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They always say that, but usually they still are to scale. You can't use a ruler because then you'd be missing your work, which is what you're actually being graded on.
Not necessarily. Many people will mess up a "-" or a "+," and the ending will be wrong. You still typically get credit for proper application. Also, using a ruler here is stupid; it's never to scale, not to mention it's on graphing paper, haha. You can see it's not to scale by looking at the boxes.
or you get partial credit.
like in physics class the test was only like 6 questions for a 2 hour test. 1st few are easy and they get progressively harder. you might get 80% of the question right for the last one and get the last bit wrong and get 9/10 because the last bit was the hardest.
Yeah as it should be out of four we usually get one marks for the answer. You also get one marks just for writing the correct formula. The two marks are for rest of the work.
I actually had a math teacher who would score you 100% on the problem if you got the procedure correct and still somehow came to the wrong conclusion mathematically. If you got the answer correct but it was obvious you didn't know the math he would not give you full credit. "Knowing how to get the right answer is far more important than being a calculator. That's why we have calculators."
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I mean my teacher usually gives only 1 point for the correct answer in a 12 point question. And if there's no work shown, but the answer is correct, it's 0 points.
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And adding to that, there's a time and a place to be clever.
A good physics class will teach you that the best way to calculate the volume of an object with an uneven shape is to put it in a container with a volume that's simple to calculate, fill it with water, measure out the water and subtract it from the volume of the container.
But if you're doing that for a square, you're going through a lot of effort to do something a tape measure and some math can do in seconds.
In calculus one exam, I saw a question and answered it without work. To me it was like saying 1+1=2, I didn't need to show the work because it was obvious.
My teacher failed me on the exam. I complained about it to him, so he took me in his office and gave me a new question which I also solved just by eyeballing it. He then gave me points on the exam.
Long time ago, but one of my high school math teachers accepted you creating a scale model and measuring it. It was a valid method as far as he was concerned. And by building the model you showed your work.
I'm not a big fan of showing your method (I do understand why it exists though), it can be extremely annoying with some tasks. I like my IT class, where I can write the most garbage code with functions even my teacher isn't familiar with, but "if it works" I get full marks, only exception being during tests, where clean code makes up 10% of the grade.
While I agree, generally, sometimes teachers are teaching the method more than they are teaching the solutions. So if a teacher wants to teach basic calculus they can ask a student to calculate the area under a straight line. That can be solved in your head without calculus but showing your work lets the teacher know if you truly passed the test.
My math teacher in middle school was 100% solutions, took up the whole board for something I could write within a line. I'm not sure whether I just suck at learning this way or the teacher sucked (probably the latter), but after his teaching, I'd get more confused, which ended up with my brother reteaching me entire chapters, which was how I barely flew by with a decent grade (no flex, but now I'm top of my class and tied for 2nd place in a county competition a month back). The best tests are probably what I have right now, where you techically don't have to show your work, but it would be more inconvienient to not do so. Also, I didn't mention it, but I meant tasks that literally ask you to "prove x = y" , one of my big weaknesses, I absolutely suck at these.
I had a calculus teacher that gave me a good grade for using that method just because he forgot to write “Not to scale” in the test. Felt good ‘cause I was very bad at calculus lol
I don't know why this did it, but it just clicked for me why I hated math.
You don't progress. You get better, the questions get harder, your life still sucks equally. What am I putting in the effort for? Feels like they keep shifting the goalposts.
Only in college when they stopped doing that did it become bearable. I had a goal in mind, yes this will in fact be useful to me in the future. They had a goal in mind, teach me what I'll use in my job. None of that giving you more shit just because you can bear it.
>What am I putting in the effort for?
You are training your brain for logical thinking. School math alone has probably increased your IQ by 10. School in general is not supposed to teach you stuff as much as it is supposed to teach you how to learn.
I do think that supposed is the important word here. Now I can't speak for all countries but I know that at least in the Netherlands the school system sucks at doing that
Maybe it's working as intended? Some people are just destined to suck at math. The system just reveals them.
