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Questions about the algebra course

November 8, 2007, 9:46 pm

Jackie asked a series of good questions about the textbook-free modern algebra course and some of the student outcomes I was seeing in it. I tried to respond to those in the comments, but things started to get lengthy, so instead I will get to them here.

Do you think the results are only a result of a textbook free course?

To repeat what I said in the comments: I think the positives in the course come not so much from the fact that we didn’t have a textbook, but more from the fact that the course was oriented toward solving problems rather than covering material. There was a small core of material that we had to cover, since the seniors were getting tested on it, but mostly we spent our time in class presenting, dissecting, and discussing problems. We didn’t cover as much as I would have liked, but this is a price I decided to pay at the outset.

Most traditional textbooks don’t lend themselves well to this kind of class design. The ratio of text to problems in a typical textbook is probably something like 5:1 — a lot higher than that in some books. When you have a book in the course, it almost forces itself into the center of the class universe and everything tends to revolve around it, and take on its flavor. When the book spends most, almost all, of its pages on stuff for students to read rather than on problems for students to solve, then I guess it’s possible to have a problem-solving oriented class, but you’re going to be swimming upstream the whole way.

It works better, I think, to have no central book — and instead, provide problems via the course notes with just enough information to solve the problems. And if the students need more information, make it an assignment for library research or web queries.

Were there any negative outcomes? Anything you didn’t like as a result of choosing to structure the course in this manner?

There are some important algebra topics, in rings and particularly in fields, that are not going to get the time they really deserve. And I had to cut short or cut out some topics in group theory that are normally standard fare. At least, I see this as a negative; whether it really makes a difference in the long run is yet to be determined.

The way I select students to do course tasks in class basically involves randomly ordering the students and having them attempt the problems one after the other. It seemed like several times, students who had not presented much ended up first on the list on the days they didn’t have something and last on the list on the days they did. Call it bad luck or Murphy’s Law or what-have-you; but I didn’t like how there was no mechanism for making sure the lower-scoring students got more chances to work.

Some students in the class still struggle with basic problem-solving skills and writing proofs. I think they have enough education to carry out successful problem-solving on proofs most of the time. But not having me lecture has meant that they don’t get to see professionally put-together proofs very often unless they go do some reading.

And I think that this course structure caused stress and even ill will among the students who were not used to having so much personal responsibility in their college work. I think that’s an unintended consequence of implementing a course design that is basically sound; I regret that it happened, and I’d like students to have a more uniformly positive experience in the class, but I’m not going to change the basic course design.

Would you do this again?

You bet, although I believe this way of running the class works in some situations and wouldn’t work in others. I thought about running my differential equations class next semester like this, but that course is so focused on methods that a blind application of this course structure onto that course doesn’t seem appropriate. Maybe I’ll come up with some variant that works.

What would you keep the same? What would you change?

I would definitely keep my method for assigning problems to students, my rubric for grading course tasks, and just the overall procedure for running the class sessions that I used. And I’d keep the feature where students get to choose the weights on the various assessments.

I’d do a little more with the course wiki. Right now students are expected to write up their solutions to course note tasks on the wiki, but there is no point value in doing so nor a penalty for not doing so. The exams are open-wiki, though, so there is some incentive for writing results up well. But I think I would make the posting of solutions mandatory and enforce the rule.

I’d also try to have a complete set of notes before the course began. I have been writing things as I go, and it’s led to some snafus I could have avoided.

I might try writing the course notes so that rings and fields come first.

I’d seriously consider having proof techniques be offered as the subject of weekly help sessions or additional course work. Some students are still struggling with basic problem-solving techniques, and they really need more help than what they are asking for.

That’s that for the questions. Any more?

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