How our 1,000-year-old math curriculum cheats America's kids • Hacker News Board

Re: How our 1,000-year-old math curriculum cheats America's kids

#71

Post by dllthomas » Mon, Mar 03, 2014, 6:31 PM UTC

Patrick_Devine wrote: post #69

wisty wrote: post #46

Earlier quoted context omitted.

> Except that once you hit even basic algebra, you quickly run out of applications a young student can relate to. Algebra is problem solving. You have a formula describing the problem, and want to re-arrange it to find one of the variables. It has a lot of useful and logical applications. Trigonometry though ... screw that. "Bob the builder has made a truss, and wants to figure out the angle A. He doesn't own a protr…

There's a really, really simple way to get kids to love trig. Get them to write a video game. Seriously, as a video game programmer, you use trig _every day_. If you want to find the distance between two points when you have the angle (eg. I'm firing a projectile at a certain angle), use cosine for the length of the x axis and use sine for the y axis. You get the hypotenuse from using pythagoras' theorem. If you want…

"If you want to find the distance between two points when you have the angle (eg. I'm firing a projectile at a certain angle), use cosine for the length of the x axis and use sine for the y axis. You get the hypotenuse from using pythagoras' theorem."

Using cosine and sine and then Pythagorean theorem to get the length of the hypotenuse doesn't make sense - in order to get the length of the X and Y components with cosine and sine you need to already know the length of the hypotenuse.

Re: How our 1,000-year-old math curriculum cheats America's kids

#72

Post by theandrewbailey » Mon, Mar 03, 2014, 6:42 PM UTC

wisty wrote: post #46

bane wrote: post #33

I was a terrible math student in school. Looking back, it wasn't because the material was hard, or boring, but because it was completely unmotivated. They may as well have been asking me to organize piles of toothpicks or count ceiling tiles to fill up the class periods. There was simply no sense to it. I think this is partially understood, and the attempted solution is to try to find applications for the math you're…

> Except that once you hit even basic algebra, you quickly run out of applications a young student can relate to. Algebra is problem solving. You have a formula describing the problem, and want to re-arrange it to find one of the variables. It has a lot of useful and logical applications. Trigonometry though ... screw that. "Bob the builder has made a truss, and wants to figure out the angle A. He doesn't own a protr…

> Trigonometry though ... screw that. "Bob the builder has made a truss, and wants to figure out the angle A. He doesn't own a protractor, and can only measure a few of the lengths." Seriously?

You can also throw in some economics: Bob would be fired and/or get better equipment.

Re: How our 1,000-year-old math curriculum cheats America's kids

#73

Post by Patrick_Devine » Mon, Mar 03, 2014, 7:01 PM UTC

dllthomas wrote: post #71

Patrick_Devine wrote: post #69

Earlier quoted context omitted.

There's a really, really simple way to get kids to love trig. Get them to write a video game. Seriously, as a video game programmer, you use trig _every day_. If you want to find the distance between two points when you have the angle (eg. I'm firing a projectile at a certain angle), use cosine for the length of the x axis and use sine for the y axis. You get the hypotenuse from using pythagoras' theorem. If you want…

"If you want to find the distance between two points when you have the angle (eg. I'm firing a projectile at a certain angle), use cosine for the length of the x axis and use sine for the y axis. You get the hypotenuse from using pythagoras' theorem." Using cosine and sine and then Pythagorean theorem to get the length of the hypotenuse doesn't make sense - in order to get the length of the X and Y components with co…

You're right, I did state it a little awkwardly, but the statements are correct. I'll give a more concrete example:

I'm firing a projectile at 52 degrees and it needs to move 10 units. I'm at (5,7), where does the projectile end up?

delta x = cos(theta) * 10 delta y = sin(theta) * 10

So my final position is (5 + 6.16, 7 + 7.88), or (11, 15).

If I already knew how far the delta X and delta Y were, I could get the length of the hypotenuse with sqrt(6.16^2 + 7.88^2). That equals roughly 10, of course. If you want to try this out yourself, just remember that most trig functions are done in radians, so convert theta to radians with pi * theta (degrees) / 180.

Re: How our 1,000-year-old math curriculum cheats America's kids

#74

Post by sitkack » Mon, Mar 03, 2014, 7:11 PM UTC

Pxtl wrote: post #52

bane wrote: post #33

I was a terrible math student in school. Looking back, it wasn't because the material was hard, or boring, but because it was completely unmotivated. They may as well have been asking me to organize piles of toothpicks or count ceiling tiles to fill up the class periods. There was simply no sense to it. I think this is partially understood, and the attempted solution is to try to find applications for the math you're…

The problem is that if you don't fill the period with busywork? The students don't build up the intuitive, gut-level skills they need to handle the higher-level stuff. Math requires building muscles in your head, and muscles take reps. Lots of reps. Let's look at the elementary level: it's not enough to simply introduce BEDMAS or least-common-denominator and write a few problems that get the student to check off "oka…

So many incorrect words, tired analogies and pithy statements.

Re: How our 1,000-year-old math curriculum cheats America's kids

#75

Post by sitkack » Mon, Mar 03, 2014, 7:12 PM UTC

SamuelMulder wrote: post #55

bane wrote: post #33

I was a terrible math student in school. Looking back, it wasn't because the material was hard, or boring, but because it was completely unmotivated. They may as well have been asking me to organize piles of toothpicks or count ceiling tiles to fill up the class periods. There was simply no sense to it. I think this is partially understood, and the attempted solution is to try to find applications for the math you're…

I think you're absolutely right that math has to be motivated. A lot of the effort to motivate it is to provide problems that students understand relate to the real world. Most of them come across as contrived. You hit on a good concept with the idea of incorporating the history of math. I'm working on a Geometry curriculum that does just that. Understanding math in the context of a grand story of mankind trying to u…

Is your work done in the public? It would be nice to put it on a public repo and get others feedback and help.

