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I studied Mechanical Engineering, and it was my experience that several professors are only interested in having the students learn how to solve problems (which

by gusmd 9y ago

I studied Mechanical Engineering, and it was my experience that several professors are only interested in having the students learn how to solve problems (which in the end boil down to math and applying equations), instead of actually learning the interesting and important concepts behind them. My wife went to school for Architecture, where she learned "basic" structural mechanics, and some Calculus, but still cannot explain to me in simple words what an integral or a derivative is. Not her fault at all: her Calculus professor had them calculate polynomial derivatives for 3 months, without ever making them understand the concept of "rate or change", or what "infinitesimal" means. For me that's a big failure of our current "science" education system: too much focus on stupid application of equations and formulas, and too little focus on actually comprehending the abstract concepts behind them.

acjohnson55 9y ago
Nailed it. I remember "hitting the wall" in Honors Algebra II, when I just couldn't keep up with all the new things I was expected to compute: radicals, synthetic division, logarithms, etc. It was a major dent in my math confidence, which up until that point had be reinforced by being told I was "good at math". I didn't start regaining that confidence until Chemistry, when I learned what pH actually meant. That sparked the epiphany that scale was deeply important in nature, and with that motivation, logarithms seemed much simpler. We so quickly forget that most math wasn't discovered as some abstract exercise. But we still teach it that way, with the concepts before the applications.
- kaitai 9y ago
  This is compounded in the weird American class called "precalculus," which is just a random grab bag of math crap that might maybe needed before calculus but might not. In most precalc classes I've encountered, not only is there no explanation of why the concepts will be used in calculus, but there is little attempt to relate the concepts covered in the class. Let's go from linear equations to complex numbers to polar coordinates! And let's not mention that complex numbers and polar coordinates are related! To top it all off, a lot of young college students taking precalculus are taking it as a terminal math class -- they'll never take calculus! It's just for a credit! So you've got some poor kid who hit that wall in high school and is repeating precalc and going through some unit on polar coordinates who will never take another math class again and will somewhat justifiably think this whole thing is stupid. In theory, I strongly support "math for liberal arts"-type classes instead in college. When done well they might cover voting systems and how you can prove there isn't a perfect one, gerrymandering and how you can use math to get several solutions, perspective drawing and its relation to projective geometry and Renaissance art, a bit of number theory and basic cryptography....
  - dsfyu404ed 9y ago
    >"math for liberal arts"-type classes I took a class that met in a room used by a class like that the period prior and got to listen to the better part of it. In the one lecture the prof coaxed them into creating an algorithm for the number of moves to solve a rubix cube based on the number of cells who's configuration is known and where those cells are located on the cube. In a different lecture they were doing the math necessary to cut hypoid gears on a manual milling machine. They didn't even know what they had did until he tied it back to the underlying concept. The quality of those courses depends on the prof.
    - kaitai 9y ago
      > The quality of those courses depends on the prof. Entirely. In theory they are great :) The one you listened in on sounds interesting!
  - acjohnson55 9y ago
    > In theory, I strongly support "math for liberal arts"-type classes instead in college. I love it. They could call it "math"! ;) Seriously, I think that captures an important concept: for the most part, math was developed to serve the needs of humanity. I used to wonder, how do we know our numbers are the "true" numbers? Did we just happen upon one way of computing, and there are countless alternatives that could have been explored? Of course, the answer to that is actually "kinda, yeah". Abstract algebra leads to all sorts of systems that behave more or less like our familiar numbers and operations. And besides the whole numbers, which represent physical quantities, every extension to things like integers, reals and complex numbers are used not because of their tangible reality, but because they do a good job of modeling human concerns. Because my brain has a limited ability to pursue abstraction for its own sake, its this aspect of math that really captivates me. I think that's true for most people.
- Kluny 9y ago
  > when I learned what pH actually meant potential (for attracting) Hydrogen. I had to look it up.
ythn 9y ago
Reminds me of an anecdote in Richard Feynman's book in which the Brazilian education system revolved around memorizing definitions without understanding the underlying concepts: http://v.cx/2010/04/feynman-brazil-education http://v.cx/2010/04/feynman-brazil-education
- gusmd 9y ago
  That was such an interesting read. I live in the US, but am actually Brazilian, born, raised, and educated there (BS and MS). I did have some GREAT professors in college who you could tell loved their subjects so much, and would give amazing, passionate lectures, full of real-life examples, etc. Those shaped my career. But some others were just like the ones in the article. Funny enough, all the good ones were much younger professors (like, in their 30's, 40's), with very few exceptions. Since the original article is from the 80's, maybe Feynman's feedback had some effect? I did go to one of the best universities in the country, so maybe my experience is also different from other people's. I hope it isn't, and I hope it continues to get better over there.
ehsankia 9y ago
It's actually a little scary how much of what we end up doing in life depends on the kind of teachers we get at a younger age. I can trace my academic pathway almost entirely by a few key teachers that had a huge impact on my interests. A really good art teacher or a really good math teacher can really change the kind of future you'll have.
VyseofArcadia 9y ago
> My wife went to school for Architecture, where she learned "basic" structural mechanics, and some Calculus, but still cannot explain to me in simple words what an integral or a derivative is. Not her fault at all: her Calculus professor had them calculate polynomial derivatives for 3 months, without ever making them understand the concept of "rate or change" I've taught Calculus close to a dozen times now. I talked about integrals. I talked about derivatives. I tried to get into the intuitive nature of rates of change and the limiting process of Riemann sums. I used analogies and real-world examples and illustrations and interactive computer demonstrations. Students don't listen to that part of the lecture. They just don't. They listen to the part where I start doing problems on the board, because to them math is about doing things, not concepts. That's only reinforced when they're asked on tests to just do things rather than demonstrate understanding of concepts. If, in a college class, you try to change that up by asking concept questions, you get bad end-of-semester evaluations because you've challenged them in a way they didn't expect and their parents aren't paying good money for them to be challenged. (And realistically it's hard to ask concept questions at that level of mathematical maturity anyway. As answers you get mostly word salad with a smattering of misused jargon. I've tried.) If you try to mix it up and use techniques from inquiry-based learning (Moore-style, flipped classroom, etc.) then you get a stern talking to from administration. > , or what "infinitesimal" means. Probably because even defining infinitesimals with anything resembling rigor is tricky, let alone using them productively. I wouldn't even try it in less than a junior or senior class. There is no such real number that is smaller (in absolute value) than every other real number yet bigger than zero. Infinitesimals, at the calculus level, are a convenient hand-wavy fiction to mask limits and a notational artifact from simpler times. > For me that's a big failure of our current "science" education system: too much focus on stupid application of equations and formulas, and too little focus on actually comprehending the abstract concepts behind them. I tried. Every single time I taught the class I tried to teach concepts. It's really easy to fall to the temptation of just working problems on the board every day, because trying anything else will just give you grief. Grief from the students, grief from your colleagues, grief from the administration. Grief from people like you who constantly chastise us for not being able to explain to teenagers that they should pay attention for the whole class. (I love my adult students though. Non-traditional students are the best.) It's not worth rocking the educational boat if you don't already have tenure. If you do rock the boat you get a reputation for being hard or weird and students avoid your class anyway. You hit a nerve. I've left academia for this and other reasons, but as you can tell I'm bitter about it.

