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Do the math: too much calculus? (2012)

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

#181

Post by tnecniv »

ivansavz wrote: post #18

I think linear algebra is a much more valuable and general-purpose math tool. I'm not sure how feasible it would be to teach linear algebra topics "properly" to high schoolers, but even a half-assed linear algebra would be more useful than calculus. The connections to geometry, general systems thinking, formal math methods, and countless applications of linear algebra are just the kind of thing students need to get t…

LA wouldn't be any harder to teach than Calculus. In fact, if you wanted to teach proof based math that isn't Geometry, it's probably the easiest subject area.

I don't think you can get rid of Calc in HS though. It's just too useful. I think room can be made for both subjects, though.

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

#182

Post by jiaweihli »

I grew up 3 years ahead of my classmates in math. I found everything up until calculus to be easy but elegant - algebra, geometry, probability, trigonometry. Much like programming, there were often multiple ways of the solving the same problem, and deriving a formula was feasible and logical.

In contrast, I found calculus to be mind-numbingly boring. It required memorizing and reciting formulas upon formulas. It was the first time I felt that math was tedious, and pushed me away from majoring in math in college.

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

#183

Post by cageface »

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.…

Linear algebra is also a lot more useful in real world applications than calculus. As it stands calculus seems as much like some kind of college hazing ritual as it does an essential part of anybody's education.

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

#184

Post by gohrt »

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…

Your idea did not translate into English. I think you are trying to say that most decimals we see in real life are approximations, not exact measurements, while fractions are exact?

This has nothing to do with calculus, though.

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

#185

Post by gohrt »

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.

"pre-trig" doesn't exist most anywhere.

"pre-calculus" is whatever isn't covered in intro to algebra and geometry, but needed for differentiation and integration:

https://www.khanacademy.org/math/precalculus

* Trigonometric equations and identities

* Conic sections

* Vectors

* Matrices

* Imaginary and complex numbers

* Sequences, series and induction

* Probability and combinatorics <-- more of a side topic, usually.

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

#186

Post by gohrt »

lordnacho wrote: post #93
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.

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 thing…

Did you learn all of K-12 math in one year? Which year?

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

#187

Post by hal9000xp »

I do recommend to read these articles:

http://www.artofproblemsolving.com/articles/calculus-trap

http://www.artofproblemsolving.com/articles/discrete-math

http://www.artofproblemsolving.com/articles/what-is-problem-...

Short recap: Mathematics is not bunch of dull rules. Education system puts way too much emphasis on memorization of dull rules instead of problem solving and developing strong intuition. Calculus overrepresented and discrete math underrepresented in education system.

As a person who currently is rediscovering math from scratch, I find these articles very insightful. I rediscover math from problem solving/intuitive point of view rather than beating my head against the wall of formal definitions.

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

#188

Post by rocqua »

analog31 wrote: post #175
pps43 wrote: post #133

Earlier quoted context omitted.

The problem is, it's hard to understand statistics without knowing at least basic calculus. As soon as you move from coin flips to probability density, you need derivatives and integrals. These days you can solve many practical statistical problems with Monte Carlo, but understanding why those curves look the way they do is still very useful.

I had kind of a strange experience. While in college, I worked as a math tutor. Since I had taken one semester of stats, the tutoring center decided I was qualified to run a tutoring session for the non-calculus stats course. I was happy for the money, and had been reasonably successful with other tutoring assignments. When we got to continuous distributions, we kind of hit a wall. Here's the puzzle. Suppose the data…

The chance of choosing 0.5 from the interval 0 to 1 is 0. So if you want the change of choosing between 0.4 and 0.6 in that interval, you can't just sum all chances between 0.4 and 0.6 you'd have infinity x 0 which isn't 0.2 .

Instead, to deal with this 'a lot of really small things' we need a slightly different approach. Then draw a pdf, and talk about area under the curve. Perhaps relate this to the discrete case where the curve is just really blocky.

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

#189

Post by JohnStrange »

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.…

But doesn't understanding statistics require a solid understanding of calculus anyway?

Or do you mean statistics as a bunch of applied methods, where you follow some recipes without understanding the math behind them? It's taught that way even at university level, but I can't see how this could be helpful in the long run.

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

#190

Post by lordnacho »

gohrt wrote: post #186
lordnacho wrote: post #93

Earlier quoted context omitted.

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 thing…

Did you learn all of K-12 math in one year? Which year?

You certainly can't learn it as separate things. I had classes called "Mathematics" every year, all the way to the end of high school.

Got a bit more separate at university, but not really.

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