Re: How our 1,000-year-old math curriculum cheats America's kids

#76

Post by sitkack » Mon, Mar 03, 2014, 7:15 PM UTC

bane wrote: post #47

wisty wrote: post #46

Earlier quoted context omitted.

> Except that once you hit even basic algebra, you quickly run out of applications a young student can relate to. Algebra is problem solving. You have a formula describing the problem, and want to re-arrange it to find one of the variables. It has a lot of useful and logical applications. Trigonometry though ... screw that. "Bob the builder has made a truss, and wants to figure out the angle A. He doesn't own a protr…

> Algebra is problem solving. You have a formula describing the problem, and want to re-arrange it to find one of the variables. It has a lot of useful and logical applications. It does, but for average Joe and Carla, who's day job involves making sure the box of sprockets sitting on the loading dock matches the P.O., and who's most pressing math problem is balancing their check book every few days and using turbo ta…

With that kind of attitude we are just going to make more average Joe and Carlas. If you take what you are saying to a logical conclusion it leads to the exclusion of the many in fear of over education which I would argue can never occur.

Re: How our 1,000-year-old math curriculum cheats America's kids

#77

Post by sitkack » Mon, Mar 03, 2014, 7:21 PM UTC

kaitai wrote: post #31

gus_massa wrote: post #18

Math is like knitting. It's not useful to read about it. You must do it. When reading an advanced math book for the fist time, I can spend 1 hour per page, because I must copy the proof, try a few "improvements" that are dead ends, do some exercise, and understand what is the main idea of that part. It's very difficult to mixing some modern subjects without calculation. Most of the time, the idea is to just hide the…

Since you mentioned knitting (and I agree with your analogy), check out the great intuition you can get about hyperbolic geometry via crochet and knitting. See how "parallel" lines act and the angle sums of triangles end up smaller than 180 degrees: http://theiff.org/oexhibits/oe1e.html A TED lecture is linked: http://geknitics.com/2010/11/sunday-knitting-science-hyperbo... Hyperbolic baby pants also convertible into…

This is absolutely beautiful.

Re: How our 1,000-year-old math curriculum cheats America's kids

#78

Post by dllthomas » Mon, Mar 03, 2014, 7:22 PM UTC

Patrick_Devine wrote: post #73

dllthomas wrote: post #71

Earlier quoted context omitted.

"If you want to find the distance between two points when you have the angle (eg. I'm firing a projectile at a certain angle), use cosine for the length of the x axis and use sine for the y axis. You get the hypotenuse from using pythagoras' theorem." Using cosine and sine and then Pythagorean theorem to get the length of the hypotenuse doesn't make sense - in order to get the length of the X and Y components with co…

You're right, I did state it a little awkwardly, but the statements are correct. I'll give a more concrete example: I'm firing a projectile at 52 degrees and it needs to move 10 units. I'm at (5,7), where does the projectile end up? delta x = cos(theta) * 10 delta y = sin(theta) * 10 So my final position is (5 + 6.16, 7 + 7.88), or (11, 15). If I already knew how far the delta X and delta Y were, I could get the leng…

Yes, I certainly wasn't disagreeing that trig is useful for games. The "if you want to try this out yourself" comes across a little patronizing in this context...

Re: How our 1,000-year-old math curriculum cheats America's kids

#79

Post by sitkack » Mon, Mar 03, 2014, 7:40 PM UTC

WalterBright wrote: post #39

Math curriculum may be rote and boring, but if you don't master arithmetic, fractions, exponents, etc., you're going to have a lifetime of poor decisions regarding investments, financing, etc., which will be very costly.

You can teach exponential growth, compound interest and ratios before mastery of the mechanics. To many, mastery of the mechanics inoculates them not from darkness but from a scientific mind.

I know many people with a mastery of arithmetic and fractions yet still make poor mathematical decisions. Conversely, I see people make projections and use algebra w/o even knowing they are doing it.

Learning assembly isn't is a prerequisite for making useful higher level software. Knowing all the words doesn't make us a better essayist. Yes the low level stuff can make the result better, the spark still has to exist for the flame to grow.

Re: How our 1,000-year-old math curriculum cheats America's kids

#80

Post by SamuelMulder » Mon, Mar 03, 2014, 7:41 PM UTC

sitkack wrote: post #75

SamuelMulder wrote: post #55

Earlier quoted context omitted.

I think you're absolutely right that math has to be motivated. A lot of the effort to motivate it is to provide problems that students understand relate to the real world. Most of them come across as contrived. You hit on a good concept with the idea of incorporating the history of math. I'm working on a Geometry curriculum that does just that. Understanding math in the context of a grand story of mankind trying to u…

Is your work done in the public? It would be nice to put it on a public repo and get others feedback and help.

I'm still struggling with how to handle this. On the one hand, it makes a lot of sense for it to be public. On the other, I've given up a lot to spend time developing it (including going part time on my day job), and I would love to be able to devote more time to it, which would require making some money off of the material in some way.

I've been thinking about doing a kickstarter, but I'm interested in exploring other models. I don't have a ton of time, and I'm always torn between spending time trying to figure out how to publish/market/exploit the material versus spending the hundreds of hours reading history and math and trying to actually write the curriculum. So far I've just been punting on it till I get this first course done.