One more physics education rant: Naming Names
By Thoreau
The ostensibly calculus-based introductory physics book by Knight is not really a calculus-based book. Sure, integrals and derivatives pop up here and there, but the vast majority of the problems can be solved without them, and calculus is hardly emphasized at all in most of the text and examples. The few problems that do use calculus are generally the hard ones near the end of the problem set, and with very little in the text to prepare them for these problems it’s hard to assign them.
Much the same can be said about other intro physics books, but Knight is particularly egregious. The best response would be that I should just lecture on what I want, post my notes, and come up with my own problems. This is much easier said than done, especially when you are inexperienced. I don’t want to create this stuff from scratch until I have some experience. So I’m reduced to using the book as it is.
This has been in the back of my mind for a while, but I was able to cope with it because, well, it’s just freshman stuff. But next year I’m supposed to teach the upper division classical mechanics course, and I’m realizing that my students will not have had a truly calculus-based freshman mechanics course, so all of the stuff that I’d like to do must instead be put off until I first redo mechanics (in abbreviated form, of course) with calculus. This does not make me happy.
If it were just one book, well, so be it. But I’ve encountered this attitude from a lot of people interested in physics pedagogy: As near as I can tell, they believe that calculus (a subject to which no less of a physicist than Newton made huge contributions) doesn’t have much place in the freshman physics classroom.
Comment by adam s —
May 7, 2009 @ 2:50 pm
I had this problem on the PE this April where within the last 20 minutes of the test I flipped to an equation for acceleration, which had been integrated on down to the distance covered over some fixed time. I think I got it. 1/2at^2. it’s the most calculus I have done since 1999. I certainly didn’t cover it in my studying.
1. they always try and cram too much into a semester.
2. isn’t freshman physics a weed-out course anyway?
you’ve got to get their toes wet, so I would say be highly selective in the problems you use, and in teaching them when and how to apply calculus.
Comment by Currence —
May 7, 2009 @ 3:40 pm
We used Kleppner/Kolenkow, which was pretty awesome and calculus-y, if I remember correctly.
Comment by EscapedWestOfTheBigMuddy —
May 7, 2009 @ 3:45 pm
In doing some adjunct teaching last summer I was surprised at the clarity of some of the algebra based arguments–they seemed much better than the ones I remember from high school. But I was disappointed at the use of calculus, those arguments seem to have gotten worse
The thing is the algebraic arguments were clean, but they took time. Lots of time.
There is so much to cover in an introductory course, that I would think that being able to say” v=dx/dt and a=dv/dt, and you can work out the consequences for yourself (just remember the constants of integration). Now lets do a couple of examples…” would be a great relief.
Comment by Astroprof —
May 7, 2009 @ 6:33 pm
Yes, I have noticed a number of calculus-based books put the calculus in almost as an after thought — oh, yeah, you can also do calculus here. One problem is that many colleges list calculus as a co-requisite for the course rather than a prerequisite. So, many students see the calculus in their physics class before they see it in their math class. I make it clear to my students on the first day that we will be using calculus throughout the course.
Comment by hf —
May 7, 2009 @ 6:37 pm
Well, it’s bad but not all that bad. Remember that in the calculus class, a good number of the examples are from mechanics, unless your math faculty suck.
Just do some examples on the board. It’s another concept generation veal should get used to, namely, stuff covered only in lecture and yes you are responsible for it.
Comment by kishnevi —
May 7, 2009 @ 8:59 pm
The effect of what you are saying is that freshman physics should be taken only by students who have taken freshman calculus–in effect, you’re saying they need to wait until sophomore year to start physics. Do you really want that?
And you are assuming that physics classes should be taken only by students that are interested in continuing through the entire physics curriculum–instead of, say, a student of average intelligence who has decided that a general introduction to physics is a better science requirement choice than biology or chemistry.
Inserting a section that makes clear the close relation of higher mathematics and physics is fairly reasonable, but you have to make allowances for the students who haven’t gotten to the higher math yet–and may never do so.
(Unless your school has a big enough program that it can offer duplicate tracks–one for the general student body and one for the students actually interested in becoming physics majors.)
Comment by Kevin J. Maroney —
May 7, 2009 @ 11:55 pm
Kishnevi, I *think* that Thoreau is saying that an intro physics textbook that is billed as being calculus-based should do a better job of being calculus-based.
I note, however, that the word “calculus” does not appear in the blurb for Randall Knight’s Physics for Scientists and Engineers: A Strategic Approach with Modern Physics and Mastering Physics at B&N (”the most widely adopted new physics text in more than 50 years”). I assume that’s the book Thoreau is dissing, but maybe there’s another?
