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Do the math: too much calculus? (2012)

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Re: Do the math: too much calculus? (2012)

#91

Post by lordnacho »

krschultz wrote: post #77

I graduated with a mechanical engineering degree, meaning I took 3 semesters worth of Calc and 3 more semesters worth of differential equations. So I'm not one to hate on math or calculus specifically. But I think high schools should focus more on statistics. Statistics is relevant to more fields than calc. It matters a lot more in business and in all the jobs where you use calc you will also have to use statistics.…

I second that. Stats is so much more applicable, and it is also the area where common sense will fail you the most. Simple things like birthday paradoxes, Gambler's fallacy, Monty Hall problem, and so on are all contrary to common sense yet not taught in schools.

And you need stats all the time. Every time someone says crime has never been worse, you need to know how to decide if you believe it. When someone says flying is safer than driving, you need to know how to compare. A lot of stats thinking is also not formulas, but qualitative things like "Am I comparing apples to oranges".

Calculus by contrast is pretty common sensical. Acceleration is the derivative of velocity, you find the local extremes by finding the zeros of the derivative, the integral of a net shaped field is the rim... that all makes sense with some pictures.

I also haven't come across it much in finance, apart from derivatives work, where funnily enough you can't do with high school calculus, but you need stochastic calculus. Which contains some quite statistics related concepts.

Re: Do the math: too much calculus? (2012)

#92

Post by gozur88 »

AstralStorm wrote: post #17

Personally, I have always wondered about the prominent position trigonometry and geometry get. As it is typically taught, it is the most useless thing, the time spent there would be much better spent on algebra, calculus. From basic theorem of algebra flows trigonometry and a lot of number theory, while from calculus with some linear algebra flows geometry. The rationale is probably history.

Trig is a pretty useful subject for the skilled trades. Framing a house, as mmmpop notes, but also things like plumbing and cement work. If you don't go on to college, or you don't major in engineering or math, calculus is pretty useless. I've never once used calculus outside work, but I have used trig.

Re: Do the math: too much calculus? (2012)

#93

Post by lordnacho »

jameshart wrote: post #23
rhizome wrote: post #19

Earlier quoted context omitted.

I would have done much better in math if the class after Geometry was something other than pre-trig.

As an alien to the US education system, I am always completely confused by these 'pre-' course designations. What on earth is 'pre-trig' or 'pre-calc'? I mean, I got all the way up to undergraduate level in mathematics and I never needed to learn 'pre-' anything.

Same experience here. I went to international school, so I often ended up with American friends who'd talk about Algebra 1/2/3, pre-calc, trig, geometry, etc.

Makes no sense to me. All those things are related. There's a picture that shows you why Pythagoras' Theorem is true. And why the difference of two squares is never prime.

You'll have had a whole summer holiday between trig and algebra if they're separate things. Surely they are taught as a kind of whole?

Re: Do the math: too much calculus? (2012)

#94

Post by Someone »

jameshart wrote: post #23
rhizome wrote: post #19

Earlier quoted context omitted.

I would have done much better in math if the class after Geometry was something other than pre-trig.

As an alien to the US education system, I am always completely confused by these 'pre-' course designations. What on earth is 'pre-trig' or 'pre-calc'? I mean, I got all the way up to undergraduate level in mathematics and I never needed to learn 'pre-' anything.

I'm already baffled by the distinction between algebra, trig, and calculus.

Where I live, it was just called 'math'. The first time I encountered algebra was in university, and that started with groups (a set and an operation on pairs of items in the set)

As to the 'pre': I have a masters in math, and lots of what we did was in some sense pre.

For example, calculus on real variables showed you how to define differentiation and integration and how to rigorously prove lost of theorems (pro tip: if you can't make heads or tails of an exam question, at least write down "let epsilon > 0")

Next, we basically went through the same set of theorems but in multiple dimensions, but showed that those rigorous proofs had glaring holes, but hey, now you know better. Also: infinities are weird (pro tip: the area under a 2D curve can depend on the order in which you add up its parts).

Next, calculus on complex numbers extended that and showed that those rigorous proofs had glaring holes, but hey, now you know better (pro tip: every contour integral you compute at an exam has a value of plus of minus 2n pi, with n typically being plus or minus one)

For math majors, the next step was measure theory: that definition of integration we started with? Forget it. Lebesgue came up with something that's better. And by the way, those proofs we told you about have glaring holes (let's spend a few hours proving that cutting a rectangle across a diagonal gives you two parts that each have half the rectangle's area). A few of the functions that we proved cannot not be integrated can be, if you use this new definition of how integration works.

That seems a waste of time, but I don't think it is. Very few people can jump in at the deep end and survive; the first iterations are necessary to prepare one's mind for the next steps.

Given the above, I think you will have had various 'pre-' things, even though they weren't named so.

Re: Do the math: too much calculus? (2012)

#95

Post by ashark »

sdenton4 wrote: post #79
dboreham wrote: post #36

Earlier quoted context omitted.

