Tuesday, September 17, 2013

What's Wrong with Undergraduate Education

I wrote an article last year about what's wrong with high school math. I thought it was a pretty good article. But just last week a guy in Switzerland posted an article about what's wrong with graduate-level education...actually it was his letter of resignation from his PhD studies. It was a devastating critique of the pretensions and self-delusions of higher-level academia, and it instantly attracted a collosal number of hits. It speaks to a lot of the reasons why I never got a PhD.

But in between the high school level and the PhD level, there is the huge field of undergraduate education. I've written a few articles on my other blog about some of my experiences as an Education student, but I have a much more important story to tell about my experience years ago in the Faculty of Engineering. After all, everyone already suspects (at least I would) that Education profs are just a bunch of fad-following pretenders...but engineering? That's got to be for real...isn't it?

In fact, there is a tremendous weakness in engineering education which is a direct consequence of the things that Gene Bunin wrote about in his PhD expose. It's because the whole  of academia...arts, sciences, engineering, what have you...is entirely based on the trickle-down theory of education: that the undergraduates will get an "excellent" education because they are in the presence of high-level academics doing "excellent" research. The theory breaks down because the whole premise of "excellence" in research is based on cliques of professors patting each other on the back for generating meaningless grist for the publication mills.

In engineering the consequence is that instead of studying under practical-minded engineers with real-world experience, students learn from academic Engineering PhD's who wouldn't know the first thing about putting up a strip mall (never mind a bridge, or a foundry!) but know all about how to get "research" published in journals. And a major aspect of this cult of publication is to put supreme value on everything new and "original", which has a flip-side of viewing classical knowledge with scorn and disdain. To most professors, undergraduate education is nothing but a mass of boring formulas that have to be mastered before you are qualified to do "important" research at the "cutting edge of knowledge".

In engineering the harm is double-edged: not only do you have a complete absence of the practical knowledge you are going to need on the job (I never heard of the "Building Code" until years after I graduated!) but the theoretical knowledge...the thing that the education system supposedly prides itself on...is a disaster. Accreditation committees compete with each other to prove that they are maintaining ever-higher standards of "excellence", so the curriculum gets cluttered up with so many advanced mathematical topics that it is utterly impossible for any normal student to understand what he is supposed to be learning. There is no choice but to memorize formulas and drill on problem sets so you can pass the exams. Understanding what you're doing?...that's out of the question.

I never saw the truth of all this more clearly than when I went around the Faculty of Civil Engineering, twenty years ago at the University of Manitoba, asking professors and students the Diving Board Question.

I was working at the time as a Lab Technician in the Structures Lab. My job was instrumentation: we would glue strain gauges up and down a steel or concrete beam, subject it to stresses, and measure the distortion in the gauges. It was quite fascinating, and I found myself learning quite a bit about structural theory. (My undergrad degree was in Electrical. And no, I never saw the Electrical Code either until I graduated.)

Anyhow, one day I had just finished helping  a Master's Student run his load tests, and as I was eyeballing the strain gauge data, I remarked to him that until I had started working in this lab, I had never understood how a diving board works.

"What do you mean?" he asked me. I explained that I never realized that the curvature of the board was everywhere different as you moved down the board from one end to the other...that it didn't simply bend into an arc of a circle.

My friend was still baffled. I drew a sketch to show him what he meant. "That's not how a diving board curves", he said. And he drew his own version, which was different from mine.

This was too much. I had to ask someone else. And the next thing you know, I was going from one grad student to another, setting out the problem and asking for their solution. And everyone had a different answer!

Over the next week I asked maybe fifty grad students and as many undergrads, and seventeen professors. Only eight of the seventeen profs got it right. Of the students, I was appalled to find only three that answered correctly.

This was no trick question, or an accident that could be blamed on one bad undergrad prof. The question I was asking was basically the iconic case of a bending beam...you literally couldn't ask a question more central to the basic understanding of beam theory. And the grad students were mostly international, from the four corners of the world. What I was seeing was a true reflection of the way civil engineering is taught in the universities.

Later I wrote this story up and submitted to the Winnipeg Free Press, where it ran as an opinion piece. I was immediately condemned by the engineering and academic communities. One professor of Electrical Engineering wrote a letter to the paper where he explained that Marty Green was this kind of smart-ass who was known for going around asking trick questions to embarass people. I will never forgive Bob McLeod for that. He was certainly not there when I asked anyone the question, so how would he know? What he did was as bad as the police officers who back each other up when one of them is accused of beating a suspect...it's a lie that people justify by a misguided sense of collegial solidarity.

