I do confess, though, that (like all professors who really care about educating students) I go back and forth about whether I've structured the class properly. It's definitely set up like a traditional lecture course, and while I try to be interactive with the students, it is a far cry from some of the modern education research approaches. I don't use clickers (though I've thought seriously about it), and I don't use lots of peer instruction or discovery-based interactions. The inherent tradeoffs are tricky: we don't really have the properly configured space or personnel resources to do some of the very time-intensive discussion/discovery-based approaches. Likewise, while those approaches undoubtedly teach some of the audience better than traditional methods, perhaps with greater retention, it's not clear whether the gains outweigh the fact that nearly all of those methods trade subject content for time. That is, in order to teach, e.g., angular momentum really well, they dispense with other topics. It's also not clear to me that these methods are well-suited to the Kleppner-Kolenkow level of material.

As unscientific as a blog posting is, I'd like to solicit input from readers. Anyone out there have particularly favorite approaches to teaching intro physics

*at this level*? Evidence, anecdotal or otherwise, that particular teaching methods really lead to improved instruction, at the level of an advanced intro class (as opposed to general calc-based physics)?

## 21 comments:

Hey Doug - good questions! I also do the traditional lecture for freshman and sophomores. However, I do add in some of the "peer instruction" during the homework help session. I wander around and answer questions, but they mostly work out the problems with each other.

Ultimately I think everyone should teach how they are most comfortable teaching. That will undoubtedly lead to the best experience for the student.

At MIT, the advanced freshman mechanics class still uses traditional methods while the standard freshman mechanics class uses "high-tech" teaching methods. I think you might find the following article and the comments to be of interest. I get the sense that the undergrads are not the biggest fans (that said, I'm a grad student at MIT and thus I probably don't have the most accurate sense of the situation on the ground)

http://www.nytimes.com/2009/01/13/us/13physics.html

Personally, for an advanced class like the one you are teaching, I think the traditional method is best

This mechanics book you have been using looks quite interesting - but I would suspect that students would have to already be in love with physics to use it appropriately.

For the intro calc-based physics, I really like the Matter and Interactions book from Chabay and Sherwood. It isn't just another version of Haliday and Resnick.

Also, if you want to do student response questions, it can be a pain to come up with your own multiple choice questions. The instructor's resources for Matter and Interactions has tons of great MC questions ready to use. Also, the text includes numerical calculation ideas - which I consider to be extremely important for beginning science majors.

Not a thought on class structure, but on course material having taken 111, majored in Chemical Physics at Rice, and now moved on to grad school.

While it felt cool to learn relativity as a freshman, the material was covered over again to approx. the same level of depth in 202 (having taken 111 and PChem before I took that class, I never bothered to show up and got one of the highest grades in the class) and then again in greater detail in 302. They don't do relativity in 101 if I remember correctly, yes?

Replacing that, I've got a couple of other suggestions for material:

I wonder if it would be worth doing a little bit on solids and fluids (probably to the level of the Feynman Lectures) instead. It'll be a useful intro for any physicist not going immediately into physics but something related (such as geophysics) and may help folks who decide to go into CM or AMO. Personally, I really could have used that info coming into grad school (Wait, you've got P-, S-, R-, and L- waves? How did THOSE come about?). It is a little tricky since it's easier to deal with these after having seen E&M (so the Laplacian doesn't look so scary) but perhaps it can be done.

Alternately, and this may be a long shot since the "learn how to program" classes are CAAM 210, NSCI 230 (does anyone actually take that?), or DiffE (tangentially), I wonder if it might be worth having students learn some basic numerical physics - maybe get them started with Mathematica? I've found that learning to do computational physics essential for everything I do, and I had resisted learning how to do it until I hit grad school. And having a "make a small program and play with the numbers" problem on the homework sets would be a welcome break.

Doug, let me ask you this, seriously:

do we really need those integrals ?.I can explain how to calculate the z-component of the electric field along the axis of a charged ring without integrals. I an use the result to explain how the disk works (granted, for that you would need integrals but, do we expect students to re-derive the formula on a test ?). The cases where integration is really needed are so few, in introductory physics...

My note for first year physics (both calculus and non-calculus) are almost identical. I am not sure if the emphasis on calculus is warranted at this level.

I do a couple of things differently from the traditional lecture.

For instance after delivering the lecture I break the students into groups and have them work on examples from the text. I answer questions but they work out the techniques and then present the solution to the class.

I also use blackboard and use the quiz tool within blackboard to deliver a very basic 5 question conceptual quiz that closes just as the lecture starts. Basically I want the students to have read the material.

I split the homework into two phases. The quiz tool can be used to assess understanding of the material very broadly using multiple choice questions and questions with randomly generated data.

