## Real World Applications

For the discussion of math. Duh.

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kira
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### Real World Applications

In the Algebra classes I teach, we're talking about polynomials (you know, factoring, graphing, solving, the whole bit). Anyway, as students are wont to do, they keep asking "When are we going to use this?"

Sadly, the text book isn't much help. They don't care if they can model the St. Louis Arch and find how high it is by locating the vertex of the polynomial model. (This is the same textbook that claimed it was a good idea to learn how to do permutations and combinations because you'll "be able to find out how many different striped hats you can knit".)

I've grown tired of responding with a simple: "Do you plan on going to high school? Then you're going to use this." And I really want to get them into a project or something now that it's getting toward the end of the year.

The only thing I could brainstorm was modeling a halfpipe (I've got quite a few skaters/bikers) but I'm not even sure that a parabola is the right shape for a halfpipe.

Does anyone know any useful (hopefully fun) real world applications? Please?

miles01110
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Take them to the top of the building and have them jump off. Whoever predicts their landing location the closest gets an A.

hyperion
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### Re: Real World Applications

kira wrote:"Do you plan on going to high school? Then you're going to use this."

And therein lies the problem.
Peshmerga wrote:A blow job would probably get you a LOT of cheeseburgers.
But I digress.

kira
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### Re: Real World Applications

HYPERiON wrote:
kira wrote:"Do you plan on going to high school? Then you're going to use this."

And therein lies the problem.

Wherein lies the problem?

el sjaako
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Maybe you could do something with firing missiles over mountain ranges? Or cannonballs over friendly ships into enemy ships?

I know this problem would be something incredibly real to them, but I think that prior to the common use of computers people used resistors and electricity to quickly calculate cannonball trajectories, and I wouldn't be at all surprised if these were really polynomials. This is from memory, I don't know how accurate that statement was.

If that's to violent you could do something with mileses suggestion, but instead of throwing children throw... something else.

If all else fails tell them that this will all seem comparatively practical when they start calculus. Most of my class (including me) still has only a vague idea what that can be used for.

edit: ugh my spelling. I think I fixed most of it
Last edited by el sjaako on Sat May 05, 2007 4:13 pm UTC, edited 1 time in total.

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Maybe you could have them calculate optimal areas of stuff. Something like 'given x meters of fencing, what is the largest rectangular area you can enclose?'. It's a pretty simple calculus problem, but you could solve it graphically, and it also kind of highlights some of the problems that polynomials, and eventually calculus can solve.

Not sure how much fun that would be though.

kira
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el sjaako wrote:Maybe you could do something with fireing missles over mountain ranges? Or cannonballs over friendly ships into enimy ships?

That is a clever idea. I just might have to co-opt it.

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kira wrote:
el sjaako wrote:Maybe you could do something with fireing missles over mountain ranges? Or cannonballs over friendly ships into enimy ships?

That is a clever idea. I just might have to co-opt it.
or build a little spring plunger dealy like they have in pinball machines, at an angle you choose, put a taget out on the floor, put a scale on the side so that they know how much force is stored in the pluger as it's pulled back, and give a each group one shot and to compleat the assignment they have to hit the taget with that one shot (I was just takeing algebra and it got really annoying that they weren't useing things that I could actualy use, to teach me the math)

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They can solve the first problem of the xkcd substitute teacher test with quadratics.

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My physics class in high school (it was algebra based) had us start a steel ball on top of a little ramp at the edge of a lab table, and we had to get it into a cup on the floor. If we got it on the first try, we got an A. If we didn't, it was not an A. The math involved is fairly simple, and with enough fun pictures and dotted lines it should be within reach for a class.
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gmalivuk
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### Re: Real World Applications

kira wrote:Sadly, the text book isn't much help. They don't care if they can model the St. Louis Arch and find how high it is by locating the vertex of the polynomial model.

Isn't the Arch an upside-down catenary, anyway? The book should use suspension bridges (the kind like the Golden Gate) if it insists on using parabolas.

I wrote a calculator program in middle school or high school that involved a tank launching nukes at an underground bunker. Kind of scortched-Earth, but lots more boring.

