[ansible]

> I paid attention to lectures and stared at the text, but couldn't really understand the material. For the first part of a linear algebra course, students who don't mind blindly following mechanical processes for solving problems can do very well.

I had a similar, though sort of opposite experience.

In high school, I breezed through the material, and started teaching myself calculus during the summer to prepare for university. Other than being a lazy student, I had no problems taking the 2nd semester advanced calc 2 and 3 courses my freshman year. I totally get what's being taught. There weren't a ton of practical examples, but I can easily see (for example) what the purpose of integration is, and how and why you'd do it in two or more dimensions. I could work the equations, no problem. Everything is great.

Along comes sophomore year, and still thinking I am hot stuff, I take advanced linear algebra and differential equations. More of the same, I thought.

Well... we seemed to spend the entire semester just solving different kinds of equations. No explanations given as to what they are for, where they are used, or what the point of any of it was. I struggled, for the very first time.

I either got a D or F for the mid-term exam, which was shocking to me.

We had one chapter where we were doing something practical. This is where you have a water tank, and a hole in to bottom. Because the pressure lessens as the tank empties, the flow rate is not constant. However, you can solve this via diff equations, and I really grokked it. I finally saw the point for some of what we had been doing. But it was just that one chapter, we skipped any other practical aspects for what we were studying.

I did end up pulling out a 'C' with that class, to my relief. Sure, most of the blame for my lousy performance must rest with me, because of my poor study habits. And a little blame can go to the TA, who wasn't a good communicator, so that hour every week was kind of useless. But I also blame the material and how it was presented.

[crispyambulance]

I think that whether or not students do well, there's a common theme in university math curricula for non-math majors. Basically, math gets taught as a kind of "toolbox" of techniques. Unless there's a strong follow-up in subject matter courses (for example in engineering coursework), those math skills effectively evaporate.

Some places use a rigorous "proof-theoretic" approach in math curricula. It's much harder and takes more time, but it's better than merely grinding on hundreds of easy calc-101/diff-eq problems, because students gain an understanding that doesn't erode as easily once they forget "the tricks".

More CS, engineering and science students, IMHO, should dabble in math department courses beyond the the usual "required" sequence for their majors. It can be eye-opening and provide long lasting benefit to take a hardcore real-analysis course, abstract algebra or a number of other courses in math.

[dunefox]

> More CS, engineering and science students, IMHO, should dabble in math department courses beyond the the usual "required" sequence for their majors

That was absolutely not allowed at my faculty (admittely computational linguistics, but I would have massively benefited from math courses). No courses other than the predefined ones, no matter how relevant. Now I have to learn so much afterwards, it's not even funny.

[crispyambulance]

> ...have to learn so much afterwards, it's not even funny.

It's true.

The sad thing is these problems start well before university when high schools pressure students into "advanced" math coursework without demonstrating mastery of previous topics. It builds a shaky foundation and sets the student up for a lot of needless difficulty later on.

Much better to slow down, focus on fundamentals early on and then build breadth in university coursework.

[sandyarmstrong]

Oh man, Differential Equations. After doing well in Calc 1-3 I thought it would be no big deal. I paid attention in class and barely did the homework because it all seemed so straightforward but it was boring and I was not engaged.

I came in for the first exam, sat there for maybe 15 minutes reading the questions, and realized I had no idea how to solve any of them.

Luckily it was before the drop date! That was a turning point where I decided to only take classes that seemed fun. For me that was discrete math, number theory, abstract algebra, etc.

[hhmc]

It's probably an oversimplification, but differential equations -- as a field of study -- tends to be much more a grab bag of tricks than many branches of mathematics.