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I TA'd for an undergrad ODE course for two semesters. I'm a grad student at a public university with very good undergrad engineering students. Nonetheless, with

I TA'd for an undergrad ODE course for two semesters. I'm a grad student at a public university with very good undergrad engineering students. Nonetheless, with the course I taught, at least, the main problem was that WAY too much was packed into a single semester. I suspect that this is the same everywhere. For example, about a month and a half of the course was devoted to systems of linear equations. These were students who, a priori, knew basically no linear algebra, being asked to understand an entire linear algebra course, with some extra stuff thrown in (you know, the differential equations), in six weeks. In order to solve a general system of constant coefficient linear odes, you have to take a matrix and compute its Jordan canonical form. The students I taught were performing this calculation by the end of the unit, but it was of course a joke. On their exam, they were asked to do this calculation (in differential equations language), and most of them were able to do it because they were good students and had memorized the procedure. Then, in another question, they were presented a 5x5 matrix, told that its only eigenvalues were 2 and -2, and asked if it was invertable. I don't think anyone gave a reasonable answer. What is the point of that? Edit: Everyone should be aware of this amazing Gian-Carlo Rota quote, the entirety of a book review on contemporary philosophers: "When pygmies cast such long shadows, it must be very late in the day."

gh02t 9y ago
> These were students who, a priori, knew basically no linear algebra, being asked to understand an entire linear algebra course, with some extra stuff thrown in (you know, the differential equations), in six weeks. Yep, Diff Eq 1 (ODEs) and Diff Eq 2 (PDEs) for us as undergrads were exercises in memorization, even as a math major. I didn't really understand them until after I took a (well, several) linear algebra classes, after which it clicked that it was basically all the same theory.
eli_gottlieb 9y ago
You don't make students take Linear Algebra before differential equations? I thought students were supposed to take Lin-Alg alongside their Calculus 2 or Multivariable Calculus course, then have all that in their heads for DiffEqu.
- BeetleB 9y ago
  >You don't make students take Linear Algebra before differential equations? In my university curriculum, linear algebra was taught after. Perhaps my ODE course was watered down, but that wasn't a problem at all for us.
  - ianai 9y ago
    We had to take 2 linear algebra and an ODE course (amongst other things). The first LA class was second year level and the second was senior level. The ODEs were in between. I feel that's a good way to go about it.
tomxor 9y ago
>The students I taught were performing this calculation by the end of the unit, but it was of course a joke. On their exam, they were asked to do this calculation (in differential equations language), and most of them were able to do it because they were good students and had memorized the procedure. This is a prime example of what I believe is wrong with traditional education (i'm not judging your teaching ability of course), as you are obviously aware, this is more of a box ticking activity than learning in the sense of having any actual understanding. This has always personally caused me a great deal of trouble, for whatever reason I can only learn substantially through understanding - attempting to memorise procedures when I don't have time to understand the underlying workings is like trying to eat cardboard for me, in that sense I am a bad student and am exiled to purely self taught methods. Although I am quite content learning on my own, it makes me feel like much of my formal education was a big waste of time, If I could go back in time knowing this I would avoid it altogether. My experience is hopefully a more dated view by now, I also hold out hope that the new exposure the internet has given courses through MOCs who provide no kind of certification will by proxy refocus traditional education more on the value of learning than certification. Also in the UK at least there are some new ranking systems emerging for universities that are more focused on learning like TEF, although indirect that is at least a step in the right direction.
- sordidasset 9y ago
  I'm in the same boat as you. 25 and starting my career, severely limited by my poor performance in school. Sundays are study days from now on. Hopefully I can catch up.
  - tomxor 9y ago
    I think it's widely accepted that if you are in tech, your success is far more dependent on your actual ability, and schools haven't ever exactly been able to help with tech careers so far. It's only University level certifications that make any difference for your prospective employers, but that does not necessarily guarantee the skills you need as an engineer (if that's what you are aiming for), and many businesses recognise this. I got into full time programming job at around your age after a variety of education routes in sciences and arts (no comp-sci) and variety of crappy jobs. No one seemed to be particularly interested in my lack of certifications when it came to interview time (even though they all have them on the job app). Once I could talk shop and show some small pieces of work and my potential could be recognised I was hireable. I'm not saying it's ever easy to get a foot in the door, but if you focus on the work, your ability will show through in the interview process (if they are not simply a large corporation hiring through box ticking criteria, probably a bad place to start out when you are a junior anyway).

gh02t 9y ago

> These were students who, a priori, knew basically no linear algebra, being asked to understand an entire linear algebra course, with some extra stuff thrown in (you know, the differential equations), in six weeks. Yep, Diff Eq 1 (ODEs) and Diff Eq 2 (PDEs) for us as undergrads were exercises in memorization, even as a math major. I didn't really understand them until after I took a (well, several) linear algebra classes, after which it clicked that it was basically all the same theory.

eli_gottlieb 9y ago

You don't make students take Linear Algebra before differential equations? I thought students were supposed to take Lin-Alg alongside their Calculus 2 or Multivariable Calculus course, then have all that in their heads for DiffEqu.

BeetleB 9y ago
>You don't make students take Linear Algebra before differential equations? In my university curriculum, linear algebra was taught after. Perhaps my ODE course was watered down, but that wasn't a problem at all for us.
- ianai 9y ago
  We had to take 2 linear algebra and an ODE course (amongst other things). The first LA class was second year level and the second was senior level. The ODEs were in between. I feel that's a good way to go about it.

tomxor 9y ago

>The students I taught were performing this calculation by the end of the unit, but it was of course a joke. On their exam, they were asked to do this calculation (in differential equations language), and most of them were able to do it because they were good students and had memorized the procedure. This is a prime example of what I believe is wrong with traditional education (i'm not judging your teaching ability of course), as you are obviously aware, this is more of a box ticking activity than learning in the sense of having any actual understanding. This has always personally caused me a great deal of trouble, for whatever reason I can only learn substantially through understanding - attempting to memorise procedures when I don't have time to understand the underlying workings is like trying to eat cardboard for me, in that sense I am a bad student and am exiled to purely self taught methods. Although I am quite content learning on my own, it makes me feel like much of my formal education was a big waste of time, If I could go back in time knowing this I would avoid it altogether. My experience is hopefully a more dated view by now, I also hold out hope that the new exposure the internet has given courses through MOCs who provide no kind of certification will by proxy refocus traditional education more on the value of learning than certification. Also in the UK at least there are some new ranking systems emerging for universities that are more focused on learning like TEF, although indirect that is at least a step in the right direction.

sordidasset 9y ago
I'm in the same boat as you. 25 and starting my career, severely limited by my poor performance in school. Sundays are study days from now on. Hopefully I can catch up.
- tomxor 9y ago
  I think it's widely accepted that if you are in tech, your success is far more dependent on your actual ability, and schools haven't ever exactly been able to help with tech careers so far. It's only University level certifications that make any difference for your prospective employers, but that does not necessarily guarantee the skills you need as an engineer (if that's what you are aiming for), and many businesses recognise this. I got into full time programming job at around your age after a variety of education routes in sciences and arts (no comp-sci) and variety of crappy jobs. No one seemed to be particularly interested in my lack of certifications when it came to interview time (even though they all have them on the job app). Once I could talk shop and show some small pieces of work and my potential could be recognised I was hireable. I'm not saying it's ever easy to get a foot in the door, but if you focus on the work, your ability will show through in the interview process (if they are not simply a large corporation hiring through box ticking criteria, probably a bad place to start out when you are a junior anyway).