Sunday, August 28, 2011

Pedagogical Problem

So, I have a relatively important decision to make before I finalize my syllabus for my Calculus I classes, and, since my friends contain a statistically significantly higher proportion of educators than the general population, I thought I would solicit some outside opinions. Accordingly, please feel free to weigh in with your thoughts in the comments, if you have some to contribute, as this is the purpose of this post. I may not follow advice received, but I always consider it.

My problem is thus: the course grade contains a portion allotted to weekly work. Homework and quizzes are the two main options. Last time I taught this course I opted for the default of quizzes, because it was the recommended option and it was the first time that I taught the course. However, despite my emphasizing the importance of working through the, non-graded, homework problems, I do not believe much of my class did, and I think their grades suffered consequentially. I could continue with this method, since their grade is, ultimately, their responsibility, however I am tired of feeling like I am failing my students, and would like to take a less scorched earth approach this year.

One option, and this is the one which I am currently favoring, is to inform them that the quiz problems will be selected from the suggested homework problems. This seems like it might provide added incentive for students to work the homework problems, as well as assist them in knowing how to study for the quizzes. On the other hand, however, it means that the quizzes will not be as representative of the exam, which is what I normally like to do with them, as on the exam I try to ask questions that emphasize what I think is important from the material.

What I had decided to do prior to thinking about it during the course organizational meeting was to simply have them submit the homework problems then grade an unannounced subset. If I am mainly trying to get them to do the homework, why introduce the middle man in the form of quizzes was my train of thought. Since there are so many homework problems, it would be incredibly time consuming for me to grade all of them, thus the unannounced subset bit. However, it occurred to me that this might still be hard for me to do efficiently if homework was messy. Thus I would have to impose some organizational requirements, which, although salutary for my students as budding mathematicians, would likely require a lot of effort on their part to implement for all the homework questions. In the end this seemed likely to result in more work for my students than simply allowing them to do the homework in whatever form makes sense to them then having them take additional quizzes.

Finally, I considered doing a hybrid of homework and quizzes. Homework most of the time, as detailed above, but four quizzes on weeks prior to exams. Ostensibly to provide a review, my actual reason for wanting these quizzes was the aforementioned goal of providing them with an example of how I write questions before they see them on the test, since I sometimes consider book problems too insipid to simply mimic.

So, if you have any thoughts on this topic, feel free to leave them with me :)


Kate said...

I agree that it is best to assign them homework, and I like your idea of giving them a "break" (at least from writing up the problems) by giving them a quiz before the exams. As you said, this is also useful to give them an idea of your style and to get them to review the material. Overall I like the combo option the most.

What makes it difficult to grade a subset of the homework problems?

Another option--depending on the type of student you have--is to have them self-grade their homework. It's a good exercise for them but of course you won't always get accurate results. Then you check their self-assigned scores by grading a subset of the problems.

elfarmy17 said...

As someone currently enrolled in Calculus AB & BC...
My teacher doesn't grade any of our nightly homework, but assigns weekly/biweekly Homework Sets that are, as well as giving quick quizzes every so often.

Seems to work if all of the advanced math teachers at my school do it.

Karen said...

One instructor at OSU did something that worked pretty well when I was a TA... He made it so that there was a quiz each week with 3 problems worth 10 points total. If they got 2 out of 3 (or 7 points... 1 point was pretty much a freebie), they got 100% on the homework. If they didn't get 2 out of 3, you'd look at their homework and grade for completion. Two of the quiz problems weren't too challenging (and were generally VERY similar to the homework!!), and one was a little more challenging. It wasn't as horrible to grade, and it motivated them to do homework.

Frank said...

This would indeed be the dilemma, Sir Kenny, and of course, I have a few comments.

First off, since this is a calc 1 course, your students unfortunately, are not "budding mathematicians," but are kids who need a math credit to fulfill the math requirement for their degree. Of course, you will have some math majors in there, but not many. This is important for you to realize, because most of your students will not care one bot about the knowledge they gain, just the credit.

Secondly, when at the University of Wisconsin, albeit years and years ago, I do not remember one prof who collected and corrected homework, not one, and not even in the early days of the calc sequence. My experience was tests and quizzes only, and I had one guy, an exceptional teacher who obviously didn't like to grade much, only go on the mid term and the final. That was it, two grades, each worth 50% of the total grades. Talk about giving new meaning to studying.

Third, I want to commend you on your ability to take other perspectives into consideration and then making your own decision, as this is so rare. So many people make decisions and then blame them on circumstances. Nope. This is your class and your decision, and good for you for recognizing that.