The fun bit was including the formulas for nuclear damage at different distances. (There were messages like "you destroyed the bunker, but the blast wave at your location is 20psi overpressure, so you died, too.")

Good times.
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Whenever anyone asks "when am I going to use this?" you can always just answer, "On the final."

But it is really annoying, and there are real-world applications for many things in mathematics. It's even worse when the real-world applications are patently obvious and the students still ask. For example, a friend of mine was teaching a calculus class to a group of students who were almost all pre-meds. She was doing related rates, and talking about fluid flowing from one container into another, and then being removed from the other, and how this affects the quantity of fluid in the second container, and one of her students asked when this was ever going to be useful.

My friend just looked at the student for a few seconds blankly before saying, "Dude. This is your IV, and this is your patient. If you don't know how much drugs you're pumping into your patients, you will kill people."

Of course, how much math you use will certainly depend on what you end up doing, and actors and artists probably don't use a lot. But if you go into banking, investing, economics, medicine, engineering, architecture, science, programming, or a million other things, you will use math on a daily basis.
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FiddleMath
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Math is applied via... science, mostly. Lots of people have already talked about simple physics applications. Chemistry is pretty cool too, because it's the category that involves exploding things. Explosions are cool.

Many, many things act like exponents. Money, over time, has exponents happen to it. Both disease and meme propagation is exponential, more or less. Population models, also exponential. Technology? Also exponential, though sometimes a little harder to quantify. (If you ever get the chance, impress upon students what exponents do, and how they apply to money. I know too many silly people who got themselves in debt, and didn't learn until afterwards what exponents do.)

Thing is, almost every real-world application of mathematics isn't very simple - you usually have to explain why the variables are tied together as they are to yield any sort of explanatory sense, and that takes some time. As I recall, math textbooks (and curricula) avoid those kinds of examples wherever they can - but they're the kinds of examples that you'd actually need to give to demonstrate the utility of mathematics.

Of course, the real reason that one knows math is because it's a small set of generative ideas that can help model, oh, practically everything, helping you leverage your giant human mind to help you do work. But it's probably hard to explain that directly to high school students who don't particularly want to learn it. On the other hand, you could maybe demonstrate it through lots of (highly varied) examples, if you gave that enough time...

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The problem with explaining where you're gonna use things like polynomials is that they're so ubiquitous that you use them for bloody everything...

Pathway
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### Re: Real World Applications

kira wrote:
HYPERiON wrote:
kira wrote:"Do you plan on going to high school? Then you're going to use this."

And therein lies the problem.

Wherein lies the problem?

Therein.
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### Re: Real World Applications

gmalivuk wrote:Isn't the Arch an upside-down catenary, anyway? The book should use suspension bridges (the kind like the Golden Gate) if it insists on using parabolas.

Doesn't a suspended chain follow a cosh curve or something?

Trajectories (e.g. kinematic equations) are the big easy thing for quadratics. I'm trying to think of another example that doesn't use calculus but I'm finding it difficult...

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Tell them that if they don't want to learn anything more than a 4-function calculator can, they can go work at a grocery store the rest of their lives.

MFHodge
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The problem is that (IMHO) it is difficult to understand the practical without understanding the math first. But I do agree with setting up a ballistics experiment. You don't have to explain the details of where the equations come from. Just show the formulas and let them plug and chug. Should be fun.

kira
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I think a lot of this is very neat -- but the main problem is that these are 8th graders. They want to know how the math that they are learning is related to real life problems.

I have tried many times to patiently/irritatedly/loudly explain that they need this math for the more advanced stuff that they will learn later. I have tried to explain that the reasoning skills that they learn from this math will be very useful later. I have tried to explain that it's ignorant to decide not to learn something.

I guess I'm just a little frustrated on that point. I think the trajectories will be useful, but they will undoubtedly point out that a computer probably already knows how to solve this problem for them.

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### Re: Real World Applications

kira wrote:
HYPERiON wrote:
kira wrote:"Do you plan on going to high school? Then you're going to use this."

And therein lies the problem.

Wherein lies the problem?