Comment by Thoreau —
May 8, 2009 @ 1:03 am
That is the book I’m dissing. It’s not in the B&N blurb, but calculus is mentioned somewhere in some of the literature, and my department adopted it for our ostensibly calculus-based course. Yes, yes, I should be blaming my department (and I do) but even a lot of the other books generally use calculus pretty sparingly. Knight is merely the worst of a category, rather than in a unique category.
As to freshman vs. sophomore, most intro physics classes require one semester or quarter of calculus, so somebody could start a truly calculus-based course in the middle of freshman year.
Comment by Thoreau —
May 8, 2009 @ 1:05 am
BTW, I’m not talking about physics classes for students who want a physics course to satisfy their general science requirement. I’m talking about ostensibly calculus-based courses for engineering students who are supposedly taking these courses to learn material essential for engineering.
Comment by joel hanes —
May 8, 2009 @ 3:49 am
In my engineering curriculum at A Great Land Grant Institution, physics was the sophomore hard-science class for just this reason.
Freshmen took a full year of chemistry; meanwhile their freshman calculus classes prepared them to actually comprehend physics the next year.
Comment by Doug T —
May 8, 2009 @ 8:08 am
Concerning taking the class at the same time as the first calculus course, would it be possible to teach the basic non-calc stuff in the first 2/3 of the semester (or so), and then go back in the final part of the semester and illustrate how calculus underlies and generalizes all the previous results?
That way you’re teaching the basic concepts (F=ma, momentum, conservation of energy, etc.) using math that is familiar to them, so they can focus on the concepts, and then adding the calculus wrinkle at the end, when hopefully they’ll have had the math to deal with that.
I’d think that would help them learn calculus, too. I know I never really understood Stokes law until I applied it in E&M.
On a tangent, maybe it was just my own personal experience, but I feel like advanced mechanics is a class that’s sadly underemphasized in most physics curricula. I guess it’s been crowded out by quantum mechanics, but I felt like our course on that ended up trying to cram too much stuff into one semester, and left most of us students without a real understanding of the concepts. Which is too bad, because those concepts are critically important to all sorts of physics, including quantum mechanics. (You can do quantum without having a deep understanding of Hamilton’s work in the classical realm, but I wish I hadn’t had to.)
It’s also just amazing, cool, elegant stuff.
Comment by adam s —
May 8, 2009 @ 8:33 am
oh so these are engineering students? then let them have it. weed them out for us out in the field. PLEASE!
Comment by Barry —
May 8, 2009 @ 9:42 am
Comment by joel hanes —
“In my engineering curriculum at A Great Land Grant Institution, physics was the sophomore hard-science class for just this reason.”
That’s a great idea.
Comment by mds —
May 8, 2009 @ 10:49 am
I attended a small public Midwestern liberal arts college, and they were easily able to offer three levels: Physics for Poets, Physics for Biology Majors and Other Pre-Med Tracks, and Physics for Physics and Chemistry Majors. Only the third was calculus-based, and it in fact did have to wait for our sophomore year, so that we could complete Calc I and II first. It was a little weird to have so few physics courses our first year, but there were plenty of Gen Ed requirements to get out of the way, along with Gen Chem I and II.
We used, um, that pink textbook that seemed to have at least some degree of calculus in it. Then again, that memory might be colored by how much our instructor flogged us with math in our homework and exams. And regardless, once we hit Mathematical Physics, and Arfken’s evil blue book, we had more than enough calculus to chew on.
Comment by HyperIon —
May 8, 2009 @ 11:14 am
Is Halliday and Resnick still in print? That’s what UF used in the 70s. Does it qualify as “calculus-based”?
Comment by Seward —
May 8, 2009 @ 4:07 pm
Thoreau,
OT:
FEE has a nice lecture the economics of science that you can download as a podcast. A lot of it covers the history of modern government involvement in science.
Comment by CCPhysicist —
May 8, 2009 @ 8:59 pm
Great article.
I put most of my comments on this subject in my blog.
Our math faculty, as good as they are, do not do much with the mechanics applications in calculus, and I know why (since they are down the hall, not in a different building). They know very little physics. Some did not even need to take more than a semester of physics, less if they took more chemistry, so they are not comfortable teaching it. Since many students take calculus before physics, the students also don’t know even the basics (let alone the relation between pressure and force) so they are not comfortable learning it. Result: pure math with limited applications.
Here I’ll also add that I try to limit the course to essential topics, but you better have good judgment before doing that. I know one school that went so far as to drop thermo from the course. Not so good for a student who wants to be a mechanical engineer!