I can prove that it wasn't a trick question. No, I can't prove it to you or to Bob McLeod, because you weren't there. But I can prove it to myself because I was there. First, I always took great pains to sketch out the situation, discuss what I meant by "curvature", and ask the subject if he understood what I was asking. I even drew little strain gauges on the beam, showing them hooked up to a meter the way I do it in the lab, to show that the "curvature" was exactly the thing that we measured with strain gauges. Only then would I ask him to sketch the distribution of curvature along the board...just as though you had a series of ten strain gauges equally spaced...what would the readouts look like?

I said I would prove it wasn't a trick question...well, that's not the proof. The proof comes later. After they gave me the wrong answer, I would draw the graph showing the right answer, and then I would ask them if they agreed. No, they would shake their heads, that doesn't look right. Or they'd come up with some flim-flam nonsense argument about the anisotropic properties of the wooden board to justify themselves.

That's not what you do when you've been suckered by a trick question. You say, "Oh, of course I knew that. They way you asked the question, it sounded like you asking this." No one said that to me.

There's one more proof that it wasn't a trick question, but I'm going so save that for later, when I take up the question of why everybody gets it wrong. Right now I want to return to the question of why I'm so pissed with Bob McLeod for publically dismissing my case on behalf of the university. I believe that there is a tremendous sickness in higher education and something needs to be done about it. People ask me, well what would you do? I tell them it doesn't matter what I propose...nothing is going to happen as long as people don't recognize that there is a problem in the first place. As long as these profs go running around to conferences, publishing papers and patting each other on the back, and giving each other awards for "excellence", and talking about how they're pushing back the frontiers of knowledge...as long as they don't admit to themselves that something is wrong!...there's no hope. What I did by publishing that article was to open the door a tiny crack, to the possiblity that people should think twice about what goes on in academia.  If Bob McLeod hadn't jumped forward to slam that door shut, I suppose someone else would have probably done it instead. But he's the one who did it, and I can never forgive him for that.



Anonymous said...

Dear Marty,

I was a bit surprised, because I could immediately recall a really good structural engineer (who also happens to be a prof at an IIT) who had done his PhD from Manitoba roughly about two decades ago or so.

But, of course, I didn't doubt your story either. People often are taught and examined to learn by rote. Excellence in grades almost always depends on whether you can rapidly solve the stereotypical problems or not---and, with relative grading, simply, whether you can do so faster than the next fellow, or not.

Anyway, I am, in a way, poor in doing analysis and very poor in recalling formulae. (In general, "poor in maths.") So, despite my specialization being computational mechanics, I couldn't recall the simple beam theory, but, still, even as I went on reading your post, I had this "intuition" that you would be right, and yet, simultaneously, I could also recall a bit of that theory and so could get a sense of why those graduate students and professors would react the way they did to you.

I mean, I did recall that in the simple beam theory, the derivation is a bit weird: you first assume a constant curvature (i.e. assume a circular shape), then express strain, and from strains, using Hooke's law, get to the stresses, and from there, you get to the bending moment and shear forces. I recalled that much---the _order_ of the _concepts_. And it was thus that I could see where the graduate students and professors might be coming from.

Yet, I had the "seat of the pants" feel that your observations would be right. And, also that an advanced consideration such as inhomogeneous material, non-Euler beam theory, etc. shouldn't really be necessary to explain it.

So, I decided to do a quick "reality" check. I consulted the Wiki page: http://en.wikipedia.org/wiki/Euler-Bernoulli_beam_theory. I got my suspicion confirmed, but a reference of the kind I wanted wasn't very directly written down in there, and so, I did a further Google search on "curvature of cantilever beam," consulted the first link it throws, ... and there we have it. Please see: http://www.capphysics.ca/PhysLab/Phys114115/exp_2%20-%20loaded%20beam/content/BEAM.pdf.

On p. 4 of this document, it clearly states that (for small deformation), the _local_ shape can be approximated as a circle. On p. 16, it directly states that the curvature decreases "as the wall is approached."

People obviously failed to distinguish between the circular curvature assumed for the _local_ _differential_ element via deriving the _differential equation_ of the beam on the one hand, and the value of the local curvature that is obtained _upon integration_ of that differential equation after applying a certain combination of the 4 boundary conditions (because it's a fourth-order differential equation). The two are different.

