The purpose of High-Level Math

[TheLQ offline]

So after about 5 class periods of what I thought was completely useless stuff (variation equations, plotting complex quadratic equations, finding the vertical and horizontal Asymptote of rational algebraic functions), I asked in class where does this apply in real life. What followed was something very weird...

First the entire class started groaning, with one person saying "I hate it when people ask how it apply's in Real Life". Umm... well, isn't that what high school (and school in general) supposed to be preparing us for? I tried to ask for a specific field that it would be used in. Ms. Lucas (the teacher) asked if I wanted to go into computers, I said yes, and then she said that it would be used there. Hmm... well thats strange, because after 5 years of programming (and 2 months at a programming company) I have never used this stuff. I also pointed to other fields where it supposidly apply's (mainly construction, where some of the examples come from in our book), and said that they would never use it. Then her arguments degraded into personal attacks, calling my ignorant and unknowning of other fields. She said that would be used "somewhere". I asked what was the point of learning it, to which she said it was for this class and to pass the test. I pointed out that's learning for the sake of learning, and she said that was exactly what it was. WTF?! Then others around me told me just to go back to sleep. Then I realized nobody was going to listen, I dropped it.

What was learned here? Math teachers believe in learning for the sake of learning, Ms. Lucas is a b****, and people at my school hate asking questions.


With me about to write a persuasive letter for english, I decided to write mine about the BS of math. To do it, I needed to interview people in the field. So I interviewed my computer teacher, Fischer

Fischer is a Computer Systems Administrator/Network engineer turned teacher. He's been in the field for 15+ years, has 220+ Certifications (he got them when he was bored), and runs his own networking consulting company. He knows and teaches a broad range of subjects; from basic hardware to crytanography and networking procoals. This guy knows what he's doing. So I asked him where was math used in his field.

In terms of networking, its alot of basic addition and multiplcation. How much feet of Cat5 cable do I need to get from point A to point B? I have X users, how much storage space should I create in the NAS? How much will X cost? It extends farther then that, but still, there isn't much high level math at all. I don't see them using the midpoint formula, or practically any of the stuff from geometry. This person probably did all his calculations on the back of scap sheet of paper or a simple Excel spreadsheet.

In crytanography however, things get weird. There is really no limit to what you can do. Has anyone seen the calculations required for an MD5 hash? Pretty simple. Compare that to Truecrypt's XTS Mode of encrypting block devices or pool mixing function. Crypto is limited only by the imagination.

But really, how many people out of a normal high school are going to become cryptanolists?

What about programming? Well I've been a programmer for years and I've looked at the source code of many programs (even attempted to understood Firefox and its walls of C) and there is actually not alot of high level math. I actually don't see stuff like the quadratic formula anywhere.

In chemistry? Well that kinda goes a little farther in math that most subjects, but still stays pretty basic. Still wondering why I needed to know how to find Asymptote's of functions...

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In short, I have yet to find an application for half the shit that they teach us. Where the hell am I going to use the length of the shadow of a known tall building to calculate the shadow length of something else? Never, I'll just use the same tape measure and MEASURE IT! And even if you say "Well it could be used as a simpler way of calculating height", your stupid because that measurment is probably horribly off and won't be accepted as a good measurement for use in planning.

Why the hell are we even taking math after Algebra 1? Geometry is nothing but proof's ("Proove that this triagle is congruent to the other if Line AB is paralell to..."), and algebra 2 and calculus are nothing but useless crap. Algebra 1 is ONLY useful because of a few subjects that they cover that might be useful in chemistry.

I kinda agree with Fischer who has strong views on the educational system that he teaches for: Math should be taught as how it is applied in real life, not taught then shown (barley) how it applies. Once the basics are taught, then show that if you want to do X, use REALISTIC formula Y. This makes sense, and since people know now how to apply it to Life, they might actually remember it.

