Ok, a bit of context: I am currently a Ph.D. student in Maths; and I have been teaching various parts of courses in university maths and physics for eight years now (starting in my second year of undergrad.). I have run tutorials/recitations on subjects ranging from discrete maths to graduate partial differential equations to quantum mechanics to electromagnetism on two different continents. While this is nothing special, almost every graduate student in any subject has to do some teaching, I have summarized my experience to give weight to the following statement.
I have seen the future for science and engineering and I AM AFRAID.
As you may have guessed, most of the students I've taught are of the engineering/computer science mentality. Yes, some are maths and physics majors; but they are the vast minority of my students. Anyway, I usually end up teaching differential equations to these budding, eager minds of tomorrow; this is usually the last math course many engineering students will ever have to take. It's not important to understand what differential equations are beyond the fact that they play the central role in physics which, in turn, is the base of all engineering sciences.
Let me come back to the reason why I am afraid. I would not be concerned if students struggled with differential equations; it can be a pretty tough course and quite dry for those who are not fascinated by maths like I am. I am afraid because many of these budding engineers can't do simple algebra; some can't even manipulate fractions. This isn't so prevalent with my students in Australia (where I currently go to school/teach), universities are much more selective on this continent than they are in the US (due to the fact that you can still get a nice trade job that's protected by the gov't with a HS or community college degree... but I'll go into that another time). Anyway, by the time students get into one of my classes, they have been weeded down considerably more than anything in the US system; and hence, they typically do very well in my tutorials.
Now, before I tell you about students in the US, keep in mind that is where I did my undergrad. Instead of giving you a whole long spiel, let me give you a snapshot of the last class I taught in the US. The class I was assigned to was a honors level course in partial differential equations. This was a third/fourth year course that only the most outstanding undergraduates were allowed to take. Almost all of my students were engineers. Make no mistake, this course was hard... but these were the brightest students in one of the top applied maths/engineering universities in the US (the campus was 35k-40k students). Not ONE student got a perfect score on ANY homework throughout the entire semester. That's right, there wasn't a single perfect score in that class. What was worse was something like half of those students didn't have basic algebra skills. A few couldn't consistently manipulate fractions.
So, let me recap here. What I last observed was that the very top eschelon of engineering students, students who were being groomed to go into engineering design for disciplines ranging from civil to aerospace engineering could barely do algebra in their final maths course at Uni. This SCARES me. These people will be designing the aeroplanes, cars, bridges and electronics of tomorrow and most of them don't have a mastery of the most basic levels of algebra.
If you think I'm over-reacting, take a look at this:
This was the Tacoma Narrows bridge located in Washington State. This bridge was built in 1940 and literally got blown apart due to bad civil engineering. Essentially, the winds on the canal the bridge spanned caused the bridge to start torquing and oscillating in just the right manner that caused the bridge literally to shake itself apart. Technically, the winds drove a structural resonance in the bridge that caused it to rip itself apart. This phenomena could have been avoided if the engineers did a proper analysis that is essentially based on simple differential equations. Now... if your engineers can't do algebra... they sure as heck can't do differential equations and thus they can't prevent things like this from happening. Scary huh? Now imagine the analogy for aeroplanes: if this type of phenomena isn't properly accounted for, it correlates to the wings on the aeroplane vibrating out of control (yes they can vibrate at very high frequencies) until the literally rip themselves apart. In the case of a passenger jet, this would also mean the fuselage would be ripped apart as the wing goes straight through the body of the plane. Scared yet? Oh oh! Let's not forget how Nasa lost a several million dollar satellite because engineers couldn't convert units in a thrust calculation. Not only that, when they realized the satellite was going off course, THEY DID IT AGAIN! Subsequently, that satellite was permanently lost. Yeah, Nasa engineering couldn't figure out how to multiply by a conversion factor. If you aren't scared by now, there is something wrong with you.
Personally, I love flying and used to have the highest confidence in the structure and design of modern aeroplanes. After teaching so many engineering students; I now can't help tensing up whenever I'm on a plane in turbulence.