In the US, problem #1 is that it is very hard to find people who understand Mathematics sufficiently well to teach it effectively, who are willing to work for the salary typically paid to a teacher. For example, my 8th grader is being taught "Higher School Algebra" by a teacher who last year taught 5th grade and by all accounts has to leave the classroom often to get tips on the material from the 7th grade math teach…

Yeah, the line in the article about demand for calc teachers outstripping the supply suggests an obvious remedy... Unfortunately, the fragmented (ie, redlined) us public school system means that higher teacher play is impossible in lower income areas. So private schools will pay more for the calculus teachers, and the low income public schools will continue multi-classing pe teachers for the task. And in another twen…

> Unfortunately, the fragmented (ie, redlined) us public school system means that higher teacher play is impossible in lower income areas.

The lowest-income school districts around here pay higher salaries than the nicest districts by a solid 20-30%. Most teachers with options still won't work there because the environment is frustrating, unrewarding, dangerous, and toxic.

Re: Do the math: too much calculus? (2012)

#96

Post by [deleted] »

baldfat wrote: post #56
CalChris wrote: post #9

Earlier quoted context omitted.

Berkeley EECS grad. I didn't go the device physics route but I used calculus about twice in 4 years except in physics classes.

The beauty of calculus is that you actually understand the Real World. For example I taught my daughter factions this way. Me: "These factions you see them? Now see these decimal points?" Her: "Yeah I hate factions they are stupid!" Me: "Factions are the only consistently real numbers below 1 and decimal points for the most part are made up numbers. 1/3 is 1/3 and never .3333." Her: "I always thought it was the otehr…

[deleted]

Re: Do the math: too much calculus? (2012)

#97

Post by eanzenberg »

rconti wrote: post #84
baldfat wrote: post #6

I think we teach Calculus wrong in a deep fundamental way. We should incorporate more high math concepts earlier into education BUT people are always afraid of anything past 4th grade math! "A minority of students then wend their way through geometry, trigonometry and, finally, calculus, which is considered the pinnacle of high-school-level math. But this progression actually “has nothing to do with how people think,…

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…

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).

Re: Do the math: too much calculus? (2012)

#98

Post by ghaff »

lordnacho wrote: post #91
krschultz wrote: post #77

I graduated with a mechanical engineering degree, meaning I took 3 semesters worth of Calc and 3 more semesters worth of differential equations. So I'm not one to hate on math or calculus specifically. But I think high schools should focus more on statistics. Statistics is relevant to more fields than calc. It matters a lot more in business and in all the jobs where you use calc you will also have to use statistics.…

I second that. Stats is so much more applicable, and it is also the area where common sense will fail you the most. Simple things like birthday paradoxes, Gambler's fallacy, Monty Hall problem, and so on are all contrary to common sense yet not taught in schools. And you need stats all the time. Every time someone says crime has never been worse, you need to know how to decide if you believe it. When someone says fly…

I suspect calculus is less commonsensical to most people than you think :-) That said, I've argued the parent's point for years. Basic stats/probability/economic biases are really fundamental stuff and don't require a lot of complicated math if you don't want them to.

There are some basic calculus concepts that are useful. Area under a curve. Basic derivatives (for finding maxima/minima, etc.). But the truth is that I've rarely used calculus outside an academic setting and I use at least basic statistics/probability thinking all the time.

Re: Do the math: too much calculus? (2012)

#99

Post by gnarbarian »

jessriedel wrote: post #81
gnarbarian wrote: post #58

Earlier quoted context omitted.

Sorry here is a better source: https://nces.ed.gov/fastfacts/display.asp?id=75

You continue to not back up your claim. That link talks about "all post secondary institutions", not universities. Why don't you just edit your original comment to remove the claim?

I am using statistics that I know to be true about my university (University of Alaska Anchorage). As far as I know UAA is typical for state run universities.

I am having a hard time finding aggregate data online that supports (or contradicts) my claims on a national level beyond what I have already provided. Unfortunately the edit timer has already expired for my comments so I can't delete or alter them. If you can find reliable data that contradicts my claims reply to my root post and I'll be happy to upvote it.

Re: Do the math: too much calculus? (2012)

#100

Post by jameshart »

greendragon wrote: post #45
jameshart wrote: post #23

Earlier quoted context omitted.

As an alien to the US education system, I am always completely confused by these 'pre-' course designations. What on earth is 'pre-trig' or 'pre-calc'? I mean, I got all the way up to undergraduate level in mathematics and I never needed to learn 'pre-' anything.

They're not always required, but they try to bridge what you already know (or are supposed to know) with what is to come and move at a slower pace. It's also sometimes like an extra option for the less mathematically inclined who are still required to take such a number of math courses. On the other hand the only 'pre-' course I ever took (I tested out of pre-algebra somehow) was 'pre-calculus with honors'. I don't r…

There's a difference between AP calculus in Alberta and British Columbia? :)
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