"do work so you can do more work later that you won't need to do ever again"
Peshmerga wrote:A blow job would probably get you a LOT of cheeseburgers.
But I digress.

kira
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### Re: Real World Applications

HYPERiON wrote:
kira wrote:
HYPERiON wrote:
kira wrote:"Do you plan on going to high school? Then you're going to use this."

And therein lies the problem.

Wherein lies the problem?

"do work so you can do more work later that you won't need to do ever again"

Indeed. That is exactly what they think. Unfortunately, this explanation serves to quiet them better than the more rational explanations of "This is teaching you logic" and various examples of how math is actually used in the real world.

gmalivuk
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### Re: Real World Applications

SpitValve wrote:Doesn't a suspended chain follow a cosh curve or something?

Yes, that's a catenary. (The Gateway Arch is an upside-down one because that makes the strongest arch.)

That's why I specified the type of suspension bridge where each bit of cable has about the same weight pulling straight down on it. In which case it is a parabola. (Obviously a Golden-Gate-type suspension bridge isn't *quite* like this, but the downward force on most of the curving cables mostly cancels out the lateral component of the weight of the rest of the cable, which is what otherwise makes things hang in catenaries.
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kira wrote:I guess I'm just a little frustrated on that point. I think the trajectories will be useful, but they will undoubtedly point out that a computer probably already knows how to solve this problem for them.

Analogously, they don't need to more than a hundred words or so, because they can just look the rest of them up in a dictionary. On the other hand, this would make them totally unable to read or write on a decent level of fluency, and would mean that language has no inner meanings, just formal denotations...

The folly of thinking about mathematics that your students express is exactly the same as the folly of thinking about language (or music, or art) the same way. Plus, someone has to be able to write the programs and make the computers, and then other people have to know how to find polynomials for the machines to solve.

The relevant fable may be The Feeling of Power, by Isaac Asimov.

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Of course, I can't actually explain what I'm saying in terms I think a majority of eighth-graders could understand. Good luck. :/

Solt
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This reminds me of the math topic in the news forum. Math majors don't learn practical uses for math (nor do they care to, apparently), but they're the ones that end up teaching kids. Unfortunately, kids can't appreciate the beauty of a pure subject like math like we adults can.

Kira, you'll have to teach them some basic physics. I think in 8th grade science I knew the kinematic equations of motion (not the derivations, of course), so it shouldn't be that hard for them. Unfortunately, the polynomials that result from, for example, the mother kinematic equation (at^2 + vt + x_0 = x(t) ) are exactly the kind you'd want to use a calculator to solve if you are an 8th grader, because they rarely work out as nicely as the examples you usually do.

And if they ask why they need math, tell them that unless they're good at writing (humanities) or memorizing lots of stuff (medicine/biology), they're going to end up serving people who know math. That and they'd be living in fucking huts and dying of cholera if it weren't for math.
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the mother kinematic equation (at^2 + vt + x_0 = x(t) )

Ummmm, that is a mother with a brain tumor (missing your 1/2 coefficient in front of your acceleration term). I'm not trying to be picky, it's just something I noticed because that equation will be forever burned into my skull.

As a math major myself (pure), going into my 2nd year this fall, I must say I could care less about the application. The beauty of it all is AMAZING. It's really hard to express it to someone, as they would never know. I think the best quote was in The Divine Proportion by H.E. Huntley. Paraphrasing it... The beauty of your work will never be really understood by your spouse, friends, or family as they could not comprehend the beauty of it's rigor.

Truth is what I look for, and theres so many versions of it which is amazing (Euclidean Geometry and all the other variants).

If they want applications, tell them the whole world operates under equations, many of which are polynomials. If they could use all their algebra skills to combine all these equations, it'd probably come out perfectly to 1.

Ramble.
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the mother kinematic equation (at^2 + vt + x_0 = x(t) )

Ummmm, that is a mother with a brain tumor (missing your 1/2 coefficient in front of your acceleration term). I'm not trying to be picky, it's just something I noticed because that equation will be forever burned into my skull.

Heh, I never memorized it. Most of my classmates did, but since I knew calc and they didn't, I just derived any equations I needed by integrating or solving differential equations. It's why calculus was invented, after all.
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Solt
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the mother kinematic equation (at^2 + vt + x_0 = x(t) )

Ummmm, that is a mother with a brain tumor (missing your 1/2 coefficient in front of your acceleration term). I'm not trying to be picky, it's just something I noticed because that equation will be forever burned into my skull.