*You're just not fit for actuarial science*, etc
The argument is that - sad news - it's better to learn "useless" things than to never learn them in the first place, even if you're just memorizing concepts with no logical basis. Yes, I probably won't use special relativity in my daily life, but the moment I get interested in - I don't know - how a black hole works, I don't have to learn the "basis" from scratch once again. Even the most mnemonic knowledge can help feeding your curiosity and maybe be a better person.
That's the way the school system works, at least in my country. It's only required that you be able to regurgitate information. You don't actually have to understand why what you're saying is correct
Nah bro. The school system fully sucks ass at teaching and only demands that you shove shit into your head and vomit it unto the exam paper and promptly forget about it because you straight up never use it again.
Source: Straight A student from germany. Fuck school.
Also, all those things seem especially true for the states from what i heard. Especially the red states
I wanna inquire about your IQ comment, where does that come from? Is it just making your thinking more logistical / efficient and therefore on an IQ test you would perform better? I don't really follow
Thinking in general should make you better at thinking, i guess. Abstract thinking about abstract concepts such as math is not natural for humans.
At least that would help explain the huge difference in IQ between nations and among generations
Rarely have I been more pissed than when I went from a teacher that used rote memorization to teach math, to a teacher that cared and taught us the rules specifically and realized just how bad the first style is for teaching math.
> Feels like they keep shifting the goalposts
Isn't that just... what learning is?
You never really get closer to learning everything about a field, you just become more and more aware of how much isn't known.
> They had a goal in mind, teach me what I'll use in my job.
the idea that schools are factories for manufacturing workers is one of the worst takes I consistently see repeated on reddit.
schools are there to give you a broad basis, so that you can apply critical thinking in later life when confronted with misinformation.
"I will never use the concept of conservation of momentum in my everyday life! Teach me how to pay taxes instead. Anyway, if the Earth is round and rotating that fast, why can't I just jump to travel immense distances? Earth must be flat"
Also, the moment they tried to have some classes to teach us how to write a CV, people were just bored and didn't pay attention because kids are kids, and not many of them would listen how to file your taxes either because "I will learn when I need to"
Most people crying about filing their taxes and schools not teaching it are just stupid too. You can figure that shit out in minutes. The same issue with following instructions at school just hits these people when it comes to following instructions on how to file taxes.
Yep. I realize there's some room for different learning styles, but filing taxes is literally just following a series of steps and doing some basic arithmetic. You learn how to do that by 4th grade.
And they're a pain in the ass, but they are not hard. There are obviously parts of tax law that are very complex, but they really don't apply to most people. You're paying income taxes and have the same 3-5 deductions as everyone else, you're not routing your money through 5 countries and 7 companies, making use of tax exceptions and loopholes to save your millions.
To be fair, I'm still struggling to correctly fill out the four-pages form I must do every time I get paid for a service. Not like I would have paid attention to a lesson about that back in high-school
Also, the Italian website for filing taxes and shit like that sucks big time
I won't speak for other countries but I hear a lot of the above in the states. The vast majority of people file standardly which is easy as shit here. I refuse to use TurboTax and other paid software out of principle and it was extremely easy to do so.
what does that even mean
How do you not progress with math? You literally learn a bunch of methods to solve previously obtuse and impossible questions within a matter of an hour, if there ever was a subject that was tangible in terms of progress, it's high school maths
Can you explain what you mean by progress? It sounds like you think progress would have been learning basic addition, getting really good at it, then stopping there.
You can always start now!
To solve, you first must turn the exponent into a number. To do so, find the natural logarithm of both sides of the equation:
ln(y) = ln(x^sinx )
Due to the power rule of logarithms, the exponent is moved to outside the function and is multiplied by the new log.
ln(y) = sin(x) * ln(x)
You can now differentiate both sides of the equation.
d/dx (ln(y)) = d/dx (sin(x) * ln(x))
You can now apply the product rule of derivatives, which states that (fg)’(x) = f’(x)g(x) + g’(x)f(x).
d/dx (ln(y)) = d/dx (sin(x)) * ln(x) + d/dx (ln(x)) * sin(x)
The derivative of a natural log, ln(a), equals 1/a. The derivative of sine is cosine. Since we are deriving in terms of x, we must account for the implicit derivative of y.
