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United States47024 Posts
On May 19 2015 00:34 Slayer91 wrote: generally to find the maximum you just find the function that describes the size of it and differentiate it set it to zero ggwp
Wait, I don't understand how you learn Calc without learning this, lol.
Like, that's literally the first "use" of taking derivatives that you actually learn.
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On May 19 2015 00:38 TheYango wrote:Show nested quote +On May 19 2015 00:34 Slayer91 wrote: generally to find the maximum you just find the function that describes the size of it and differentiate it set it to zero ggwp
Wait, I don't understand how you learn Calc without learning this, lol. Like, that's literally the first "use" of taking derivatives that you actually learn. I don't understand how Scip still got 90% on that test without learning this, lol.
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On May 19 2015 00:31 jcarlsoniv wrote:Show nested quote +On May 18 2015 23:59 Numy wrote: Soniv can you go into detail? As I said geometry isn't something that I've done or between around in tertiary education so I have no idea what it's application post schooling is.
It just seems it either teaches you the same thinking as you would do in other maths but has a deadend in usefulness to me. Much like any of the math you learn in school, the "practical" application of the examples you do through repetition is fairly nonexistent. However, it is entirely logic and process driven. Geometry is no exception. I'll be pointing to Abstract Algebra because that is when it really clicked for me. (It's also been close to 4 years holy shit, so I'm not going to be able to delve into great examples) I think a big part of why Geometry seems kind of pointless in high school is because you're given a whole set of rules to follow, and then you follow them. I know for me, we had to memorize all of these rules and then use them on exams, and it felt really daunting and tedious to have to stuff everything in your brain and remember them for the process. But in Abstract Algebra, we were given no such large set of rules/axioms/corollaries/etc. We started with a very basic assumption (or a few assumptions, I honestly can't remember too well). This was necessary to start with because you have to understand that the math you're looking at is predicated on certain conditions. We then had to use these to build out very basic proofs of abstract concepts (one of the first things I remember was having to prove how a*b was commutative, where * is an undefined operation). From then, we were only ever allowed to reference an axiom/law/what have you if we had proven it in the past. This meant that we built an understanding of logic and process based on things we've already proven to be true in the past, rather than referencing a huge library of rules we were given at the start and told to memorize.Having this understanding when I actually took college Geometry my senior year (I did my classes in a really weird order) helped me understand why the process really matters. I know this was kind of a...high level look at it. But hopefully it at least conveys my thoughts coherently.
Makes a lot of sense to me. So essentially what you saying is geometry at school is useless but doing it at a fundamental can be greatly beneficial? I don't quite get why we tend to focus on all these rules at school level the in later in life we go back and do all the fundamentals. It's like we get thrown into an ocean and told to swim then after we can barely swim we go back to the training pool and learn all about how to swim.
On May 19 2015 00:39 Fildun wrote:Show nested quote +On May 19 2015 00:38 TheYango wrote:On May 19 2015 00:34 Slayer91 wrote: generally to find the maximum you just find the function that describes the size of it and differentiate it set it to zero ggwp
Wait, I don't understand how you learn Calc without learning this, lol. Like, that's literally the first "use" of taking derivatives that you actually learn. I don't understand how Scip still got 90% on that test without learning this, lol.
Some palms were "greased"
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United States47024 Posts
Because the fundamentals are sometimes so detached from what seems practical to a middle/high school student that it'd be very hard to teach that and have it remain interesting to a lot of students, lol.
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On May 19 2015 00:33 Carnivorous Sheep wrote:Show nested quote +On May 19 2015 00:25 GhandiEAGLE wrote: Heck yeah. But English is a free A even if I wasn't good at it. Bad allocation of skills >.> High school English is the devil. Probably the closest thing to a crapshoot in terms of grading out of all high school courses. Tell me about it. The only concrete grading we have is a series of vocabulary quizzes, in which I already know all the words, and in which my previous knowledge is nevertheless irrelevant because I have to know the definitions entirely verbatim from an obscure dictionary I'd never heard of before. And there are 300 of these words on any given test.
For instance, I know what Capitalism is. What I'm less likely to know that, on this test, to get it correct I have to write
Capitalism (n): an economic system in which businesses are owned by private citizens (not by the government) and in which the resulting products and services are sold with relatively little government control
It has to be exactly the same as that, down to the last comma, semicolon, and space.