So, if it's me, I go by just test and quizzes, and in fact, Kenny, this is essentially what I do in a high school setting with the same level of kids you are talking about. First semester I do give a homework weight of 10%, and then second semester the weight is 0%, and yes, the kids who blow off homework do much worse than those who don't, but too bad for them. What I tell them is that for 12 years teachers have taught you that homework is done for the teacher's benefit, but that is so much crap; it is done for the student's. Do it and the quizzes and tests become less rigorous; blow it off and get hammered.

A final thought is your concern that you are burying a lot of your kids by not grading homework. Kenny! They are burying themselves! You work at a highly prestigious Big 10 (although there are now 12 members, so maybe you can do some math work to help them see that there is some faulty addition going on) university and I would submit to you that you should be making it more rigorous for your kids and not easier. And no, you don't need a 90% failure rate to prove that you are a bad ass, but I also don't think you should overly concern yourself about your failure rate, as let's face it, if a kid really is ready to take calc 1, he/she should be able to pass with just a little effort, as it just isn't that tough in comparison to the other math classes that are out there.

So, this is long, probably too long, but I have wrestled with the same things that you are thinking about and have come to the conclusion that tests and quizzes are the way to go, and that homework should be viewed as practice only, and if a kid is looking for a homework score to buoy up the grade, well, that just isn't going to happen.

Peace to you and may you have a great semester. I'll be looking forward to hearing of your decision.

Kelsey said...

I can certainly why this is a hard choice. I'd much rather grade quizzes than homework-mostly for the neatness factor, like you mentioned. I also can appreciate seeing test-like questions on the quiz. Maybe you can compromise? Only offer quizes, but make some of the questions come directly from the homework (they'd be like freebies), and others are examples of how you write questions for the final? It'd certainly be an incentive to do homework if even a portion of the quiz questions were straight from the homework.

Kenny said...

Thank you to everyone for their suggestions and thoughts! I mention what I decided to do at the bottom.

@Kate: The difficulty in grading a subset of the problems is that there are a lot of suggested homework problems, so finding the few I want to grade midst the noise could be difficult, even if they did them in order.

@ElfArmy: My sister commented to me, and I thought it was so accurate that it warranted passing along, that despite the fact that they are taking similar classes, advanced high school students and average college students are widely different populations. So what may work for one may not achieve the same results with the other.

@Karen: I gave this some thought, but decided it was too complicated for me to want to explain it to my class. I also worried that students might excuse themselves from doing the homework if they felt that they were going to do well enough on the quiz, then end up hurting their grades even more, sort of like the students who skip a quiz (because I excuse the lowest) then end up doing really poorly on another one. I also was worried about giving so many points for work I was (hopefully) not looking at, a free 10 points each week would add up to about 10% of their final grade.

@Frank: Every student in my course is a budding mathematician, I have to think that or I cannot see any good in trying to teach them math ;) That said, in all likelihood most of these buds will never attempt to blossom, but while they are in a math course, they will be pushed to be mathematicians.

At OSU all of my calculus courses collected homework, but I know other instructors did not. Of course, after calc it is almost necessary to do homework, as the level of inspiration required to come up with the proof of something often necessitates more time than sitting in a classroom for 50 minutes can provide. In fact, I can only remember one course that didn't have any homeworks, and I think I learned less from that course, although I still did just fine in it grade-wise.

I seem to remember that when I took your course you would excuse homework from the next chapter as long as one did well on the previous chapter's exam, am I correct in this?

I used your point about homework being for their benefit as part of my "in high school teachers teach you, in college instructors help you learn," spiel when I was talking about my syllabus. However, while I feel no desire to relax my academic standards, I am hoping to help students be more aware of how they are doing in my course. Although they are adults and should be capable of taking control of their own grades, they are just starting to be adults, and I have to admit I'm not particularly good at being an adult and I've been doing it a lot longer than they have.

I do sort of think that having some form of homework, or "effort points" to buoy up a grade is not a bad thing. First, homework requires effort, and having a good work ethic should be rewarded. Not simply because it is a laudable trait, but also because willingness to put in the work in relevant to how prepared someone is to actually do math. Second, it gives me a cushion so I can write interesting, and sometimes unfortunately long, tests. Finally, I am uncertain as to the efficacy of testing to accurately evaluate overall mathematical preparedness, especially in students with anxiety disorders, so having another form of feedback is helpful.

Well, there is my long reply to your wonderfully long post. It is always a pleasure to hear from you, at whatever length you feel like commenting.

@Kelsey: That is actually what I decided to do. I'll go with only in-class quizzes, but make most of the questions (I'm thinking 2 out of 3) come straight from the more interesting/involved/important ones on the homework. The last one can then be one of my own devising, hopefully providing some indication of what exams could look like.