Yea yea, minor details. I haven't had to use it past physics, not even in my Dynamics class (that would be too easy...). I last used it when I helped, ah, less mathematically inclined friends in physics, which is when I coined the term.

While I will probably never see it on the same level as you, I also appreciate the beauty of mathematics. What a powerful and elegant language. But it took a lot of classes before I got to the level where I was even capable of seeing anything beyond mere symbols and manipulations.
"Welding was faster, cheaper and, in theory,

produced a more reliable product. But sailors do

not float on theory, and the welded tankers had a

most annoying habit of splitting in two."

-J.W. Morris

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I'd have to say, when I did Algebra back in middle school, I could care less what I actually wanted to use the stuff for. I went along with the class in asking this because I didn't like the subject of math, I wanted to waste time in class, and I just wanted to complain about something.
I didn't think I'd do anything with math when I grew older. I liked Biology, and that only seemed to have funny little squares in it, and that was fine by me. I disliked math a great deal (partly had to do with geometry and its proofs, but that's besides the point). I had no clue that when I reached high school that I would dislike the branches of Biology that came from, and that late in high school I would go into Physics and like the class a whole lot.
I was suddenly liking math (and admitting it, too ) and I felt sad that I disapproved of math in middle school. I actually found what I'd be using all the math for, and enjoyed it.
Basically, the whole point of that repetitive paragraph was that my likes will change, and the fact that I don't know what stuff is used for now doesn't mean I won't find it out in due time, or that I will never like a certain subject.

You could tell them everything that has to do with quadratics (And there's a whole lot of stuff). Since there's also bound to be quite a few kids into programming, you can tell them how much math they will be using in programming. There's math in the gravity that pulls their skateboards down to earth (that equation mentioned earlier). One thing you could do is ask what the kids like to do, what they're interested in, and tell them how math is involved in each one of those things.

That's all I've got.

[Edit: Wow, I'm tired. There are tons of inconsistencies I notice in the whole post. Remind me to fix them when I wake up.]

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There's also parabolas as conic sections:
http://www.cut-the-knot.org/Curriculum/ ... rror.shtml
and maybe something else here:
http://www.maths.leeds.ac.uk/~khouston/ ... h1225.html

Do you really have a majority of maths teachers holding maths degrees there? We had no more than 2 teachers (out of a department of about 20) who had maths degrees at our school. It's a shame because the teachers with the degree really know the stuff better rather than the syllabus.
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Solt wrote:This reminds me of the math topic in the news forum. Math majors don't learn practical uses for math (nor do they care to, apparently), but they're the ones that end up teaching kids. Unfortunately, kids can't appreciate the beauty of a pure subject like math like we adults can. <snip>

While this is generally true, you'll probably find maybe five kids in each school (I can think of three offhand in mine, one of them being me) who do enjoy and appreciate math as a subject without practical applications. I know I've written several rants on the subject in a forum or two I'm a member of. With the rest of them, I don't know.

A ballistics experiment sounds like a good idea though.
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kira
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cmacis wrote:Do you really have a majority of maths teachers holding maths degrees there? We had no more than 2 teachers (out of a department of about 20) who had maths degrees at our school. It's a shame because the teachers with the degree really know the stuff better rather than the syllabus.

I don't know if you're posing this question to me or not -- but I think there's only one or two teachers with math degrees. What really disappointed me was the number of teachers who went for a "middle grades" certification (6th-8th grade) because they didn't think they could pass the test to get certified for 6th-12th. And, frankly, they probably couldn't.

Solt wrote:This reminds me of the math topic in the news forum. Math majors don't learn practical uses for math (nor do they care to, apparently), but they're the ones that end up teaching kids. Unfortunately, kids can't appreciate the beauty of a pure subject like math like we adults can.

Kira, you'll have to teach them some basic physics.

I think, by definition, most people who get math degrees and then go into teaching like the pure aspects of mathematics. If they really loved the applications, they'd be out there applying their math to something.