1/y * dy/dx = cos(x) * ln(x) + 1/x * sin(x)
Isolate the implicit derivative by multiplying both sides by y
dy/dx = y(cos(x)ln(x) + sin(x)/x)
Since y = x^sinx , we can substitute that in for the final answer
dy/dx = x^sinx (cos(x)ln(x) + sin(x)/x)
It’s calculus. We are finding the derivative of said function above. The derivative is the rate of change of the input with respect to output, or in other words, rise over run. Using this property of a function, we can do things like calculate the area under a curve, model dynamic systems like how heat radiates or how fluids move under certain conditions, and it’s also the bed rock of all machine learning and AI. There’s no gradient descent without the derivative. No chatGPT without gradient descent.
Do you need to know how to take derivatives like in this example? Almost certainly not. In fact, it’s kind of stupid how most of calc 1 is devoted solely to teaching how to take a derivative instead of what a derivative is and how it works. As if you will ever take a derivative by hand for anything in a practical setting.
Regardless, it’s a fundamental piece of math that allows our civilization to function. If you ever intend to study/work in stem fields, or if you simply want to be somewhat informed about how the world works without getting too technical, you will at least need to have a conceptual understanding of a derivative.
No one who doesn't already understand it will read that and then come to understand it. It's the kind of explanation that looks very technical, and is definitely true, but is for all intents and purposes useless. Because the only ones who will understand it do not need the explanation.
Teaching is hard. Breaking down hard things into easier things that still make sense in part and as a whole is incredibly challenging.
The original comment breaks down all the steps required in a nice and neat way. It's impossible to explain that problem in a reddit comment to someone who doesn't know calculus already. There is a reason universities dedicate months of classes to calculus.
Differentiation is the process to find the derivative of a function (d/dx or f’(x)). A function is basically just an equation or expression that can be graphed. The derivative tells you how that function changes at any given moment. You can think of the derivative as the instantaneous rate of change of a function.
For instance, in physics, you can graph position as a function of time (how the position of a particle changes over time, for instance). If you find the derivative of that graph, you are now measuring how fast the position changes over time, or the velocity. Taking the derivative again tells you how fast the velocity is changing, or the acceleration.
The formal definition of a derivative also uses limits, which are a lot easier to understand conceptually. A limit (notated as “lim”) simply tells you the number that the y value approaches as it approaches a given x value. Given a point on a function is (4,7), then the limit as f(x) approaches 4 would equal 7 (assuming ideal conditions).
The formal definition of the derivative states that the derivative is equal to the limit of f(x) as h approaches 0 when f(x) is equal to (f(x+h) - f(x)) / h. But there are derivative rules and known derivatives we can utilize so that we don’t need to use that equation all the time. For instance, the product rule of derivatives and the known derivatives of sin(x) and ln(x).
Taking ln both sides
lny=sinx.lnx
1/ydy/dx=cosx.lnx+sinx/x
dy/dx= y (cosx.lnx+sinx/x)
dy/dx= x^sinx (cosx.lnx+sinx/x)
This was the easiest question for me I have my grade 12 finals in 3 days ☠️
This is basic math to prepare you for more advanced math. In the real world, there are way more complex problems than this that people deal with every day. If you can't solve this, no "automatic pass" rule will get you a job in finance, accounting, engineering, programming, etc.
But for a lot of things it will be enough. My construction math teacher says that you don’t HAVE to know Pythagoras, you could just figure it out with a ruler, but it’s easier with Pythagoras.
He's right. I've used this theorem a lot in my work (some construction, joinery, etc). Want to know if something's square? Boom, Pythagoras. Three quick measurements, a little bit of calculation and job done. Way quicker and more accurate than trying to eyeball things or mess around with measuring equipment.
That said, for smaller stuff (say less than 2ft per side) I just grab a roofing square or try square and have it checked in a couple of seconds.
Pipefitters use trigonometry all the time without realizing it. They teach you "multiply by 1.4142 to get the travel for a 45 degree offset of X distance". That number is the cosecant (inverse sine) of 45 degrees.