Which brings up another point: Isn't it strange that people forget math and social studies first but remember chemistry or English? Whats the diffrence, chemistry is hard and english can get hard when your teacher forces you to write a paper on why the author used the word "I". Because they are APPLIED! In Chemistry you do lab's where you take your knowledge of calculating the concentration of HCl and dilutions and actually do it. In English you use it every day, do lots of reading, and learn how to sound smart. APPLIED!

Thoughts?

[Taelia offline]

So after about 5 class periods of what I thought was completely useless stuff (variation equations, plotting complex quadratic equations, finding the vertical and horizontal Asymptote of rational algebraic functions), I asked in class where does this apply in real life. What followed was something very weird...

First the entire class started groaning, with one person saying "I hate it when people ask how it apply's in Real Life". Umm... well, isn't that what high school (and school in general) supposed to be preparing us for? I tried to ask for a specific field that it would be used in. Ms. Lucas (the teacher) asked if I wanted to go into computers, I said yes, and then she said that it would be used there. Hmm... well thats strange, because after 5 years of programming (and 2 months at a programming company) I have never used this stuff.

This is just like what would happen if Jeremie, Odd, Ulrich, Yumi, Sissi and Aelita would ask Ms. Hertz about her lesson on, say, oxygen. Or titanium, or robotics.

[Carth]

So after about 5 class periods of what I thought was completely useless stuff (variation equations, plotting complex quadratic equations, finding the vertical and horizontal Asymptote of rational algebraic functions), I asked in class where does this apply in real life. What followed was something very weird...

First the entire class started groaning, with one person saying "I hate it when people ask how it apply's in Real Life". Umm... well, isn't that what high school (and school in general) supposed to be preparing us for? I tried to ask for a specific field that it would be used in. Ms. Lucas (the teacher) asked if I wanted to go into computers, I said yes, and then she said that it would be used there. Hmm... well thats strange, because after 5 years of programming (and 2 months at a programming company) I have never used this stuff.

This is just like what would happen if Jeremie, Odd, Ulrich, Yumi, Sissi and Aelita would ask Ms. Hertz about her lesson on, say, oxygen. Or titanium, or robotics.

Taelia, those lessons WERE useful to them, because the plot called for them to be taught. That said, your post contributed nothing to the topic at hand, and was frankly quite rude. Please apologize.

As for the high level math, I think they're trying to develop problem-solving skills and logic, but considering most math consists of plugging things into formulas that they give you that tosses that out the window. It's a tradition, more than anything, I think. I'm asking the same questions myself- why teach us stuff we won't use?- but I'm going to hope for the logic answer. Good job looking into it, though! Maybe it's about time that had a reassessment.

[Overcaffeinated Sloth offline]

Welcome to the secret of high school! Truth is, you don't need too many of the facts they cram in your head. Most classes are covers for teaching abstract skills Math classes tends to be practice for comprehending and executing directions and compressing abstract logic into a usable form. And, yes, staying awake in things that normally rock you to sleep. now THAT's a good life skill. It's also a dimension to test how well you can perform in a subject, how much you participate, and can be used to judge problems you may have while functioning in this 'real world'. By doing this in several classes, it also gives students who are more inclined towards maths and sciences or language and arts the same opportunities to perform these checking rituals.


Instead of thinking about how you'll use the specific problems and formulas in computer science, think first about understanding a special 'language'. Solving a problem. Following directions, mastering skills, and making something out of that, and building into something different. You tell me how that's NOT computers. Try looking past the grades and homework, and look at what you've learned, not what you've been taught.


And it's rather poignant that I'm saying this on my last day of obligatory school.

[Taelia offline]

Taelia, those lessons WERE useful to them, because the plot called for them to be taught. That said, your post contributed nothing to the topic at hand, and was frankly quite rude. Please apologize.

Sorry, Carth. I misread the words. Forgive me.

[Tekirai offline]

I'm not too sure how maths subjects are sorted out in America - it looks like you have different classes for different things, like Algebra 1 and 2 and stuff... not too sure how it works, but I'll explain this anyway. Might be interesting for some.

