[eagsalazar2]

99% of kids who were "always good at math" will continue to be good at math in college. So the entire article is a rant against a straw man to make a case for his beliefs on how math should be taught. Not that I disagree that math education is stupid, but just saying this rant is has no foundation.

The 1% of kids who did well in high school and then fail in college because they are so attached to their rote memorization of techniques have a profoundly broken approach to problem solving that is bigger than the education they received. I've tutored many kids exactly like that and it is very hard to pry them free of that mentality. It is part of their personality. Also, those kids were never really good at math in high school either and were battling (using tutors for help frequently) uphill to get through their entire primary curriculum.

The much bigger and real tragedy of math education in the US is the very large percentage of kids who have been labeled as "not good at math". Those kids 99% of the time are actually plenty good at math but have fallen out of the system because of frustration and a poor fit for their learning style. Those kids don't end up in universities trying to take calc for science majors at all because they believe they aren't capable and that is a crime.

[ColinWright]

  > 99% of kids who were "always good at math"
  > will continue to be good at math in college.

As someone who works as a part-time teaching fellow at a UK University, this does not match my experience. I find that many who do well at school do not, in truth, understand what they're doing. Some do, but many have become adept at magically divining the right process to follow, and then following it without mistakes.

So your claim that this is "a rant against a straw man" does not match my experience. As a result, I'd be interested to know what leads you to make the claim I quote. Do you have figures, or personal experience? And are you talking about math as in Analysis, Number Theory, Logic, Topology, and similar, or are you talking about "Math Methods" such as are required in subjects such as Physics and Engineering?

For reference, this:

  > The much bigger and real tragedy of math education
  > in the US is the very large percentage of kids who
  > have been labeled as "not good at math". Those kids
  > 99% of the time are actually plenty good at math but
  > have fallen out of the system because of frustration
  > and a poor fit for their learning style.

That is absolutely true., and is why I give some 150 talks every year to school age kids, trying to encourage them to engage (continue, return, or start) with math.

[eric_h]

A friend of mine who does math tutoring for high school seniors and college freshman told me that many of her students who did well on their AP Calculus exams did not actually understand what a derivative/integral was. They could procedurally find the derivative/integral for a given function, but they didn't know what it meant.

Admittedly, this is anecdotal, but it does seem to support the argument/rant in the article.

I feel that I, personally, was very lucky in my high school mathematical education in that my teachers exposed us to the concepts/meanings of all of the operations we were doing long before they exposed us to the procedural trivia of finding integrals/derivatives and the like. It is unfortunate that not all schools are like this.

[tunap]

Just another anecdote... when I passed Calc 225 my 1st semester my counselor informed me my math prerequisites were fulfilled(counting college prep in HS). She did not encourage me to consider pursuing further, just that I didn't need to take any more and focus on "business". Working PT/3rd shift & taking 19+ credits a semester I figured my path was paved in business so I took her advice...Until 2nd year, taking motherload of hard classes, I was informed she was incorrect & I had to take probability. I missed first the first week of class, assuming cakewalk, and never caught up. The dominoes fell from there, my GPA suffered & after 2 years of midnight merchandising I realized I did NOT want to work sales or anything remotely retail. After grad, I washed out of corp sales job & Merrill job in under 8 months. Went back to construction and the picture hasn't been especially rosy ever since. Cest la vie.

TLDR: Take the maths for the sake of knowledge, even if you don't 'have to'. It can't hurt.

[mtourne]

I recently read the book Calculus Made Easy. The way it teaches the material is very intuitive and if you understand the premises you should be able to re-derive all of the formulas yourself. I would highly recommend it to high school students and teachers alike.

I remember being taught about derivatives with the formal limit formula, then all the tricks for finding them (power rule etc), and finally finding function extrema using derivatives; all before developing much intuition about the concept.

[josephschmoe]

I disagree. This attitude...and teaching style often extend well into college.

I literally had a professor who read from the book for lecture and then did his tests out of the book. Granted, it's probably one of the best physics text books ever written (David Griffiths) but it's very, very difficult to learn this way. Students resort to memorization when they have no other options. Nearly every student could solve problems within a range of 'like' problems (change a variable or two, a power, etc.) but had no actual ability to solve truly unique equations in the subject or even formulate their own questions.

This was a 3rd year physics course at a top-50 school.

[garenp]

FWIW, I'd probably put myself in the same category the OP writes about.

I hit a wall in calculus 2 in University, because previously I had been able to rely on simply showing up and not putting in much effort to still do "pretty good". That was the first time I did poorly in any math/science course, and was a pretty big wake-up call. As a result, I ended up having to study more to fill in the gaps.

I was naive, came from a poor background with crappy public schools, and didn't think of math as particularly important to focus on until I saw how useful it was in physics. I don't think it's an all too uncommon story.

[mcguire]

There's not really a conflict here.

"Math" up through high school in the US, and through that freshman calculus course, is mostly about calculating the right answer to a problem. Math is a much bigger subject; calculations are a trivially small part of the whole.

On the other hand, "The much bigger and real tragedy of math education in the US is the very large percentage of kids who have been labeled as 'not good at math'" is also very true. And many of those people might not be good at calculations but would be fine with the rest of the subject.

[eagsalazar2]

I think many of you are misunderstanding my point. I'm not saying math education is good or that students are well prepared. I'm saying that most students who succeed in HS will continue to succeed in college in spite of everything else. I definitely agree most freshmen students don't understand calculus in any deep way but most good students will by the time the are done with their freshman series. So again, I'm not defending the system, I'm nitpicking the argument :)