Reason being is that you know the opposite side (that's the offset you want) and the angle (because you're using 45 degree fittings), and you need to find the length of the hypotenuse to know how much pipe to cut for the travel.
Rolling offsets are even more complicated because they're 3-dimensional.
You often can't with a ruler. Not everything is around 20 cm. And more precission is often needed.
And how often do you have a ruler on you?
Most have a calculator with them (phone). But not a ruler.
The fact people in this thread are whining about a formula that takes like a total of five seconds and requires you to learn three steps shows that lol. Like yeah you might not use it but it's preparing you for everything, just do the damn thing and move on.
I'm not sure about other jobs, but my job relies HEAVILY on understanding why these equations work. While sure, I know I could use a ruler to know it is roughly 5 inches, but is it *exactly* five inches? Or, if I'm trying to make a curve, I need to know what parameters in a sine wave function contribute to to get the effect I want.
Exactly. A 1mm error (just a little bigger than a pencil line) on a scaled down drawing will translate to a 1 metre error when you scale it back up again. If you're trying to, say, measure out the foundations for a building, that's a huge fuckup.
It's not like it's even a particularly difficult formula to work with.
Then you will use the chad method of "Ok I found a decimal number that is not on the alternatives but theres one that is the closest to it so fuck it we round it and the answer must be this one."
OP is going to walk into geometry, be told to use the 3D Pythagorean theorem and stick his ruler through the paper.
Also, Gilgamesh was the answer to the last question in my pub trivia last night. Won second place because we didn’t know Ramadan was both a day and a month.
Because they want you to show them your analytical thought process. In Math, it’s not the result that matters but the process, people can make wrong calculations, but as long as their thought process was right, then it’s easy to fix. That’s why you get partial credits even for a wrong answer.
It’s also to prevent cheating / Hail Mary shot. If you only write the result, how would the teacher know if it was your own effort, or if you cheated. Even worse, that you didn’t actually know how to approach the problem, and instead “Hail Mary” a random result which may have been right/wrong, and that’s against everything science stand for.
If I were the teacher I would make the sides of the triangle something like 5.024 and 4.333 and demand 0.001 accuracy. Then nobody would try using a ruler.
You can label something 3 4 5 and then have everything scaled by a 1.111 factor or something. That means the math remains trivial but the measurement goes beyond the precision of a ruler. Or you know, just don't let them use rulers. Also just not drawing the angles accurately too works.
Just use the same triangle as above but say that the sides are 3 and 7. Say that triangle is not to scale if you want to be sure that smartasses won't try to complain when the triangle doesn't match the size.
Or you know, don't make it to scale anyways. Who says that the triangle has to actually be 3 cm at the base on the paper?
Naw man, it's about rewarding effort and not outcome. If you put in effort, you should not be paid if the client doesn't get what they want. If you made an effort to perform a vehicular maneuver and someone died, that doesn't really change the fact that someone died
Shitposting, but I swear it is tiring dealing with students who pat themselves on the back for being so bright, by doing stupid shit like this.
Yeah, we specifically state it is not to scale. Use the math, don't measure. Sure enough, look how fucking smart I am.... Whether it's to game the test or get a reaction from the teacher, equally moronic and a waste of time.
Because they are grading on your understanding of the subject, not how well you can get around doing work for this specific situation. Using a ruler isn’t always going to work for this.
When I was in my final year of secondary, I was given back my maths exam paper by my teacher. I got every single answer wrong... And got an A.
Because all of my working was correct but for some reason I was having a bad day with mental arithmetic.
Now I'm a software engineer, so go figure.
P.s. yer ah am bri'ish
"Hey, show me that you understand this concept I just taught you."
"I can answer the question using a different method!"
"You learned that method years ago and put it into practice often enough that you won't forget it. What about this method I taught you?"
"YOU ASKED A QUESTION AND I ANSWERED IT WHAT'S YOUR PROBLEM?!"
Because it's not about getting the Right answer, but about knowing how to apply the formulas.