For the particular problem of the cantilever beam, yes, the curvature increases linearly as we go from the diver's end towards the support.

Since the Euler-Bernoulli beam equation is only an approximation to the real cantilevers, in experiment, you might have perhaps observed a non-linear increase. However, this equation has proved its worth in many different scenarios. Though the diver's board would be better modeled with a large deformation theory, the Euler-Bernoulli beam theory _should_ still give a good indication of the general _trend_, and as a general trend, you must observed a decreasinng curvature as x increased (or as you went away from the support).

... A non-uniform curvature showing such a trend is what we always observe when we take, say, a plastic foot-rule and idly play with it by bending it. Which, incidentally, was the observation source from where my "intuition" had come, in the first place---not a back-of-the-envelop "calculation," or even recalling the simple fact that the deflection of the beam is cubic in x, but that bit of a plain, simple, direct observation.



Anonymous said...

I always write at length, and ran out of space in my comment above.

A couple of points:

(i) No, not all PhD folks are there only to get PhDs and in the process found a publishing mill of their own---at least not yet, and at least not so in the engineering departments.

(ii) In my latest post on my blog, I have made reference to your take on John Baez' crackpot index. ... I enjoy your blog, and hope that your troubles with the university are sorted out in your favour, ASAP.


Marty Green said...

Thanks for the good wishes, Ajit. You anticipate some of the points I wanted to return to when I finish this story tomorrow. But I'm still trying to remeber who your colleague was...I left the U of M exactly 20 years ago, so he was probably a student when I was there.

The thing is, I worked in the Structures Lab, so I knew all the PhD students (including a lot of Middle Easterners) but I don't remember any Indians. But there were one or two of Structural profs from India who where, I think, strictly theoretical, so I might not have even met their students. I can't remember their names because I didn't have much to do with them (and you people have such long names anyhow). But they were part of my "survey" and I'll mention them again when I return...

Anonymous said...

Hi Marty,

Re. my good wishes. Sure. Actually, they are more than just the goodwill that one keeps in general, including towards strangers... You see, your explanations (or at least those on the many topics that I read here at your blog) are obviously so good that it's a pity if even someone like you has troubles getting (or keeping) a neat teaching post.

Re. the structural engineer... Umm... He is not a colleague---I don't work at an IIT (in fact, currently, I am jobless)---but it's someone I know, sort of. It's Prof. Yogesh Desai, of Civil Engg. Dept. at IIT Bombay. ... There are two points of reference. In 2003/04, as I was just about trying to get registered for my (second) attempt at PhD (now in India, at the University of Pune), I had attended a one-day workshop on FEM held in Pune where Desai had delivered one of the workshop lectures. His lecture was marked by a definite concern for applications and, simultaneously, an unusual clarity about FEM which made it stand out among all the presentations. (It's not that the other presentations were any particularly bad; it's just that they just were of the usual kind, mainly, either the deducto-mathematical kind or the dumb-colorful-diagrams-and-very-advanced-technology kind). Desai had succeeded in bringing forth the very essence of the FEA---its basic idea---in a simple manner, in a way that would be understandable also to working engineers. He did keep the maths on the slides, alright, but his presentation didn't become a slave to those equations (or to maths in general). Instead, he supplied a rather physical viewpoint with which to understand those equations---the very idea of the FE approximation itself. So, it was easy to remember him. ... Later on, in 2009/10, when I was working as a software development consultant in SoftTech, Pune, I was helping add some additional FEM features to our existing product. At that time, we had some plans to involve IIT Bombay, in particular, Prof. Desai, in that development and validation effort. As it so happens, our CEO, Mr. Gupta (my age), had done his MTech from IIT Bombay, where as a student he was junior to Desai, which must have been during the 1983--85 times. They, apparently, had shared the same student hostel in IIT Bombay, and that's how knew each other personally right from those times. Anyway, it was in the context of that potential collaboration that, in 2010, I once accompanied our CEO for a visit to IIT Bombay, for a discussion with Prof. Desai. That's when I got to know him on a more direct personal level---though I am not sure if he could now place me off-hand, without supplying this context to juggle his memory. BTW, from his Web page, I gather that Desai was at Manitoba between 1986--1990, so he might have already graduated PhD before you entered the school.

Anyway, I look forward to your next instalment of this interesting story. (And do feel free to write anything about Indians too! An honest viewpoint is always interesting.)