The semester started last week. I am again teaching a junior/senior elective for majors and it looks like it might be a rough semester.
The course I am teaching follows a basic, required course in the major. I find the students are poorly prepared, more poorly than the class I had last semester. The students are quiet and look positively terrified. I know it takes a little while for people to warm up and start answering my in-class questions, so that will come with time. But I am being quite alarmed by all the things that they say they have never seen before, because, if that’s true, then I have to significantly rethink the class. Sure, I suppose they might be fibbing, but I do believe think most of them have simply never seen the material or, if they have, then it really didn’t stick at all and they genuinely don’t remember it.
Last week and this week, we are reviewing the material from the previous course, and it’s going very slowly. I may have to take more time simply to get them up to where they would actually need to be, which means cutting out some of the new stuff.
Also, the lack of facility with math always rears its ugly head, but at least that’s not particularly surprising. Any physical science field that requires a lot of physics has to be taught math really rigorously, and the math department does a very good job. The problem is that, owing to a recent idiotic progressive change in the curriculum for our major, which is supposed to give the students more flexibility to freely choose easy courses outside of the major customize their program of study, some important formerly required math courses have now become electives (e.g. how can linear algebra and differential equations not be required just fuckin’ blows my mind) and now many students elect not to take them. Also, many of the required math courses are mismatched in timing with the relevant courses in the major.
Perhaps more importantly, on top of pure math, the next layer is often missing, and that is the layer where the students are taught physics while using the math tools. This is where they should simultaneously be taught how to build their intuition about the physics with the help of math (math is your friend, people!!!) and how to better understand the ability of math to capture the physical world. What we need are slower-paced calculus-based physics courses and less jam-packed syllabi in the lower-level courses for our major. The way physics for non-physicists courses are taught right now is woefully inefficient: there is too much material in each one of these courses, everything is only touched upon, and the kids retain absolutely nothing. It’s a complete waste of time. Considering that many students haven’t had physics as a standalone subject until college, maybe I shouldn’t lament but should be in awe that the kids have as much proficiency as they do.
People say that we discourage our physical science majors by throwing so much math and physics and chemistry at them when they join the university. That it’s boring and kills their natural creativity and that we should get them more chances to design right away and whatnot. First, if you are going to be a professional scientist or engineer, you need to know that stuff. There is no way around it. You cannot do/create/design anything new and have it work without being able to recognize whether or not it violates the basic laws of nature. So there is no doubt in my mind that a solid foundation in basic math, physics, and chemistry is the core of physical science education. I don’t know how we make it less boring and more appealing — I thought all of it was fascinating to begin with. There are freshman design courses sprouting all around the country, many with a humanistic component, where kids are taught to interface with the communities and solve actual existing problems. I think that is great and helps motivate a lot of kids, but we can’t forget that in order to be independent scientists and engineers we have to give them a lot of basic science tools — sure, it’s cool to make a product for someone in the community as a freshman, but don’t forget that there was an instructor there to catch the (often obvious) fallacies in the many iterations of the design. For most kids, we are not stifling their unique unadultarated genius with these basic courses; we are giving them the tools so they would be able to work independently to express their creative ideas once they have their diploma in hand.
But perhaps what would help more than anything is somehow magically undoing the years of programming in middle and high school that tell kids math is stupid and boring and useless, and that only hopeless nerds like science and engineering…
xykademiqz 
Oh, where to start…
First, majoring in a subject at the interface of physical science and engineering without linear algebra and ODEs is just insane. In. Sane.
Second, regarding this:
People say that we discourage our physical science majors by throwing so much math and physics and chemistry at them when they join the university. That it’s boring and kills their natural creativity and that we should get them more chances to design right away and whatnot.
A few days ago I said something about needing much more rigorous, high-level, demanding freshman courses in physics and calculus. A very progressive colleague with diversity grants said that if we do that all of our sophomores will be white males. So, basically, he said that women and minorities can’t do hard calculus. But he’s progressive, he smiles the right way, has diversity money, and slings the right lingo. So he gets away with it.
I don’t think women and minorities will undermine the rigor of STEM, but touchy-feely white males with patronizing attitudes certainly will.