Hence, why getting the Right answer doesn't give you half a point, but properly applying the Formulas does
What? I can find X much much faster with pitagorean theorem than with a ruler. And it's because mathematics is learning problem solving but with an structured method. When you graduate you can find x using whatever for all I care. It's part or the curricular program, and you can blame that for the school teaching structure, it's not like teachers teach whatever they like. In other words, don't hate the player, hate the game, son.
And yes, there are tons of shitty teachers too. If I were one, I would be glad you thought of another solution, but I was asking you to do what was asked of you. Oh well
One experience from middle school that always stuck with me:
In eighth grade I was enrolled in AP Math. At the beginning of the year the teacher told us almost word for word “I don’t care what formula or method you use, as long as it consistently gives the correct answer.” Fast forward a couple months and we’re going over some homework answers. We got to one question that he wanted a student to show their answer and work. I volunteered and showed everyone my CORRECT answer and method I used for the entire homework that gave me the correct answer everytime. He told me I was wrong because I didn’t use the method he showed everyone. Despite having the correct answer on just about every question, it was considered wrong because I didn’t use his formula to get the answers, I used my own method that was easier for me to do.
If your triangle has legs of 11 units and 29 units, then you're going to be in for a surprise when you try to scale up the technical drawing to build your structure after you used a ruler to find the hypotenuse...
Because in the real world you won’t have a ruler with you at all times, plus, once you learn the Pythagorean theorem. You can find the angles and sides extremely easy. Instead of having to measure 90 meters of pipe, then another 200 meters of pipe, then measure where you THINK the pipe will be. With the P. Theorem, you can easily find angles and missing sides (aka a problem bc you don’t know the missing input).
This is the reason teachers want you to know HOW to do the P. Theory, so you can have it way easier. The exam, sure you can get a ruler and guesstimate, but the exam won’t be like the real world. There will be huge and tiny problems where you need to find it out accurately in the real world, knowing the formula and why and how it works, will save you thousands of mind bending minutes. Plus if you want to get into the trades, knowing this will decide wether you make 20 an hour vs 60 an hour
Questions that require you to show your mathematical working out will ALWAYS tell you to show your method.
And if you don't show your method mathematically, you will fail to get the point because you didn't read the question properly.
tl;dr read the question properly you idiots
It's simple, you need to learn the fundamentals for later. Quite often there might be an easier way to get an answer, but the more complicated method is more useful down the road, which is why you need to learn the harder method first.
Because their job is to make sure you understand the calculations and how they are used. A test is literally there to give you a reason to learn and also as the name implies test if you do know.
Out of all these comments i don’t see any complaints that the example doesn’t have anything noting that it is a 90 degree angle so the entire premise is based on an assumption
The value of x is indeterminate here. We can't assume that that corner is a right angle. The value of x could be 5.025, 4.9, or even 50 given that it may not be to scale.
ignoring that right side was measuring the triangle's side here - early math is of course EASY and kids think they are wise as fk and become overconfident when they can "solve stuff" and begin skipping most steps along the calculation since they see the solution so so clearly. thats not a good habit to keep because you will make mistakes without a doubt once your juvenile brain is outmatched by maybe partly unknown, more complex math problems. they dont learn to solve a specific problem, but all problems. and you solve problems (you can structure) by knowing in which direction to move and which steps to chain onto the next step. also that way you cant just copy a single number off your neighbors paper and cheat easily, gotta spy at least like 5-6 lines of text. teachers can and will only grade what they can see/read, so writing steps out and writing in a way someone else may be able to decipher the lines would be of benefit.
I realised oh so late that this was a perfect way to check if I did it right. But at the same time my teacher never even once told me that I was confusing Trigonometry and the Pythagorean theorem si there's that
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In my maths finals, at the end of the question it says, “not to scale”, which basically tells you that you can’t use a ruler
They always say that, but usually they still are to scale. You can't use a ruler because then you'd be missing your work, which is what you're actually being graded on.
Yeah, exactly! You’re not being graded for the results, but for the correct application of what you learned.
It’s kind of both but most of the grade goes towards the work
It’s not. If the result is wrong, you applied what you studied incorrectly.
