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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 the

by 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.
ddellacosta 13y ago
I just want to say, as someone who is now re-educating themselves in Math, I really love your Math ∩ Programming site. Thank you for this lovely resource.
akavi 13y ago
Uh, don't most students take calculus senior year of high school?
- lutusp 13y ago
  In the U.S.? Not really. This source -- http://nces.ed.gov/fastfacts/display.asp?id=97 http://nces.ed.gov/fastfacts/display.asp?id=97 -- says that in 2009, just 16% of U.S. high school students took calculus. And a common complaint by college professors is that high school calculus courses teach rote procedures without explaining calculus in any depth -- the students know how to solve calculus problems, but they don't actually understand the subject.
  - ndeine 13y ago
    That's my perspective on it. I first took calculus as a junior in high school, and the majority of it boiled down to memorizing what the derivative of `x` type of function is and what the integral of `y` type of function is. When the AP test rolled around I was really struck. The problems were about the flow rate of water descending into a tank and what happens when you put a drain here with this rate of flow, etc. Completely different from our earlier problems which could be solved by rote memorization. And from my perspective - one of a student who knew a bunch of calculus "rules" but lacked understanding of how calculus really worked - this was incredibly difficult. I got a 3, which is passing, but opted to take beginner-level engineer's calculus when I got to college anyway. Even if you "learn" calculus in high school, it does not teach the level of mathematical maturity required to understand the higher level manipulations. This kind of thought is the foundation for any good engineer, and I have no regrets about retaking the course.
acjacobson 13y ago
Thanks for posting the article. I wish I had known more about this when I was in high school. I have recently found myself becoming much more interested in mathematics when thinking about very simple concepts and asking why it is a certain way vs. memorizing the rule. I think my 10+ year aversion to the subject is rooted in the fact that it felt like nothing more than rote memorization in high school, and thus a dreary subject to learn anything about.

by j2kun 13y ago

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.

ddellacosta 13y ago

I just want to say, as someone who is now re-educating themselves in Math, I really love your Math ∩ Programming site. Thank you for this lovely resource.

akavi 13y ago

Uh, don't most students take calculus senior year of high school?

lutusp 13y ago
In the U.S.? Not really. This source -- http://nces.ed.gov/fastfacts/display.asp?id=97 http://nces.ed.gov/fastfacts/display.asp?id=97 -- says that in 2009, just 16% of U.S. high school students took calculus. And a common complaint by college professors is that high school calculus courses teach rote procedures without explaining calculus in any depth -- the students know how to solve calculus problems, but they don't actually understand the subject.
- ndeine 13y ago
  That's my perspective on it. I first took calculus as a junior in high school, and the majority of it boiled down to memorizing what the derivative of `x` type of function is and what the integral of `y` type of function is. When the AP test rolled around I was really struck. The problems were about the flow rate of water descending into a tank and what happens when you put a drain here with this rate of flow, etc. Completely different from our earlier problems which could be solved by rote memorization. And from my perspective - one of a student who knew a bunch of calculus "rules" but lacked understanding of how calculus really worked - this was incredibly difficult. I got a 3, which is passing, but opted to take beginner-level engineer's calculus when I got to college anyway. Even if you "learn" calculus in high school, it does not teach the level of mathematical maturity required to understand the higher level manipulations. This kind of thought is the foundation for any good engineer, and I have no regrets about retaking the course.

acjacobson 13y ago

Thanks for posting the article. I wish I had known more about this when I was in high school. I have recently found myself becoming much more interested in mathematics when thinking about very simple concepts and asking why it is a certain way vs. memorizing the rule. I think my 10+ year aversion to the subject is rooted in the fact that it felt like nothing more than rote memorization in high school, and thus a dreary subject to learn anything about.