It's honestly a fuck all nightmare.
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Czech Republic11293 Posts
On May 19 2015 00:39 Fildun wrote:Show nested quote +On May 19 2015 00:38 TheYango wrote:On May 19 2015 00:34 Slayer91 wrote: generally to find the maximum you just find the function that describes the size of it and differentiate it set it to zero ggwp
Wait, I don't understand how you learn Calc without learning this, lol. Like, that's literally the first "use" of taking derivatives that you actually learn. I don't understand how Scip still got 90% on that test without learning this, lol. do you see any questions regarding calculus at all in the exam I linked? There are quadratic equations, some extremely simple geometry you could solve without knowing literally anything, some very simple combinatorics and shit like that. And the test still has 25% failure rate. Holy shit czech republic has to be literally the most retarded country in EU.
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On May 19 2015 00:41 TheYango wrote: Because the fundamentals are sometimes so detached from what seems practical to a middle/high school student that it'd be very hard to teach that and have it remain interesting to a lot of students, lol.
Yup.
I remember learning the full equation for derivative towards the start of AP calc, and then learning the shortcuts afterwards. And I distinctly remember thinking "why the fuck didn't he just teach us this to start, it's so much easier".
A lot of it boils down, I think, to the fact that for the majority of our tenure in school, the focus is on results and getting the correct answer. So we didn't care about learning how to get the answer, just that we got the right answer. But understanding the "back end" of things really does increase your understanding of the whole.
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United States47024 Posts
On May 19 2015 00:44 jcarlsoniv wrote: A lot of it boils down, I think, to the fact that for the majority of our tenure in school, the focus is on results and getting the correct answer. So we didn't care about learning how to get the answer, just that we got the right answer. But understanding the "back end" of things really does increase your understanding of the whole. Admittedly, after working for a few years, you come to realize that as it turns out, most people don't actually give a fuck about anything other than the result, and not how you got there.
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On May 19 2015 00:41 Scip wrote:Show nested quote +On May 19 2015 00:39 Fildun wrote:On May 19 2015 00:38 TheYango wrote:On May 19 2015 00:34 Slayer91 wrote: generally to find the maximum you just find the function that describes the size of it and differentiate it set it to zero ggwp
Wait, I don't understand how you learn Calc without learning this, lol. Like, that's literally the first "use" of taking derivatives that you actually learn. I don't understand how Scip still got 90% on that test without learning this, lol. do you see any questions regarding calculus at all in the exam I linked? There are quadratic equations, some extremely simple geometry you could solve without knowing literally anything, some very simple combinatorics and shit like that. And the test still has 25% failure rate. Holy shit czech republic has to be literally the most retarded country in EU. Well the test I linked is probably also only made by the top 10% of the country (in math that is), while your test gets made by everybody.
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On May 19 2015 00:47 TheYango wrote:Show nested quote +On May 19 2015 00:44 jcarlsoniv wrote: A lot of it boils down, I think, to the fact that for the majority of our tenure in school, the focus is on results and getting the correct answer. So we didn't care about learning how to get the answer, just that we got the right answer. But understanding the "back end" of things really does increase your understanding of the whole. Admittedly, after working for a few years, you come to realize that as it turns out, most people don't actually give a fuck about anything other than the result, and not how you got there.
hah, fair enough
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On May 19 2015 00:47 TheYango wrote:Show nested quote +On May 19 2015 00:44 jcarlsoniv wrote: A lot of it boils down, I think, to the fact that for the majority of our tenure in school, the focus is on results and getting the correct answer. So we didn't care about learning how to get the answer, just that we got the right answer. But understanding the "back end" of things really does increase your understanding of the whole. Admittedly, after working for a few years, you come to realize that as it turns out, most people don't actually give a fuck about anything other than the result, and not how you got there.
Well most of the time at least in my fields you have systems in place that can get you to the answer easily. The issue is understanding what's fundamentally going on so you can adjust this system to match whatever is going on in reality. Other times the process to get the answer is the answer itself.