by gusmd 9y ago

acjohnson55 9y ago

Nailed it. I remember "hitting the wall" in Honors Algebra II, when I just couldn't keep up with all the new things I was expected to compute: radicals, synthetic division, logarithms, etc. It was a major dent in my math confidence, which up until that point had be reinforced by being told I was "good at math". I didn't start regaining that confidence until Chemistry, when I learned what pH actually meant. That sparked the epiphany that scale was deeply important in nature, and with that motivation, logarithms seemed much simpler. We so quickly forget that most math wasn't discovered as some abstract exercise. But we still teach it that way, with the concepts before the applications.

kaitai 9y ago
This is compounded in the weird American class called "precalculus," which is just a random grab bag of math crap that might maybe needed before calculus but might not. In most precalc classes I've encountered, not only is there no explanation of why the concepts will be used in calculus, but there is little attempt to relate the concepts covered in the class. Let's go from linear equations to complex numbers to polar coordinates! And let's not mention that complex numbers and polar coordinates are related! To top it all off, a lot of young college students taking precalculus are taking it as a terminal math class -- they'll never take calculus! It's just for a credit! So you've got some poor kid who hit that wall in high school and is repeating precalc and going through some unit on polar coordinates who will never take another math class again and will somewhat justifiably think this whole thing is stupid. In theory, I strongly support "math for liberal arts"-type classes instead in college. When done well they might cover voting systems and how you can prove there isn't a perfect one, gerrymandering and how you can use math to get several solutions, perspective drawing and its relation to projective geometry and Renaissance art, a bit of number theory and basic cryptography....
- dsfyu404ed 9y ago
  >"math for liberal arts"-type classes I took a class that met in a room used by a class like that the period prior and got to listen to the better part of it. In the one lecture the prof coaxed them into creating an algorithm for the number of moves to solve a rubix cube based on the number of cells who's configuration is known and where those cells are located on the cube. In a different lecture they were doing the math necessary to cut hypoid gears on a manual milling machine. They didn't even know what they had did until he tied it back to the underlying concept. The quality of those courses depends on the prof.
  - kaitai 9y ago
    > The quality of those courses depends on the prof. Entirely. In theory they are great :) The one you listened in on sounds interesting!
- acjohnson55 9y ago
  > In theory, I strongly support "math for liberal arts"-type classes instead in college. I love it. They could call it "math"! ;) Seriously, I think that captures an important concept: for the most part, math was developed to serve the needs of humanity. I used to wonder, how do we know our numbers are the "true" numbers? Did we just happen upon one way of computing, and there are countless alternatives that could have been explored? Of course, the answer to that is actually "kinda, yeah". Abstract algebra leads to all sorts of systems that behave more or less like our familiar numbers and operations. And besides the whole numbers, which represent physical quantities, every extension to things like integers, reals and complex numbers are used not because of their tangible reality, but because they do a good job of modeling human concerns. Because my brain has a limited ability to pursue abstraction for its own sake, its this aspect of math that really captivates me. I think that's true for most people.
Kluny 9y ago
> when I learned what pH actually meant potential (for attracting) Hydrogen. I had to look it up.

