credit requests is along these lines: "I think your top priority should be trying to learn the class material, rather than spending your time on extra stuff." Sometimes I also use the unfairness-to-the rest-of-the-class argument. One student's response to that: "That's okay; I promise I won't tell."

Along not-too-different lines: how about students requesting/expecting a "practice exam" as a means of getting a better grade? Said exam shoud of course consist of the same number and type of problems as the actual exam, so that they can memorize the steps required and then reproduce them. I never fall for these either. I just tell them to do the homework problems, and ask me for more if they run out.

Inside the Philosophy Factory said...

I'm no reconsidering the extra credit I allow -- although it is open to everyone and is really extra --- i.e. not what they should have learned in class.... I think it gives the wrong impression, namely that moxie can replace actually learning the material.

Thanks for giving me something to think about once again..

A little night musing said...

disturbingtheuniverse - on the "practice exam" question (I am right with you BTW), I recall that I read somewhere and I am now racking my brain to remember where it was, that "practice tests" improved the students' evaluation of the course EVEN THOUGH they did not improve the students' performance on the tests themselves. In other words (and again, this is me recalling and I may be recalling incorrectly) it seemed that these researchers found that students felt "helped" by the practice tests even though there was no objective evidence of improvement. (I'd be really glad if someone knows where to find this thing I'm vaguely remembering.)

Is it possible that those who fail to give out "practice tests" are evaluated less positively, even though it may be the case that what they are doing is more effective in terms of education?

JBL said...

Nightmusing, the study you are referencing you almost certainly heard of from this very blog:



A little night musing said...

Thanks, JBL, that might be it although I have a vague memory of having read a bit more detail (but I could be hallucinating that!)

Troublesome Frog said...

My calculus professor had an interesting algorithm for weighting exams that seemed relatively fair. The final exam was worth 50% of your grade if it was higher than your semester average and 25% of your grade otherwise. The reasoning was twofold: First, a student that had consistently shown mastery of the subject should not be penalized too heavily for a particularly bad 3 hour period during a stressful week. Second, a student who struggled all semester and was able to master the subject in time for the final exam should have a reasonable chance at passing the course. It was a generous policy, and it complemented his policies of being completely uncompromising on scoring, never offering extra credit, and never deviating from a very strict set of minimum standards to earn points.

He was a remarkable instructor, but like many math professors, he earned a reputation for being hard nosed because he didn't manipulate scores in secret back room deals. It always seemed to me that he did an excellent job of making his expectations clear and giving students every opportunity to meet them.