Third, regarding intro physics: The firehose issue is half of it. Every physics department in the country covers too much material, and they always blame the engineering school. But they also strip out the calculus, and they have only the admissions office and k-12 system to blame. Go look at any of the popular intro books. Say, Halliday and Resnick. Yes, there is some calculus in the derivations. Yes, there are a handful of end-of-chapter problems that require calculus. But the vast majority of the problems can be solved without calculus.
Here is what my attitude is. You might have the ability to do math and calculus-based physics, but maybe you come from a crappy school, or maybe you never thought you were very smart, or maybe you were relentlessly fed the information that girls and black kids can’t be scientists and you belong to these demographics. I think everyone would agree that we would ideally like to identify people who have the potential to do well but who may not have even thought that STEM would be a path for them. I think having introductory courses that are light on math may open these subjects to people who don’t come in with the best preparation for whatever reason.
Maybe people who could do all sorts of things decide they want to pursue a major because of the societal impact they could have if you let them engage in a community project early on. But most of the projects that are done this early are actually very hands on, can be done and are done by someone with a high-school diploma. Perhaps the moral of the story is that most kids would be happy doing something with their hands and really don’t need college…
But in college, in the physical sciences, sooner or later you have to pay the piper and get the math and physics that you need in order to do your job. I think a lot of department and college administration want to have their pie and eat it too: we are introducing all these technically-light courses at the start of the studies in order to attract students. But then we also want to guarantee that they finish in 4 years. And that they can have a gazillion free credits that they can spend however they like. What that does is squeezes out the math and physics that they really need, it’s not just that us out-of-touch professors enjoy torturing people, this stuff is important and has to be done at some point if you want your degree to be worth squat.
I don’t know what the answer is. If you have a kid who went to a good high school and knows what they want, they might be ready to just get into the more complicated stuff and will be bored with the lighter fare. Then you might have a cohort where some might be able and interested, but are not prepared or are otherwise unsure, and could get up to speed pretty quickly if offered the right courses. For them, there should be a different path towards the major. I am not saying that it’s easy to try to fit a variety of preparations, I don’t know how to do it. But I know that by junior or senior year everyone better be able to do some freakin’ calculus.
As for the math-light fare, there is plenty that can be done with little math in lower-level physics. For instance, I realized yesterday my class does not know what happens when you put a dielectric in an electric field (hint: polarization). They all know that there is this thing called the relative permittivity and they can plug it into formulas, but cannot actually describe what is going on in the material (field displaces the positive and negative charges so little dipoles are induced, what’s a dipole anyone?) For instance, if we are going to skip math in intro physics courses, maybe we could actually spend time on describing qualitatively the stuff that is going on; after all, I learned a lot of physics in middle and high school, much of it without calculus.
Finally, I think much of the problem is that everything is always someone else’s problem and someone else’s fault. I can blame it on intro physics and math, they can blame it on high-schools and middle-schools… At some point we have to take responsibility for teaching the students what they need to know even if they should ideally already know it. There should be gatekeeper courses, staffed with the best teachers, that should be rigorously taught and that a student would have to pass with no less than a B to even get into the higher level courses. A variety of remedial courses could feed into these ones. This probably works in very prestigious places; in many others, setting the bar too high hurts enrollments, and we can’t have that, now can we?
Yep, in the end, it’s all about enrollments.
I’m open to the argument that maybe freshman year isn’t the time to hit everyone _too_ hard. I’m skeptical, but I get the argument, and if somebody comes up with a compelling alternative, one that still involves some significant rigor sooner rather than later, I’ll defer.
The problem is that it’s never the right time. “Well, we can’t be too hard in freshman stuff, because…” OK, sophomore stuff? “No, no, you see, they only got so far as freshmen…” Well, junior year we really need to go rigorous to get them where they need to be? “No, no, once they’re juniors, if they’re still in the major, you really have to be committed to keeping them, rather than doing a bait and switch and hitting them with things they weren’t prepared for…” OK, senior year? “Now, now, they’re seniors, they need to graduate, you can’t ambush them.” Master’s? “Well, really, a Master’s program should be a bridge to the PhD, run in a compassionate mode that recognizes the gaps that need to be filled to get students prepared for the PhD.” (Somebody is currently writing a grant like that.) PhD? “Now, now, ask yourself, do you want to be supportive and get people through, or do you want to just hit people hard and set these intimidating expectations that will have implications for diversity?” (Those are the words of a guy on my hall who wants to collaborate with PhD programs to get more students in.)