ythn 9y ago

Reminds me of an anecdote in Richard Feynman's book in which the Brazilian education system revolved around memorizing definitions without understanding the underlying concepts: http://v.cx/2010/04/feynman-brazil-education http://v.cx/2010/04/feynman-brazil-education

gusmd 9y ago
That was such an interesting read. I live in the US, but am actually Brazilian, born, raised, and educated there (BS and MS). I did have some GREAT professors in college who you could tell loved their subjects so much, and would give amazing, passionate lectures, full of real-life examples, etc. Those shaped my career. But some others were just like the ones in the article. Funny enough, all the good ones were much younger professors (like, in their 30's, 40's), with very few exceptions. Since the original article is from the 80's, maybe Feynman's feedback had some effect? I did go to one of the best universities in the country, so maybe my experience is also different from other people's. I hope it isn't, and I hope it continues to get better over there.

ehsankia 9y ago

It's actually a little scary how much of what we end up doing in life depends on the kind of teachers we get at a younger age. I can trace my academic pathway almost entirely by a few key teachers that had a huge impact on my interests. A really good art teacher or a really good math teacher can really change the kind of future you'll have.

VyseofArcadia 9y ago

> My wife went to school for Architecture, where she learned "basic" structural mechanics, and some Calculus, but still cannot explain to me in simple words what an integral or a derivative is. Not her fault at all: her Calculus professor had them calculate polynomial derivatives for 3 months, without ever making them understand the concept of "rate or change" I've taught Calculus close to a dozen times now. I talked about integrals. I talked about derivatives. I tried to get into the intuitive nature of rates of change and the limiting process of Riemann sums. I used analogies and real-world examples and illustrations and interactive computer demonstrations. Students don't listen to that part of the lecture. They just don't. They listen to the part where I start doing problems on the board, because to them math is about doing things, not concepts. That's only reinforced when they're asked on tests to just do things rather than demonstrate understanding of concepts. If, in a college class, you try to change that up by asking concept questions, you get bad end-of-semester evaluations because you've challenged them in a way they didn't expect and their parents aren't paying good money for them to be challenged. (And realistically it's hard to ask concept questions at that level of mathematical maturity anyway. As answers you get mostly word salad with a smattering of misused jargon. I've tried.) If you try to mix it up and use techniques from inquiry-based learning (Moore-style, flipped classroom, etc.) then you get a stern talking to from administration. > , or what "infinitesimal" means. Probably because even defining infinitesimals with anything resembling rigor is tricky, let alone using them productively. I wouldn't even try it in less than a junior or senior class. There is no such real number that is smaller (in absolute value) than every other real number yet bigger than zero. Infinitesimals, at the calculus level, are a convenient hand-wavy fiction to mask limits and a notational artifact from simpler times. > For me that's a big failure of our current "science" education system: too much focus on stupid application of equations and formulas, and too little focus on actually comprehending the abstract concepts behind them. I tried. Every single time I taught the class I tried to teach concepts. It's really easy to fall to the temptation of just working problems on the board every day, because trying anything else will just give you grief. Grief from the students, grief from your colleagues, grief from the administration. Grief from people like you who constantly chastise us for not being able to explain to teenagers that they should pay attention for the whole class. (I love my adult students though. Non-traditional students are the best.) It's not worth rocking the educational boat if you don't already have tenure. If you do rock the boat you get a reputation for being hard or weird and students avoid your class anyway. You hit a nerve. I've left academia for this and other reasons, but as you can tell I'm bitter about it.