4 ms·

I can relate to that. College-level calculus burned me so much, I didn't had the algebra background necessary to grok it, much of it is memorizing heuristics a

I can relate to that. College-level calculus burned me so much, I didn't had the algebra background necessary to grok it, much of it is memorizing heuristics and "tricks", and college professors (specially in my public uni) didn't had much patience either. I even did well in other math-related classes, but calculus was a chimera. Unfortunately, I fell so much behind the curriculum that I had to drop out of college to start working full-time. Lately I've been picking up other math-related online classes, and I finally realized that I had never had real exposure to mathematics, and that high-school curriculum is something else. So, there's that too... we are mostly scammed into thinking we've learned something during high-school, and then life happens and you actually figure out you don't know shit. Hopefully I'm a curious person, so I'm always learning something by myself, mostly to broaden my knowledge in other topics, but to not let the gears grind too.

taternuts 13y ago
I definitely remember the first time I could no longer slack off, take 0's on homeworks, and ace tests to get a C+/B and it was in high-school :( I jumped to AP Calculus without taking the pre-requisite AP class everyone else had taken, and I thought I was so cool and smart. By the weeks end I no longer felt so cool and smart - I was completely lost.
- hcarvalhoalves 13y ago
  Calculus sucked more for me because here in Brazil the education system doesn't include it in the high-school curriculum, so unless you're on some top private school, you only first hear about "calculus" in college. In the USA and other places there's exposure to it prior to college, which I believe is sensible. As a side note, I can't stress enough how bad the education system is in Brazil (in the sense of lack of structure, motivation, etc.), even at college level. Almost everything I know is self-taught (including English). I sometimes hear complaints about public school in the USA, and there's a meme that americans are "dumb", but it seems miles ahead to what I had access to.
  - tjr 13y ago
    I don't know if things differ by location or have differed by time, but in my observation many U.S. high school students don't see calculus either.
    - taternuts 13y ago
      Yeah, luckily the area I grew up in happens to have one of the top rated public school districts in the nation, so most things that were offered in private school education-wise were offered in public school as well.
  - mitochondrion 13y ago
    From my experience, there's probably much less calculus-taking going on in American high schools than you think. Of that, even less is anything resembling calculus.
  - rrrazdan 13y ago
    In India we had pretty advanced calculus in our senior and pre senior year. This included extensive use of calculus in physics courses. Electrodynamics was totally calculus based and we used to have lots of 'word problems' involving calculus. This was pretty standard across most schools, so much so that when I went to college to do my engineering we had zero basic calculus classes and went straight to advanced calculus. I have no clue if learning advanced calculus this early helped us or not. Or exposing the whole class to these courses was such a good idea. However now they are easing these courses a bit and moving some of the tougher parts out.
mitochondrion 13y ago
Out of curiosity, whose online math have you done?
- hcarvalhoalves 13y ago
  Some I can recommend that are still available on Coursera: - Introduction to mathematical thinking [1] - Introduction to Mathematical Philosophy [2] - Machine Learning (actually a CS course, but involves linear algebra and some calculus) [3] - Calculus: Single Variable [4] [1] https://www.coursera.org/course/maththink https://www.coursera.org/course/maththink [2] https://www.coursera.org/course/mathphil https://www.coursera.org/course/mathphil [3] https://www.coursera.org/course/ml https://www.coursera.org/course/ml [4] https://www.coursera.org/course/calcsing https://www.coursera.org/course/calcsing
  - mitochondrion 13y ago
    Many thanks!
j2kun 13y ago
It is very rare for an incoming calculus student to know algebra. In fact, I often tell my students that the first goal of college-level calculus is to make them actually learn algebra. It's an extremely sad state of affairs for me (a mathematician). Relevant (an article I wrote): http://j2kun.svbtle.com/you-never-did-math-in-high-school http://j2kun.svbtle.com/you-never-did-math-in-high-school
- hcarvalhoalves 13y ago
  I can vouch for your article. I believe you captured the problem with school-level math. As an anecdote for you, since you're a mathematician: during school I had zero patience for math. I would often study just enough to get a passing grade. On the other hand, I enjoyed physics classes a lot, it involved more problem solving and holistic vision than memorization (since you can just memorize a couple formulas and derive everything else you need - e.g. the second and third equations of motion from the first). Maybe I would have enjoyed math classes more if it involved more intuition and less rote? I'm sure you'll come across kids like I've been during your voluntary lectures. PS: I'll be following your blog.
- gizmo686 13y ago
  My high school curriculum was deliberately set up so that Calculus is where we really learn algebra. 9th and 10th grade were designed to teach mathematical thinking. In 11th grade you have the choice of taking 11th grade math or Calc 1 (with permission of your 10th grade math teacher), both of which would instill algebra (technically, you are aloud to take any math elective, but I think everyone takes at least one of these two). The concept is that, because algebra is being used as a tool to solve a more complicated problem, there is no choice but to actually learn it. Having said that, we did go into it being passingly familiar with algebra, which may be more than you observe in your students. Also, I don't think it is possible to go through the 9th and 10th grade courses without developing some feel for meaningful symbol manipulation. EDIT: I just read your article, I think our math program is like you describe it should be.
  - j2kun 13y ago
    That sounds fantastic. I agree there is some baseline level of rote manipulation people can't get away with, but it's gone too far.