I was never a huge one for physics. I had arguments with Randy all the time about the relative merits of applied versus pure math. Pure math is fascinating. Applied math has all this real-life crap that gets in the way that makes it nearly impossible to actually use until you get into higher level stuff (Imagine a frictionless slope and a perfectly spherical ball...)

I guess now is the time where I go and brush up on my kinematics.

riley
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I'm a high school math teacher with a math degree, and my passion is for the fact that so much information can be modelled mathematically. My most difficult class is a group of seniors - at this school, they are required to take four years of math, but only required to PASS three years of math, so that extrinsic motivation factor can be pretty low with them. It's especially difficult because frankly, they never will use a logarithm again, and they are never, ever going to need to know the law of cosines (I didn't even know it until I started teaching). I try to make sure I never say "you'll need this for more advanced math," because they already hate math when they get to my class.

The most important way in which I combat the boredom you're talking about is by expressing my own, deep passion for the subject regularly. They all pretty much like me and my interest gets them interested by osmosis or something. I also use cheesy-ass jokes. It keeps them entertained (even if it is at my expense) and often serves as a mnemonic device for them. I use cheap tricks like heelies, those shoes with the wheels in them - I roll from side to side of the blackboard with them. I know it sounds like I sell my dignity to keep them alert, and it's probably true that that's all it is for at least some of them, but I couple my ridiculous antics with really powerful antics that surprise and impress them. Move all the desks in the room to the side and use a meterstick to draw long vectors about 3 meters long in directions they pick and let them measure the angle between them and their length, and then use those measurements to predict the distance between the ends of the vectors down to (I kid you not) a single millimeter, and they will be impressed. No one gives a crap that I haven't pointed out that yes, you can use this for the practical application of, I dunno, uhm, hanging telephone cords if you happen to know these two random distances or making a triangular fence if the farmer has specified that one angle must be 30 degrees and I can't possibly go out and measure it before hand because that would look unprofessional, I must be able to predict it with math... every practical example in every text book is necessarily inane because the kids know almost zero math, and they all PALE in comparison to the fact that I just demonstrated a knowledge of the physical reality we all share down to a millimeter.

When I was teaching trigonometry, I found an engineer's transit from the geology dept. of the local university and went out with my class and measured an 80 foot line to within a quarter of an inch from 70 feet away (we confirmed it with a tape measure). Then we moved around the school and measured various distances. At first we could confirm them, and then sometimes we couldn't (no one was brave enough to climb the radio tower with the measuring tape). I didn't have to point out the practical applications of what we were doing. At first, when we could confirm with the tape, it WAS pointless - the tape was a lot easier than the transit. But then when I suggested we measure the distance across the pond, after the students all already believed that the transit actually could measure distances as well as a tape measure, they all just understood. They were all seeing triangles in the space above the pond, and understanding what they implied. It was effing glorious.

So. I know most teachers don't get as much flexibility as I do, and you may not be able to do something like this for every class, but inventing practical applications for something is the wrong way to do it. Trajectories are not parabolas, there's wind and gravity changes and the missile might hit a goose, and the kids all understand that. They never quite believe the simplistic situations we give them, and they all think it's ridiculous that any farmer would make a rectangular fence to avoid a pond instead of just chopping the corner off and making a rectangle minus a corner. The way to go, in my opinion, is to start with a situation, and say, "How can we model this?"

Going off topic a little bit: I think it would be worth a try to stop teaching "subjects" and switch to a project-based curriculum. Go to a beach and study the history, ecology, and physics of the situation, or build a building for your school and practice writing grant applications for the funds, geometry and shop class designing the structure and ordering supplies, study the species you might displace by chopping down trees to make room for the building, etc.

I dunno. Sorry. It's just no wonder that so many kids hate math.

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### Re: Real World Applications

kira wrote:
HYPERiON wrote:
kira wrote:
HYPERiON wrote:
kira wrote:"Do you plan on going to high school? Then you're going to use this."

And therein lies the problem.

Wherein lies the problem?

"do work so you can do more work later that you won't need to do ever again"

Indeed. That is exactly what they think. Unfortunately, this explanation serves to quiet them better than the more rational explanations of "This is teaching you logic" and various examples of how math is actually used in the real world.

