Here’s a neat blog post, by way of Aretae:

- How to become a faster decision-maker (Sebastian Marshall)

Aretae summarizes (you should read the whole thing):

Success comes only with failure. Everyone fails a lot… the question is how much you do. More done = more success and MORE failure.

Now, that’s useful on its own, but I told you that so I could tell you this.

Over at the Volokh Conspiracy, Kenneth Anderson laments that pre-law students would be best served by technical degrees in things like STEM or economics, rather than a purely Arts-based degree, but run afoul of the filter course syndrome:

[A]n amazingly bright and ambitious former student who had gone off to Yale emailed to tell me that my advice [to take economics courses in pre-law] wasn’t working out. Why?

And since law school would look only at her GPA overall, no one would care that she had struggled in a tough area because she thought she needed to know it.[…]Because at a world class institution, she could do great work in history and philosophy, but despite 800 math SATs, she couldn’t keep up past the first econ class in the major.Much as I admire Greg Mankiw, in other words, a famous blog post of his on “Why take mathematics as an economist” gets to the heart of the problem. He candidly admits that it is a form of signaling even when not necessarily related to the actual conceptual material at hand.

I don’t mean that it is not hugely important for professional economists, of course it is — but that’s the point, there’s no curriculum suited for the non–professionals-in-training. Mankiw says, with charming frankness, that basically the math is one long IQ test so you can show your fellows how smart you are.

(Emphasis added.)

My first instinct, of course, is to snark about how the fluffy Arts majors with top-notch SAT scores* might not be as smart as they thought they were if they can’t hack intro calculus. But let’s be fair (yeah, I know): at a top-notch school, keeping up with the pace of study requires a lot of focus. I can imagine that there’s a fair bit of crossover between courses in keeping up with a math major — economy of scale, if you will — that just doesn’t happen if you’re trying to do a BA with a side order of number theory.*

Dr. Anderson goes into great detail developing an argument about science departments signaling their greatness by the quality of their elite graduates and so on and so forth, but essentially the role he sees for technical courses is instrumental: you learn about economics or engineering because it’s useful, not because you want to get hired by someone who’s impressed by your B.A. in Econ or your B.Eng. So if the knowledge is about utility, not signaling… why worry about playing the signaling game if it’s going to weed you out?

Let’s tie these two posts together. If you think that learning math, or programming, or econ, or any number of other “book” disciplines (I’m excluding lab-bench stuff like the hands-on side of organic chem because it doesn’t fit the title) will help you, pick yourself up a textbook and get started. Sneak into introductory lectures. Crawl around the internet looking for beginner-level resources and devour them. If you want to learn how to write computer programs, crack open a beer and a text editor and start writing Ruby code. You probably won’t get as good as quickly as you would have if you’d pursued a degree in the area, but you’ll get a *hell* of a lot better than most people without those degrees.

I hate the idea of weeder courses. During my undergrad, Calculus I & II were the STEM weeders, and the physical sciences departments hated it, because it wiped out a lot of students who might otherwise have gone on to successfully study a STEM subject, but lost confidence in their abilities because the Math department insisted on teaching these to packed 300 person lecture halls with a handful of overworked TAs to act as study buddies. I took Calc I at a small Tech College with 15 students in the class and a hands-on teacher, I learned a ton and got an ‘A’. The next semester I transferred to the University and found myself in Calc II with 300 other students, a prof who showed up, talked at us, and left (he had no office hours), and a tired TA. I actually failed Calc II the first time through (got a ‘B’ on the second try). The material between Calc I & II is not that much more difficult, but the style of teaching made a huge difference. It took a long time to get over that hit to my academic confidence.

Funny that; I struggled in Calculus I-IV as well, and I mostly attribute that to (a) not thinking math was going to be useful until I got to grad school and (b) profs, selected for and motivated by their research, being forced by the department to teach courses no-one wanted to touch. (The two counterexamples to (b) were Calculus II and Linear Algebra I, both of which featured enthusiastic profs, and in both of which I did well.)

If both of our complaints are representative, the problem might be with instructor selection rather than the “weed-out course” model. I’d guess that the Calc prof you had at the tech college wasn’t as research-oriented as the one you had at the university.

By way of an example, I TAed the computing science weed-out course (Software Engineering I — C, C++, Make, and Unix… and how to write programs rather than just code) four times in undergrad, and while a few people dropped the major a lot of people were able to keep up with the fast pace and took a lot away from the course. Part of that I attribute to my own brilliance as a TA (*cough*), but a lot of it had to do with the fact that most of the profs and the long-term head TA were heavily invested in the course’s success. In the last semester that I TAed the course, two of the profs had moved on to other things and the head TA had graduated. Things did not go nearly as well.

That is very likely. My Calc I instructor was just that, an instructor, not a tenured prof. He enjoyed teaching the class & made the effort to build a curriculum that was fun & interesting. At my alma mater, the engineering college wanted to create “math for engineers” courses, because the profs were tired of re-teaching concepts that students didn’t get the first time through. The math department threw a fit because it knew that if the engineers stopped taking MATH courses & switched to ENG courses, the math department would shrivel up. IMHO, the problem is that math profs teach to math students, and engineering & other sciences students do not grok math necessarily the same way. I don’t care about Integers or Derivatives in & of themselves, but rather, I care about how their utility will help me solve puzzles (like the CFD code I enjoy working with).

That’s how it worked out in my undergrad. MATH 101/102/201/202 were ‘geer-specific courses, covering PDEs and such in first year. MATH 114/115/214/215 were “mainstream” courses, usually requirements for all science students, and did the usual “limits and derivatives”/”univariate integrals”/”multivariate calculus”/”differential equations” thing. MATH 117/118 were “honours” math courses intended for honest-to-Jesus math majors, and started by building up arithmetic from axiomata, Dedekind cuts, and so on. But then again, the Faculty of Engineering was big enough to push around basically everyone else, and the Math department was the redheaded stepchild of the Faculty of Science.