taternuts 13y ago

I definitely remember the first time I could no longer slack off, take 0's on homeworks, and ace tests to get a C+/B and it was in high-school :( I jumped to AP Calculus without taking the pre-requisite AP class everyone else had taken, and I thought I was so cool and smart. By the weeks end I no longer felt so cool and smart - I was completely lost.

hcarvalhoalves 13y ago
Calculus sucked more for me because here in Brazil the education system doesn't include it in the high-school curriculum, so unless you're on some top private school, you only first hear about "calculus" in college. In the USA and other places there's exposure to it prior to college, which I believe is sensible. As a side note, I can't stress enough how bad the education system is in Brazil (in the sense of lack of structure, motivation, etc.), even at college level. Almost everything I know is self-taught (including English). I sometimes hear complaints about public school in the USA, and there's a meme that americans are "dumb", but it seems miles ahead to what I had access to.
- tjr 13y ago
  I don't know if things differ by location or have differed by time, but in my observation many U.S. high school students don't see calculus either.
  - taternuts 13y ago
    Yeah, luckily the area I grew up in happens to have one of the top rated public school districts in the nation, so most things that were offered in private school education-wise were offered in public school as well.
- mitochondrion 13y ago
  From my experience, there's probably much less calculus-taking going on in American high schools than you think. Of that, even less is anything resembling calculus.
- rrrazdan 13y ago
  In India we had pretty advanced calculus in our senior and pre senior year. This included extensive use of calculus in physics courses. Electrodynamics was totally calculus based and we used to have lots of 'word problems' involving calculus. This was pretty standard across most schools, so much so that when I went to college to do my engineering we had zero basic calculus classes and went straight to advanced calculus. I have no clue if learning advanced calculus this early helped us or not. Or exposing the whole class to these courses was such a good idea. However now they are easing these courses a bit and moving some of the tougher parts out.

mitochondrion 13y ago

Out of curiosity, whose online math have you done?

hcarvalhoalves 13y ago
Some I can recommend that are still available on Coursera: - Introduction to mathematical thinking [1] - Introduction to Mathematical Philosophy [2] - Machine Learning (actually a CS course, but involves linear algebra and some calculus) [3] - Calculus: Single Variable [4] [1] https://www.coursera.org/course/maththink https://www.coursera.org/course/maththink [2] https://www.coursera.org/course/mathphil https://www.coursera.org/course/mathphil [3] https://www.coursera.org/course/ml https://www.coursera.org/course/ml [4] https://www.coursera.org/course/calcsing https://www.coursera.org/course/calcsing
- mitochondrion 13y ago
  Many thanks!

j2kun 13y ago

It is very rare for an incoming calculus student to know algebra. In fact, I often tell my students that the first goal of college-level calculus is to make them actually learn algebra. It's an extremely sad state of affairs for me (a mathematician). Relevant (an article I wrote): http://j2kun.svbtle.com/you-never-did-math-in-high-school http://j2kun.svbtle.com/you-never-did-math-in-high-school

hcarvalhoalves 13y ago
I can vouch for your article. I believe you captured the problem with school-level math. As an anecdote for you, since you're a mathematician: during school I had zero patience for math. I would often study just enough to get a passing grade. On the other hand, I enjoyed physics classes a lot, it involved more problem solving and holistic vision than memorization (since you can just memorize a couple formulas and derive everything else you need - e.g. the second and third equations of motion from the first). Maybe I would have enjoyed math classes more if it involved more intuition and less rote? I'm sure you'll come across kids like I've been during your voluntary lectures. PS: I'll be following your blog.
gizmo686 13y ago
My high school curriculum was deliberately set up so that Calculus is where we really learn algebra. 9th and 10th grade were designed to teach mathematical thinking. In 11th grade you have the choice of taking 11th grade math or Calc 1 (with permission of your 10th grade math teacher), both of which would instill algebra (technically, you are aloud to take any math elective, but I think everyone takes at least one of these two). The concept is that, because algebra is being used as a tool to solve a more complicated problem, there is no choice but to actually learn it. Having said that, we did go into it being passingly familiar with algebra, which may be more than you observe in your students. Also, I don't think it is possible to go through the 9th and 10th grade courses without developing some feel for meaningful symbol manipulation. EDIT: I just read your article, I think our math program is like you describe it should be.
- j2kun 13y ago
  That sounds fantastic. I agree there is some baseline level of rote manipulation people can't get away with, but it's gone too far.