Category Archives: Education

Calculus Solutions and Errata Are Here!

I’ve uploaded a pdf of Solutions to about half the problems in the Cartoon Guide to Calculus. You can either download it or read it in your browser. You should also look at the Errata sheet, which details a number of errors in the early printings of the book. (These links are also on the Calculus page on this site.) I’ve recently sent the publisher a revised electronic file that fixes all the mistakes (and makes minor changes to the problem sets), and as soon as the the corrected edition is in print, I’ll post an update here.

Peonage for Textbook Authors

Via Professor Mike Klymkowski, here’s “Afraid of Your Child’s Math Textbook? You Should Be,” a long, thoughtful piece by Salon blogger Annie Keeghan on the state of the textbook business. It’s not a pretty picture.

Keegan describes in detail the consolidation of the industry into a few huge publishers and the market forces that impel them to push sales and volume over accuracy and coherence. For writers it means a pay cut. For students, something even worse. This has to change.

Great Bio-Ed-itorial

Bruce Alberts, the preternaturally accomplished editor of Science Magazine, has written a great editorial about bio education. I’d post the link, except that it leads to an onerous registration process. Instead, here are some quotes:

“When we teach children about aspects of science that the vast majority of them cannot yet grasp, then we have wasted valuable educational resources and produced nothing of lasting value. Perhaps less obvious, but to me at least as important, is the fact that we take all the enjoyment out of science when we do so.”

“The preference for “rigor” in science education can also interfere with the teaching of science at the college level. For example, in an introductory biology class, students are often required to learn the names of the 10 enzymes that oxidize sugars in a process called glycolysis. But an obsession with such details can obscure any real understanding of the central issue, leaving students with the impression that science is impossibly dull, causing many to shift to a different major.”

“Tragically, we have managed to simultaneously trivialize and complicate science education.”

Sounds as if he’s calling for a more—dare I say it?—cartoony treatment. The second part of his editorial, due out later this week, will let us know if I’m right.

Online teaching

Via Brad DeLong, some insightful thoughts from Felix Salmon about Khan Academy and some other online instructors. (Salmon’s post is mostly about a new enterprise called Udacity, which I hadn’t heard about before.)

Here’s Salmon:

“A large part of the success of both Khan’s courses and Thrun’s is the way that they’re presented and executed, rather than any business model behind them. Khan, in particular, is a hugely gifted natural educator…

I think that Khan and Thrun are at the forefront of a new, more personal way of teaching — think of them as having screen-actor skills in a world which has historically rewarded stage-actor skills. When you teach online, you’re teaching in a conversational manner, in a one-on-one space. And it turns out that many students — quite possibly most students — prefer being taught that way, as opposed to the old-fashioned model where a lecturer stands up in front of a crowded classroom and declaims to many people at once. Most students are naturally shy; they don’t like speaking up in class and saying that they don’t understand something. Online, they can just rewind and replay, or pause and look it up on Wikipedia.

And then of course there’s the fact that the incentives for the teacher are so much greater online, if like most teachers you’re driven by the opportunity to impart knowledge to students. “This is the best thing I can do in my life,” says Thrun. “I empowered more students in 2 months than in my entire life before. On that scale, I was off the charts in the last quarter.” And of course Thrun is barely on the charts if you compare him to the number of students that Khan has reached.

What Khan and Thrun and others are creating is a new educational paradigm, which promises not only much greater scalability than anything we’ve had until now, but also higher-quality education. That’s the real lesson of Thrun’s Stanford students taking his class online: it means that the online model really can have its cake (reach millions of people) while eating it too (be better for students than the courses offered at elite institutions).”

Still seeking biologists

I’m looking for biologists/biology teachers to discuss a biology project. The current state of biology textbooks alarms me for many reasons, and I’d like to develop a way to present important biological concepts clearly, concisely, attractively, and comprehensibly. If you’re interested in exploring the possibilities, please contact me. If you can’t do it but know someone who might, please send him or her my way. If you don’t know anyone who might, please pass the word along, in hopes it crosses the right virtual desktop somewhere in cyberspace.

Summers on the future of education

Everyone’s favorite treasury secretary college president piñata economist Lawrence Summers opined about higher education in the Times over the weekend, and, lo, it was good. Two important points, widely shared across the education industry:

“1. Education will be more about how to process and use information and less about imparting it. This is a consequence of both the proliferation of knowledge — and how much of it any student can truly absorb — and changes in technology.”

“6. Courses of study will place much more emphasis on the analysis of data.”

This affects how instructional materials are made. More on this another day.

Unfortunately, he also believes, perhaps correctly, that there will be fewer and fewer textbooks, or whatever you want to call them, done by the “best” people, who constantly revise them (now possible because of digital technology). I guess this sounds to him like a meritocracy, but to me it carries a whiff of oligarchy.

Once the few giants have been selected, don’t the barriers to competition rise high? Will the current generation of innovation tend to stifle future innovation? Can textbooks become “too big to fail”?


I’m excited about Apple’s push into textbook “space,” and I’m sure I’m not the only one. The announcement was everywhere, here on my favorite tech site The Register, for example. A look at the Apple site, though, confirms what I’d suspected: beautiful design, nifty interactive capability—and the algebra textbook still comes in at almost 1,900 pages!

It all fits in a lightweight tablet device, of course, so nobody’s back will be broken, but there’s clearly still plenty of work to be done. Luckily, there are now developer tools available to all of us who want to do this stuff and do it more concisely than the new-fangled, old-fashioned way.

Punchy Verbs, Weak Nouns

Science writing is known for punchy, active verbs. Levels of sugar in your blood plummet or soar; global temperature creeps up; a new drug slashes lipid concentrations. Things rarely rise, decline, move, or anything simple like that.

All journalists drink active verbs with the mother’s milk of beginning instruction, and we all agree that the passive voice is, if not actually bad, at least something to be used with caution. And it’s a short distance from active verbs to hyperactive ones. But I think there’s something else going on here.

Behind these urgent action words you can practically hear the writer whispering that the subject is really boring and needs punching up. Must… grab… reader’s… attention… which makes us wonder, why is that? With my temperamental prejudice that pretty much all science is thrilling, I want a more specific reason. What’s boring? Often, I think, it’s the nouns. Writers deploy punchy verbs to compensate for weak nouns that lack concreteness and immediacy. In the examples above, the nouns were all measurements. They weren’t things, but scientific assessments of things. The science writer’s view has been infected by that of the scientist, who’s always inclined to think of measurements whenever possible.

Consider global warming. Everyone says that sea level will rise (or rocket, or bulge, I don’t know). This is a statement about a level. It conjures an image of a line on a stick. But what if I said simply that the ocean will rise? It doesn’t takes much of a verb to summon up that terrifying, near-Biblical image, and all because of the stronger noun.

The Lord parted the Red Sea—with a simple verb. He didn’t adjust its level differentially.