Tell them how much engineers get paid. Lie if you have to. Also tell them about how much doctors make, and bring up the Navier-Stokes Equations (cardiology).
SargeZT wrote:Oh dear no, I love penguins. They're my favorite animal ever besides cows.

The reason I would kill penguins would be, no one ever, ever fucking kills penguins.

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riley wrote:The way to go, in my opinion, is to start with a situation, and say, "How can we model this?"
Very well-put. Because, frankly, this is how math actually gets used. Its utility isn't generally "we have these formulas," then a computer can do it. Its utility is solving problems in reality that you don't already know how to solve.

riley wrote:Going off topic a little bit: I think it would be worth a try to stop teaching "subjects" and switch to a project-based curriculum. Go to a beach and study the history, ecology, and physics of the situation, or build a building for your school and practice writing grant applications for the funds, geometry and shop class designing the structure and ordering supplies, study the species you might displace by chopping down trees to make room for the building, etc.

I dunno. Sorry. It's just no wonder that so many kids hate math.

This would be awesome. It'd probably get kids to learn more in a year than most pick up in three or four. There's nothing quite like learning things because they're the tools you need to get something done. This is precisely why I volunteer heavily with DI; if regular school was similar, we'd win.

Wants to assemble a charter school like this? Or make such resources available online, for home-school kids or the merely curious?

Nyarlathotep
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kira wrote:
el sjaako wrote:Maybe you could do something with fireing missles over mountain ranges? Or cannonballs over friendly ships into enimy ships?

That is a clever idea. I just might have to co-opt it.

You can also try to teach them the optimum way to get a basketball into a hoop, depending on where you're standing. If you can -somehow- work the exact velocity into the equation (might be too advanced for eighth graders), so much the better.

Ironic... the only way I could get myself to like basketball in middleschool is if I sat there and mentally calculated the ideal parabolic shape from my position to the hoop. The problem was that 1. I never could actualize said parabola and 2. I would stand there too long and get yelled at.

((also ironic that I'm supposed to be studying for my Discrete Mathematics final right now and am procrastinating. My friends think it's odd that I miss Algebra I, until I show them proof by induction. Ahhh, liberal arts college.))
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hī willað ēow tō gafole gāras syllan,
ǣttrynne ord and ealde swurd,
þā heregeatu þe ēow æt hilde ne dēah.

Strilanc
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I really can't think of any applications that specifically use polynomials: they're so simple they always show up with respect to other things that are used everywhere. You use them for:
- eigenvalues in linear algebra
- Taylor series in calculus
- kinematics (and lots of other physics)
- etc

I think the best way to make your point is to ask students to give situations where you wouldn't use polynomials but you would use arithmetic. Practice with friends before hand so you have a bunch of canned examples for the obvious questions like "buying groceries".

Then you should start going on about how math teachers always have to deal with this "when will we use it" crap but English teachers never get it when you analyze books, geography teachers never get it when they force you to temporarily memorize 50 countries, and art teachers never get it FOR EVERYTHING THEY TEACH.
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Solt
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I doubt high school students would understand the math, but look, Google is built on linear algebra!

Trig in the real world is a good way to show students the general usefulness of math.

What always impressed me is when someone could take a random interesting situation, then write down a whole bunch of equations to model it, then draw conclusions. It's a bit hard to do well, though.
"Welding was faster, cheaper and, in theory,

produced a more reliable product. But sailors do

not float on theory, and the welded tankers had a

most annoying habit of splitting in two."

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kira
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Alky wrote:Then you should start going on about how math teachers always have to deal with this "when will we use it" crap but English teachers never get it when you analyze books, geography teachers never get it when they force you to temporarily memorize 50 countries, and art teachers never get it FOR EVERYTHING THEY TEACH.

Actually, the English teachers at my school do have to deal with it. The kids seem to be very anti-learning. There's no intrinsic motivation there so it's hard to get them to do anything.

It's not even that bad of a school. We're not in a ghetto, or an inner city, we're rated very well by the DoE based on standardized test scores... but the students just don't want to learn.

FiddleMath
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