With black board handling the roughest level of assessment I can concentrate on a detailed working of 4 assigned problems.

Okay, the more I think about it the more I really could have used a numerical part in my intro physics class. Learning to program is probably one of the most useful job skills one could have, and it doesn't hurt to reinforce it early and often. Plus, there are all sorts of things you could do such as the trajectory of a cannon-ball with drag or having students look at the period of a large-angle pendulum.

To argue with YHN and Massimo, I liked the structure of the 111 problem sets I had with Hannon (I don't know whether you do them differently). Having a few relatively mathematically involved problems, rather than a host of multiple choice ones, really trained me to solve problems more complicated than "you travel 50 mph for 3 hours, what distance did you go" and prepared me very well for the rest of my time at Rice.

Thanks for all the responses.

Jason, I basically agree, though "undoubtedly" may be too strong.

Anon., thanks for that, particularly the comments. Very interesting to see the dichotomy between those who thing the TEAL approach at MIT is awesome and those (often students) who found that parts of it were annoying and didn't convey as much information.

Anzel, thanks. I do try to get a bit of fluids and solids in there, just a little. The one upside of relativity is that the students are really into it. It's their first exposure to something "modern" and really outside their daily intuition.

Rallain, I'll check out that book - thanks for the rec.

Massimo, if you want to find the moment of inertia of something or the center of mass of something, you often do need the integrals. Or, if you want to really show that orbits are elliptical, parabolic, or hyperbolic, for example, you need either integration or Newton-level geometry-skilled.

I also do have weekly problem sessions beyond the lectures, though in past years I've had outstanding TAs who relished the chance to run those.

You should be aware tha the students you get in first year mechanics may not necessarily be the brightest. The brightest students usually ace the AP physics test in highschool and skip ahead to E&M or beyond.

You want to give them a good foundation and understanding for the future, and not necessarily a second calculus course.

Massimo, if you want to find the moment of inertia of something or the center of mass of something, you often do need the integralsNo question about it, but is it really

necessarythat a first-year student compute moments of inertia ? I mean, do you imagine assigning on a test a problem in which the bulk of the effort will be the calculation of a moment of inertia ? For the center of mass, considerations of symmetry often go a long way. I suppose it is a matter of opinions, but that is a part that I feel I cal live without.Or, if you want to really show that orbits are elliptical, parabolic, or hyperbolic, for example, you need either integration or Newton-level geometry-skilled.OK, are we talking the same cours here, though ? Because this sounds fairly advanced for freshman physics..

Students of all sorts learn better in peer classes. The reason only introductory classes are taught with more modern techniques is that more advanced students can be expected to put the work in that the instructor didn't.

That said, if you're going to imagine that students are going to listen to what you have to say, you might get a copy of Arons' book "Teaching Introductory Physics". It covers the common misconceptions and learning errors for algebra and calculus based physics students.

Massimo, I know that's advanced, but this is the

honorscourse, and if I don't make it much beyond the regular one, then what's the point?Carl, I appreciate the tip. I have been doing this for a while, but it's never bad to have another reference. That being said, the idea that traditional methods expect students "to put in the work that the instructor didn't" is an odd way to phrase things. Students should damn well put in work, not sit there completely passively and expect instructors to somehow fill up their brains. Students doing the work is an essential part of the process, not a sign that the instructor is somehow being remiss.

Relativity IS really cool, but it meant that I ended up being very bored in 202.

KEEP the integrals. It made dealing with 301/302 substantially easier.

I personally think Kleppner is probably the most balanced Mechanics textbook for a freshman course. I agree you need to know a bit of calculus, but I don't see what's a better time to learn it than the freshman year. I think I really learnt calculus when I took the two freshman Mechanics and Electrodynamics courses. The real learning was to model worded problems in Mathematical terms, and I don't think that emphasis should be reduced.

One thing that might have biased my opinion is that most kids in my college class, including myself, had solved a large portion of Irodov's 'Problems in General Physics' book. Those problems are quite challenging and require a certain degree of mathematical acuity to crack. Having done it, I don't think it is too hard for a freshman class to solve.

In my college (in India), there were large lecture classes of ~400 kids twice or thrice a week, taught by the instructor. Then, twice a week we had smaller 'tutorial classes' of 15-20 students, each taught by a professor, where we learnt how to solve complicated problems, clarify our doubts, bring interesting problems from outside to brainstorm and solve etc. Those tutorial sessions in small classes taught by professors were the best. Unfortunately, it doesn't look like that's going to be viable at Rice.

It may not be a bad idea to formally allow graduate students to teach these small classes like they are allowed in public universities. It will help the undergrads, as well as us graduate students, who will get valuable teaching experience that we so lose out on by coming to Rice. (Really, it sucks not getting to teach even small groups like my friends in public universities do).