Over here basic maths is the stuff you would be used to, and it's taught in a single class. But alongside that there's another class referred to as additional maths. It introduces mechanics and statistics, which are much more appliable to real life than pure maths is. Pure maths being... well, 'normal maths' that you're being taught, like dealing with quadratic equations and simultaneous equations and trigonometry. Only it's slightly more advanced, since it introduces calculus and the turning points of a curved graph.

With mechanics you calculate things such as the acceleration of an object if you know how far it's travelled, what speed it was at initially and its final speed as well as how long it takes. There's also the calculation of momentum and tension in beams and pulleys in different situations, as well as the effect of having a box on a rough slope and how the friction affects the forces acting on it. It's very close to physics, but as far as I know from taking the class myself, physics at high school level doesn't take you as far as that. This is definitely useable in life at some point.

Statistics isn't that much different from ordinary maths though, but it's still useable in life as well. Working out the probability of certain things happening is something you would know, but additional maths introduces being able to estimate the median and standard deviation of a set of data using certain equations as well as being able to see a correlation without drawing a graph. Not as useable as mechanics would be, but it's still something.

I'm not sure whether or not America has an equivalent to Additional Maths, or if I'm even repeating things you people know already, but basically you're only taught things that are more appliable to real life if you just take ordinary maths classes. The things you learn probably seem really trivial, but experience is experience. You'll apply your knowledge somehow, like with anything else you pick up from the world. Add maths is supposedly a lot harder, but it's just a matter of knowing what the equations you're using actually do and how they work. 8\)

[TheLQ offline]

Welcome to the secret of high school! Truth is, you don't need too many of the facts they cram in your head. Most classes are covers for teaching abstract skills Math classes tends to be practice for comprehending and executing directions and compressing abstract logic into a usable form. And, yes, staying awake in things that normally rock you to sleep. now THAT's a good life skill. It's also a dimension to test how well you can perform in a subject, how much you participate, and can be used to judge problems you may have while functioning in this 'real world'. By doing this in several classes, it also gives students who are more inclined towards maths and sciences or language and arts the same opportunities to perform these checking rituals.

Instead of thinking about how you'll use the specific problems and formulas in computer science, think first about understanding a special 'language'. Solving a problem. Following directions, mastering skills, and making something out of that, and building into something different. You tell me how that's NOT computers. Try looking past the grades and homework, and look at what you've learned, not what you've been taught.

The issue though is that its not taught that way. Teachers teach math from the perspective of teaching a skill that will absolutely be necessary for day to day functioning in the real world. That is what my math teacher told me: The things we are taught will be useful in real life.

And yes, math does teach the ability to follow directions, make something out of it, and morph it into something different. But so does every other class. English teaches you complex words and structure of an article that you are expected to morph into your own writing and speaking. Social studies is a series of cause and effect scenario's that teach a person what countries do good and what they do bad in. Chemistry from day 1 is a series of building blocks. One must learn molar mass in day 2 to figure out Gas stoichiometry on day 102. Using that point alone is not enough to argue the existence of a class that is completely useless.

And yes, learning how to not sleep in a class that is completely boring is a good skill. But there are tons of classes that are boring (IE US History).

Over here basic maths is the stuff you would be used to, and it's taught in a single class. But alongside that there's another class referred to as additional maths. It introduces mechanics and statistics, which are much more appliable to real life than pure maths is. Pure maths being... well, 'normal maths' that you're being taught, like dealing with quadratic equations and simultaneous equations and trigonometry. Only it's slightly more advanced, since it introduces calculus and the turning points of a curved graph.

With mechanics you calculate things such as the acceleration of an object if you know how far it's travelled, what speed it was at initially and its final speed as well as how long it takes. There's also the calculation of momentum and tension in beams and pulleys in different situations, as well as the effect of having a box on a rough slope and how the friction affects the forces acting on it. It's very close to physics, but as far as I know from taking the class myself, physics at high school level doesn't take you as far as that. This is definitely useable in life at some point.

