Comment by rconti | Hacker News Reader

Comment by rconti | Hacker News Reader

Parent Full thread

IME the #1 problem is the failure to teach anything WELL. I took AP Calculus in high school, and today, as a 35-year-old, I'm still continually surprising myself with the problems I realize must be related to Calculus-- but nobody bothered to tell me. Things like the 'ol speed vs acceleration vs jerk kind of problems.

All calculus ever taught me was to apply these formulas to those problems (for some reason) and that dx/dy meant derivative of x with respect to derivative of y.

It boggles my mind that nobody simply bothered to tell us what a goddamned derivative was; what the word meant, and what real-life examples were. The "with respect to" was the most confusing and least useful concept. If we knew what the things were in the first place, the fact that one was "with respect to" the other would have been obvious. And "with respect to" could have been replaced with "relative to" in our minds, because we'd know what the things were.

Calculus seemed to be entirely repeating nonsensical mantras and applying impenetrable methods to problem sets and receiving an answer out the other end.

I'll also echo calls for more time on algebra. Surely the problem with algebra was that I wasn't a devoted enough student to repeating problem sets ad nauseum, but I just never got the 'knack' for it. I understood what I was supposed to be doing, but I was never satisfied with the answer "you'll start getting a feel for what to simplify to what after you do enough problems" as an explanation. It was frustrating to not feel like there was a concrete process to it all.

This made later Calculus and Statistics hard for me, because many exams would simply be 2 enormous problems ; the calculus I could get through but I couldn't simplify the problems quickly enough to be able to apply calculus or statistics at all.

When calculus is taught badly no one knows how to apply it even when the problems are staring them in the face.

I TA'ed physics at one of the top Ivy League universities in the US, and what I found amazing was that we didn't require calculus for our introductory mechanics course. You don't get into these universities without taking all the highest level courses in high-school, which means that almost everyone in the class must have taken at least one semester of calculus. But we still avoided the simple v = dx/dt calculations, the logic being that physics was too difficult to combine with the math they'd all learned years before.

My friends in economics told similar stories: "Don't worry, we don't have to use calculus to calculate marginal cost, we can use 'the midpoint method'", followed by 20 minutes of explaining an arcane nondeterministic procedure to approximate a derivative.

Math should be motivated by science and modeling, otherwise it's just an exercise in diddling numbers.

> Math should be motivated by science and modeling, otherwise it's just an exercise in diddling numbers.

I like a lot of what you said, but I do disagree with that point. Immediate application of mathematical concepts may be gratifying, but making it the _only_ motivating factor behind maths can result in students who conflate the underlying machinery with its application [1].

Taking a pure maths course in undergrad with related subject matter prior to one of my Controls classes made the class substantially easier to understand. Learning the abstract concepts beforehand let me see the common applications more quickly than others.

I think the biggest difference is that when I learned some Calculus through Physics, it was a little more difficult to go from a concrete basis to a more general one. My understanding ended up being based on analogies to other concepts until I went back and covered the theory again.

[1] This is all my own opinion, I'm not an educator so the most I can do is pull from my own pedagogical experience :)

Dude, the "with respect to" clause is a pretty deep idea in calculus that really matters in multi-variate but not so much in uni-variate.

I keep seeing how society needs better math education, whether it be statistics or calculus. Well no shit. Unfortunately those are extremely hard subjects to teach in high school. I'd argue statistics is harder to teach than calculus. In calculus you usually derive things by following the formulas. In statistics there isn't always a formula, logic, or path you can follow.

I took both AP Calc BC and AP Stats in HS and I'll tell you I learned a lot of calculus then and am learning a lot of statistics now (I'm 32).

See my other post, but I have to agree stats is incredibly hard to teach at the high school level. I also see the problem with grandparent's failures at applying math.

The huge problem as I mentioned elsewhere is that stats is really applied math. You do learn a lot of regurgitation-style stuff - formulas, proofs, blah blah, but it's all useless without applying it. Moreover, stats draws from so many different areas in math and requires analytical skills that are closer to many of the things scientists emphasize in learning to conduct studies and experiments. This makes it almost unsuitable to teach the more valuable parts of stats at lower levels because the students can't possibly be prepared.

At best, I think you can teach some general things about stats and the mentality I described of being analytical and skeptical. Unfortunately, stats is just really hard for anyone to properly and comprehensively learn who isn't going to be able to invest a lot of time both learning pre-requisites and then all the different areas of stats. It's like learning to be a carpenter and only understanding how to work a hammer, but not a saw, measuring tape, or anything else.

Looking at Common Core anything besides old arcane way of math will never be accepted :(

Reply on news.ycombinator.com