At some point, somebody, somewhere, has to hold students to a high standard and show them the full depth of the theory and abstraction that is inherent to the subject.
This is breaking my heart. The students that don’t get the best education in the fundamental principles will not be able to perform as well. I understand administrators thinking that hands-on experience in design is beneficial, but there is a place for both theory and application. Although theory should always precede application. I view this like teaching someone how to hang a picture: The student knows that the nail goes in the wall and the wire hangs from the string. Without knowledge in physics and math (gravity, the force of the hammer, direction of the vector forces on the wall and nail) the student will improperly position the nail and the picture will fall. They need to know why the nail points slightly upward, and why more than just the tip should be in the wall. As the core curriculum gets more and more dumbed down I’m going to hate to see what kind of engineers and scientists we churn out in the next 10 years. What’s the point of encouraging more students from joining the physical sciences if those students aren’t as competent as they should be? We’re doing them and their future employers a disfavor in this case. I wonder what can be done though. This movement away from core fundamentals is like an out of control boulder and getting in the way will only get you crushed.
I wish that I had been encouraged more in math years ago. I really like the more mathy side of my work, but just don’t have a good background in it so find my learning curve very steep. I somehow managed to work my way through Probability, which was no small feat as my calculus skills were ridiculously wanting. But a nice guy who sat near me in class became my study partner, and he taught me all kinds of cool tricks that made so much sense. I wish I had had that experience in high school rather than in graduate school, as Probability is very cool. I definitely think everyone should learn more math and learn it early in their lives — every time I turn around it seems like there is another example of how useful math can be, even outside of math and physics.
While I share your concern about under-prepared students, I want to disagree with you about the importance of early design courses in engineering majors. I have just added an optional, doesn’t count towards the major, design course for freshmen in bioengineering (http://gasstationwithoutpumps.wordpress.com/freshman-design-table-of-contents/). This is not to replace physics, calculus, chemistry, or other preparatory courses, but to give them some idea why those subjects are important to them. Trying to design a photospectrometer makes them realize why Bragg’s Law matters—something that would not occur to them in the usual cram-and-forget physics course, where they see no relationship between the physics and what they think they’ll be doing later.
I also disagree with the notion that “theory should always precede application”. In fact, they’ll retain the material better if the theory and the application are taught together, neither preceding the other. The real travesty comes when students spend all their time “preparing” by learning theory, and never get around to applying it. That is what prompted me to create a new course Applied Circuits for Bioengineers (http://gasstationwithoutpumps.wordpress.com/circuits-course-table-of-contents/) which tries to teach students useful parts of electronics circuits, without first boring them to death with an applied math course 90% of which is never used by working engineers. The prototype run of the course last year was quite successful (the students were able to design and build useful amplifier circuits), and I’m hoping that this year’s run of the course will inspire some of the students to continue into bioelectronics (where they will have to take the boring EE circuits course, but now with some understanding of what the point is).
I notice that our graduate school curriculum has also had this recent “progressive” trend, where our graduate students now get to choose whatever classes they want to take, and we don’t need to worry whether they have a good foundation in biochemistry or genetics. Of course, this becomes problematic later when they are troubleshooting experiments and then can’t easily figure out why things aren’t working, since that requires some knowledge of biochemistry.
Some of my colleagues and I have had a big debate about which we should be seriously urging to consider a PhD. (Insert “Of course, ultimately it’s their life, and if they make a different choice than we recommend, I wish them the best and hope they succeed” disclaimer here.) Some of them will recommend any student who is good at executing a project. However, there’s more to a PhD than just performing the technical tasks. You have to understand the background and theory and context behind the project, understand the abstract ideas that are being tested or that underlie the techniques, and grasp the potential bigger directions. I have students whom I would unreservedly recommend to be members of a research team, because I know they will execute the project, but I have big qualms about their ability to conceive a project.