I don't know. Maybe our whole education system just needs to change. When I told my folks that you guys in the States do standardized testing since Junior school they wouldn't believe me. Had to go bring proof to convince them. Crazy stuff
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On May 19 2015 00:41 GhandiEAGLE wrote:Show nested quote +On May 19 2015 00:33 Carnivorous Sheep wrote:On May 19 2015 00:25 GhandiEAGLE wrote: Heck yeah. But English is a free A even if I wasn't good at it. Bad allocation of skills >.> High school English is the devil. Probably the closest thing to a crapshoot in terms of grading out of all high school courses. Tell me about it. The only concrete grading we have is a series of vocabulary quizzes, in which I already know all the words, and in which my previous knowledge is nevertheless irrelevant because I have to know the definitions entirely verbatim from an obscure dictionary I'd never heard of before. And there are 300 of these words on any given test. For instance, I know what Capitalism is. What I'm less likely to know that, on this test, to get it correct I have to write Capitalism (n): an economic system in which businesses are owned by private citizens (not by the government) and in which the resulting products and services are sold with relatively little government control It has to be exactly the same as that, down to the last comma, semicolon, and space. It's honestly a fuck all nightmare. That's terrible....
I'm pretty sure my Brit Lit teacher stopped reading papers after the first 2, by then he'd already made up his mind. Fortunately, despite neglecting my summer reading assignments I was able to bs two book reviews on day 1 with no prep using The Hobbit which I had read like 8 years prior and Beowulf which I really made up just using clues from stuff around the classroom and what I had heard which wasn't much. That was a stressful period.
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On May 19 2015 00:51 Numy wrote:Show nested quote +On May 19 2015 00:47 TheYango wrote:On May 19 2015 00:44 jcarlsoniv wrote: A lot of it boils down, I think, to the fact that for the majority of our tenure in school, the focus is on results and getting the correct answer. So we didn't care about learning how to get the answer, just that we got the right answer. But understanding the "back end" of things really does increase your understanding of the whole. Admittedly, after working for a few years, you come to realize that as it turns out, most people don't actually give a fuck about anything other than the result, and not how you got there. Well most of the time at least in my fields you have systems in place that can get you to the answer easily. The issue is understanding what's fundamentally going on so you can adjust this system to match whatever is going on in reality. Other times the process to get the answer is the answer itself. I don't know. Maybe our whole education system just needs to change. When I told my folks that you guys in the States do standardized testing since Junior school they wouldn't believe me. Had to go bring proof to convince them. Crazy stuff
I was fortunately able to avoid a lot of standardized testing cuz I went to private school from 6th grade on. But it got so much worse between the time I left elementary school and when my youngest sister and now youngest brother experienced it. They're now at the private school I went to (it's Pre-K through 12), and the way they're teaching things is honestly the most illogical, asinine process imaginable - from a purely learning perspective, that is.
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How do all of you know the math terms in english, I never really had the opportunity to learn them and I have to read your posts with dictionary open.
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On May 19 2015 00:31 jcarlsoniv wrote:
But in Abstract Algebra, we were given no such large set of rules/axioms/corollaries/etc. We started with a very basic assumption (or a few assumptions, I honestly can't remember too well). This was necessary to start with because you have to understand that the math you're looking at is predicated on certain conditions. We then had to use these to build out very basic proofs of abstract concepts (one of the first things I remember was having to prove how a*b was commutative, where * is an undefined operation).
From then, we were only ever allowed to reference an axiom/law/what have you if we had proven it in the past. This meant that we built an understanding of logic and process based on things we've already proven to be true in the past, rather than referencing a huge library of rules we were given at the start and told to memorize.
This is exactly how my high school geometry was taught, with the obvious difference in general difficulty between geometry and AA. Our Geometry teacher also happened to be the Calc BC teacher as well though, so I think he was kind of preparing the students that would be capable of AP level courses, and other students just went along for the ride in what was probably a far superior learning environment.
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Wait how do you do the first one of the first paper without a calc? The rest seems doable.
On May 19 2015 01:00 AlterKot wrote: How do all of you know the math terms in english, I never really had the opportunity to learn them and I have to read your posts with dictionary open. Because all these people speak English :p But seriously, everybody except Scip and me got it taught in English, and for Scip and me I guess it's the power of the internet.
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There's a method of doing long division by hand for that first question. I never knew it at school either so I'm guessing that's why you confused. It's not that hard but it's pretty annoying to do.
edit: Or do you mean the graph one? That is pretty simple.
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United States47024 Posts
Seeing these kinds of exams years later makes you realize how much shit you learned once and never used again.
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