I guess this must be old-school around here, but I relished going through Feynman's lectures in my freshman and sophomore years. You might want to encourage your students to try their hand at those. Even if only a few get hooked to it, it may be worth the mention. :)

Doug, I don't think it's worth worrying to much that you might be shortchanging students. It's a survey course, and every single survey course ever taught required the instructor(s) to decide what to cover and what to skip. They'll miss a lot no matter what you decide to cover, and they'll learn a lot no matter what you decide to cover, so just choose well and don't stress over it.

One reason I say this is that these students, as you pointed out, will be pretty self-motivated. If they're not self-motivated, they won't learn the material no matter what you choose to cover. (I used to tell fellow students griping about Ian Duck, "He's letting you get exactly what you want out of the class - if you don't learn anything, it's your own damn fault.")

From the perspective of someone who has studied, TA'd, and/or taught at community college level, podunk state school, and research school (from which I know Anzel, of course), I'd recommend keeping the integrals and such but not making them an overbearing amount of the content. I don't recall Rice having an undergrad math methods course, just the Arfken-level class I took; I also audited a couple of classes over in MechE. Whether it's engineering, math, physics, or something else, the math practice will be useful pretty darn quick.

-AGM

Anzel's mention of geophysics does raise an interesting thought. What about talking the ESCI, BIOS, BIOE, MECHE, etc faculties and find out what they would find useful? I know the ESCI people tend to get handed stub programs and equations and shown heuristic derivations for the geologists, but they do try to get a certain level of rigor for both the geology and geophysics classes. The other faculties may do the same. Given the massive number of your students who will end up in the med center, in oil and gas, or generally fields-outside-their-major (as many of them will), it might be a very effective planning strategy to consult with them.

Also, as a practical note on engagement, there are a ridiculous number of applets and short youtube videos on physics (swings set up by climbers for pendulums, laser pointers refracting in a flow of water, youtube clip of Grond the battering ram to provide a mnemonic about conservation of mechanical energy, etc). My students really benefited from having mental mnemonics to draw from.

Caltech has a general math methods class (Applied/Comp Math 95/100) for seniors/first year grad students (1st term Complex Analysis, 2nd term ODEs, 3rd term PDEs) and the general consensus among the grad students is, minus complex, this is not particularly useful for anyone (tends to be taught at a very theoretical level). The PDEs class (the one of that set that I took) did nothing for me for that very reason. I also took the physics math methods class (for grad students, 1st term integral transforms, 2nd term group theory, 3rd term statistics. Probably much more like Arfken)--the stats was probably the most useful bit. If I remember correctly, Physics BS students need complex and PDEs, and a lot of folks find their way into CAAM 335 (that the linear algebra one, right?).

I'm a little unsure what sort of math people need to learn in PHYS 111/112 besides being able to look at a multi-step derivation with calculus and not run screaming. I came in not knowing about Taylor series until the end of my first term (I only took Calc AB, thank you small school in a rural area), so that could be briefly touched on. Maybe the most basic familiarization with complex exponentials would also be useful (though that also gets reviewed in PHYS 201 and MATH 211). Matrices are taken care of in MATH 211 and Div/Grad/Curl will be addressed in MATH 212 (and was covered in very rough detail in PHYS 112). Tensors are an adventure for much much later (hey kids, let's have covariant and contravarient indicies in a mix of Eulerian and Lagrangian frames!).

I would be very interested to hear what MECH, ESCI, etc would request for an undergrad physics course.

Hi AGM!

Great discussion. I'm going to write another post about MECH/ESCI/etc. needs in undergrad physics. I can speak to that a little, since I was actually an undergrad mech-e.

By the way, tensors do crop up all the time in places besides general relativity, you know. Anyone who works with birefringent optics or mechanics of solids with anisotropic materials sees them....

relativity is cool

It's been a long time since someone posted here, but FURTHER comment about programming. From the California Tech's (CIT's student newspaper) recent article "A Chat with Prof of the Month Gil Refael")

http://www.ugcs.caltech.edu/~techstatic/issue/20.pdf

"How would you describe your teaching style?

Informal, and also old fashioned. I use a blackboard, and I tell silly

jokes. I try to derive everything

from scratch, and I want my students to be able to deploy what they learn easily, by having an

intuitive understanding of how the

theory, the math, and the logic all

fit together.

At the same time, I’d like my students to make use of the new tools we have available, such as

computer programming, and easily accessible information on the web. In Ph12b this meant mandatory use of Mathematica in the problem sets."

Any further thought on what MechE/ESci/etc people want from undergrad physics?

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