Friday, March 19, 2010


(begin rant)

Two days ago, an email went around the math department here indicating that the higher ups were thinking about changing calculus textbooks, and that there would be a meeting today to talk about it. The meeting was essentially a presentation from a salesman from the textbook company about how great the new textbook is. A few minutes of discussion before-hand, and a comment that those making the change (I'm pretty sure it's a foregone conclusion) would hear our thoughts on the matter. I sorta felt, leaving the meeting, that we'd get a somewhat formal (at least an email) request for comments. Now, a few hours later, I'm guessing we wont. In fact, they probably just signed a contract while the guy was here today.

Sorry, I'm a bit cynical.

Before I go on, I'm probably supposed to make some disclosures. I have at times made (and am currently making) money doing things associated with the Webwork online homework system (admin, library tending). I grew up on Stewart's textbook (used it as a student, and it's what UVA has been using since before I got here). The textbook we are thinking about switching to (like, apparently, everybody else considering switching textbooks) is Briggs and Cochran. At the meeting today, I got a free copy. They also gave us an access code to their online software, MyMathLab.

In all fairness, the new book looks fine. It looks like basically every other recently-released calculus textbook I've looked at (don't take that to mean I've looked at a lot, of for large amounts of time). There are lots of pretty pictures, and apparently the author(s) are big on geometric intuition, which is great. We were also told to be impressed that in the worked examples, each step was given a little explanation. And, gosh, isn't this something amazing, the authors organized the problems at the end of each section carefully. We were told several times that this was not a lower level book, clearly something the publishers are worried about people thinking. It is, as @MitchKeller opined about the projects it has, "a bit hand-holdy".

Oh, and there'll be a new edition along every 3 years.

Of course, the textbook by itself isn't, I expect, what people are all giddy about. The textbook is paired up with MyMathLab. You can make online homework assignments and quizzes. There are little tools for the students to use to get help, like looking at worked examples, looking at a digital copy of the textbook, and probably some others I forgot. Students can also see a little "Study Guide", a sort of summary of what sorts of problems they missed, so they would know what to go back and look at. Oh, and some large collection of those pretty pictures in the text are pretty animations (calculus being about change, we were reminded by the salesman) in the MyMathLab system.

Students have the option to not buy the physical book (at least, in theory, who knows what our goofy school will require), and instead spend somewhat less and just use the e-book in MyMathLab. I seem to recall the e-book being in the $70 range, the first year textbook in the $90s, and the 3 semester book in the $130s, +$6 for the MyMathLab software if you buy the textbook. These numbers might all be before bookstore markup (we were also told to be pleased that the UVA bookstore markup of ~25% is really low... go team!), and we were told that these prices are cheaper than Stewart. The presenter today did this cute thing where he pretended not to already know the price of the books, and looked them up online.

Digital rights management didn't really come up at the meeting today, and I'm ashamed that I didn't bring it up.

Quite honestly, it seems like a not entirely bad thing. Switching textbooks isn't the worst thing we could do. Like I said on twitter after the meeting, though, it feels like shuffling deck chairs on the Titanic.

If I were given freedom to set up the course however I wanted, I wouldn't require that my students purchase this, or any other, textbook. There are simply too many free resources online for me to justify requiring students to spend that money. If students want to buy the book, or the software (more accurately: access (likely temporary) to it), good for them. Go for it. But if a student would rather use their brother's old textbook, say, or the free ones they find online, that's fine too. If instructors are going to lecture (I generally do, more than I'd like), many students can likely get by on class notes (their own, or a friend's), maybe in combination with some office hours.

Sure, the pictures in the book were nice. And the animations. But there are plenty of calculus animations online (I'm not gonna google that for you). In fact, I could roll my own (and have, happily), and would be delighted to teach students to do so as well. It'd be awesome to talk to students about pictures during class, draw them on the board, and then have them make a digital version of the picture, or an animation (for the ambitious) (and release them all under a CC license, wouldn't that be a fun thing to talk about in class). Heck, why not have the calc students write a book, complete with pictures? Write about the things they got hung up on, and what got them over it. Make a wiki. The instructor likely has access to several textbooks. Use them to put together an outline for the semester. Lecture if you want, or tell them to go see what they can learn online or at the library (then use class time to synthesize what was found). Looking up resources online, you also get to talk about evaluating resources, and how to compare different sources. You can build up a big huge list, and have students rate each source (and share your result with... everybody!).

And as for step-by-step explanations, WolframAlpha jumps to mind, but there are certainly others (I'm not gonna google that for you either). Don't like W|A's solution to a problem (they can be a bit... pedantic)? Have students talk about improvements. This also points out that those problems are pointless anyway. A computer does them more quickly and more accurately, so let it. Let's work on understanding concepts, instead of continuing to test pointless algebra tricks. Use the time that we're not doing mechanical manipulations to come to the geometric understanding slowly, guiding students to discover it for themselves.