Statistics isn't that much different from ordinary maths though, but it's still useable in life as well. Working out the probability of certain things happening is something you would know, but additional maths introduces being able to estimate the median and standard deviation of a set of data using certain equations as well as being able to see a correlation without drawing a graph. Not as useable as mechanics would be, but it's still something.

Seems that classes like physics are rebranded as "additional math". Depending on how high a student is forced to go in math, it might be the same problem that we have over here.

(BTW, I must of missed the post on where you live. Mind if I ask?)

[Tekirai offline]

Seems that classes like physics are rebranded as "additional math". Depending on how high a student is forced to go in math, it might be the same problem that we have over here.

(BTW, I must of missed the post on where you live. Mind if I ask?)

The line between mechanics and physics is debatable, but it's certainly not a substitute for physics itself. Only the aspect that involves the movement of objects. Additional maths is definitely a maths class, otherwise it wouldn't have the name. I just highlighted the mechanics part of it since it's the most appliable to things outside of class.

And this is someone in the UK. Northern Ireland to be precise. 8)

[Jazzy Josh offline]

Well, for game programming and things like that, I would believe that calculus-based physics would be useful. Which of course gives you a reason to use Calculus.

The real objective of Calculus and Precalculus in High School is to expand your mind.

[TheLQ offline]

Well, for game programming and things like that, I would believe that calculus-based physics would be useful. Which of course gives you a reason to use Calculus.

Agreed. Also though a really small sector of the market

The real objective of Calculus and Precalculus in High School is to expand your mind.

Thats exactly what someone in class said to me. I then told them to count the folds in a plastic bag to "expand their mind"

[Jazzy Josh offline]

The real objective of Calculus and Precalculus in High School is to expand your mind.

Thats exactly what someone in class said to me. I then told them to count the folds in a plastic bag to "expand their mind"

LOL.

Let me put it a different way, it helps you learn a new way of thinking, Calculus at least. Sort of the same thing when dealing with pointers, recursion, and procedural programming (I'm watching the SCIP MIT lectures, sue me.)

[austronothrusclarki offline]

The saying that maths (or history, english, science, etc) encourages learning a new way of thinking only holds once the student actually understands why it works. Any monkey and their dog can put in values and type something into a calculator if they really want to. As said above by Carth, many students only have to remember what formulae to use for what questions in tests. I ask you, who gets their head around the logic behind trig before they know how to apply it? Very few.
So maybe teachers should try to explain why these things work or, better yet, giving students more time to get their heads around it. E.g, nice that A-squared + B-squared = C-squared in a right-angled triangle, can you prove why? (I can't either.) There are 370+ proofs.
I've met some teachers that are brilliant at this.....and some that are not. I salute those that can teach the why. They aren't valued highly enough, and can foster an enjoyment of a previously disliked subject. That, I think, is what is wrong with the initally-mentioned problem.

[Chosen_one offline]

Hmm, sounds to me like you were learning precalculus. I must admit, precalculus was very boring and seemed very pointless to me.

However, math is a cumulative science. In other words, to learn more "advanced" mathematics you need to learn more basic mathematics first. It's kind of like how you need to learn the alphabet before you can write novels..

The purpose of learning what you're learning right now is to allow you to understand more "advanced" mathematics. If you take AP Calculus BC next year (or some other form of Calculus I and II class), you'll need all the information you learned in your precalculus class. And calculus is, in fact, the foundation of physics (calculus and physics were basically invented together, calculus being the mathematical component, and physics being the scientific component). So, all of the seemingly useless things, yes, even asymptotes and trigonometric functions, you have learned will be applied to calculus, which can be applied primarily to physics, and also to statistics, which, in turn, can be applied to a wide variety of fields, from biology to sociology.