Webwork has, for me, done a perfectly adequate job as an online homework system. If UVA doesn't think the problem library is nice enough, of the interface good enough, perhaps they should invest some money in improving it (I know they (at least, Dr. Jeff Holt, through a grant) have to some extent, and also that there is money floating around). Then even more people benefit (webwork is open source), and UVA gets some nice credibility. Webwork can do most of the things the guy today tried to sell us on for online assignments, though it's interface might not be as gosh durn pretty. It will not show students which section from the book they missed problems on (it's not tied to any one book). But I don't really see the problem here. I think it would be a great exercise to teach students how to evaluate for themselves which sections they need to look at.

I know I'm not going on much but youthful optimism and naivety. It's not the first time, nor likely the last. I have no expectation at all that the powers that be will take my thoughts seriously. At least here I can pretend that my thoughts are worthwhile (thanks Blogger). I'm leaving after next year anyway, and have seen no evidence (I suppose I haven't asked) that the younger grad students think like I do. I should probably just let it go (until I'm at another school). [As I was writing this post, I decided to email the math grads, to see if they'd like more flexibility in their teaching.]

All I want is for the department to allow instructors to try something different. Let us not require our students to purchase the (any) textbook. Get out of the publisher's pointless "new edition" cycle

Think about dropping the heavy emphasis on algebra.

(end rant (for now))

Wednesday, March 10, 2010

Thoughts on "Dehumanized"

You should go read "Dehumanized: When math and science rule the school." Even if you've read it before, and even if it was recently, go read it again. Perhaps a few times.

In this essay, Mark Slouka expresses disappointment that education is being "retooled... into an adjunct of business" at the expense of the arts and humanities.

This is certainly a fair thing to be disappointed about.

I've never really been "in to" the humanities. I don't remember ever much caring about my history classes, or social studies. I don't think I took many literature classes, and can't say I feel like I got much out of any that I did take. I blame nobody but myself, of course. While reading "Dehumanized" I became convinced that I have seriously missed out. It's sad that now, age 26, supposedly 1 year away from a Ph.D., I'm finally ready to go to school.

I do not agree with everything in the article, though. Throughout, Slouka seems to wish that civics were the highest goal of education. I'm not sure I see why this should be. Of course, I'm pretty sure I don't even know "what" this would be, so I don't have much basis for argument. But I think many of the goals Slouka advocates, with the apparent intention of improving individuals as citizens, are goals I do agree with.

Slouka asks, "What do we teach, and why?" Clearly a fantastic question. He even provides some answers: "whatever contributes to the development of autonomous human beings", "in order to expand the census of knowledgeable, reasoning, independent-minded individuals." I like those answers, even if Slouka seems to want these things for the purpose of "the political life of the nation." I guess I feel like I want these things for the individual, and those around the individual. Perhaps that's what politics is/are. I don't know, I probably wasn't paying attention that day.

The humanities, it is claimed, are there to talk about "what it means to be fully human," to teach "not what to do but how to be". The output is "the reasoned search for truth." But then Slouka says these things are all, "inescapably, political." Perhaps the reasons why all point out why I don't know what "political" means: "they complicate our vision", "grow uncertainty", "expand the reach of our understanding" (and thus "compassion" and "tolerance"). One goal seems to be "an individual formed through questioning". The de-toothing of humanities education is summarized:
Worried about indoctrination, we've short-circuited argument. Fearful of propoganda, we've taken away the only tools that could detect and counter it.

The arts and humanities are there to "upset people", prompt "unscripted, unapproved questions", and, according to Don Randel, "force us into 'a rigorous cross-examination of our myths about ourselves'". Slouka quotes the teacher Marcus Eure who wants students to have "depth of experience and a willingness to be wrong", and notes that "every aspect of life... hinges in some way on the ability to understand and empathize with others, to challenge one's belief, to strive for reason and clarity."

These all sound like awesome things.

What confuses me about the article is that the author doesn't seem to think math and science help with these goals. I just don't see that at all. Uncertainty? Understanding? Questioning? Cross-examination? Reason and clarity? How are those not in the realm of math and science? Sure, the topics that are questioned and reasoned about are different for mathandscience than for the humanities, as it pointed out by the article. But how can the questioning nature of mathandscience, the logic and reasoning, not be helpful in the humanities? Is it because math and science education, in parallel to education in the humanities, isn't what it really could and should be? Of course, having also just re-read "A Mathematician's Lament", I worry that this is quite likely the case. But that's probably the topic for another day.