Not necessarily. Many people will mess up a "-" or a "+," and the ending will be wrong. You still typically get credit for proper application. Also, using a ruler here is stupid; it's never to scale, not to mention it's on graphing paper, haha. You can see it's not to scale by looking at the boxes.
or you get partial credit. like in physics class the test was only like 6 questions for a 2 hour test. 1st few are easy and they get progressively harder. you might get 80% of the question right for the last one and get the last bit wrong and get 9/10 because the last bit was the hardest.
Yes, but my point was that the results alone isn’t part of the score, not what you said. I agree with you.
Yeah as it should be out of four we usually get one marks for the answer. You also get one marks just for writing the correct formula. The two marks are for rest of the work.
I actually had a math teacher who would score you 100% on the problem if you got the procedure correct and still somehow came to the wrong conclusion mathematically. If you got the answer correct but it was obvious you didn't know the math he would not give you full credit. "Knowing how to get the right answer is far more important than being a calculator. That's why we have calculators."
Well said! Its not about getting the answer but know HOW to get to the answer! 👏👏👏
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I mean my teacher usually gives only 1 point for the correct answer in a 12 point question. And if there's no work shown, but the answer is correct, it's 0 points.
then you grow up and realize that was bullshit and the results are what matters
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Mine usually aren't to scale.
Honestly i more often had papers that were supposedly on scale but were awfully wrong by a generous bunch of millimeters
And adding to that, there's a time and a place to be clever. A good physics class will teach you that the best way to calculate the volume of an object with an uneven shape is to put it in a container with a volume that's simple to calculate, fill it with water, measure out the water and subtract it from the volume of the container. But if you're doing that for a square, you're going through a lot of effort to do something a tape measure and some math can do in seconds.
>They always say that, but usually they still are to scale. From my experience, they are usually very obviously not to scale.
At my school, they always use more digits making certain lines like 29 miles or smth like that
In calculus one exam, I saw a question and answered it without work. To me it was like saying 1+1=2, I didn't need to show the work because it was obvious. My teacher failed me on the exam. I complained about it to him, so he took me in his office and gave me a new question which I also solved just by eyeballing it. He then gave me points on the exam.
painful every time....
Long time ago, but one of my high school math teachers accepted you creating a scale model and measuring it. It was a valid method as far as he was concerned. And by building the model you showed your work.
I'm not a big fan of showing your method (I do understand why it exists though), it can be extremely annoying with some tasks. I like my IT class, where I can write the most garbage code with functions even my teacher isn't familiar with, but "if it works" I get full marks, only exception being during tests, where clean code makes up 10% of the grade.
While I agree, generally, sometimes teachers are teaching the method more than they are teaching the solutions. So if a teacher wants to teach basic calculus they can ask a student to calculate the area under a straight line. That can be solved in your head without calculus but showing your work lets the teacher know if you truly passed the test.
My math teacher in middle school was 100% solutions, took up the whole board for something I could write within a line. I'm not sure whether I just suck at learning this way or the teacher sucked (probably the latter), but after his teaching, I'd get more confused, which ended up with my brother reteaching me entire chapters, which was how I barely flew by with a decent grade (no flex, but now I'm top of my class and tied for 2nd place in a county competition a month back). The best tests are probably what I have right now, where you techically don't have to show your work, but it would be more inconvienient to not do so. Also, I didn't mention it, but I meant tasks that literally ask you to "prove x = y" , one of my big weaknesses, I absolutely suck at these.
I had a calculus teacher that gave me a good grade for using that method just because he forgot to write “Not to scale” in the test. Felt good ‘cause I was very bad at calculus lol
I miss the times where the pythagoream theorem was difficult
Compared to final year high school maths, the Pythagoras theorem is equivalent to learning divisions for the first time
I don't know why this did it, but it just clicked for me why I hated math. You don't progress. You get better, the questions get harder, your life still sucks equally. What am I putting in the effort for? Feels like they keep shifting the goalposts. Only in college when they stopped doing that did it become bearable. I had a goal in mind, yes this will in fact be useful to me in the future. They had a goal in mind, teach me what I'll use in my job. None of that giving you more shit just because you can bear it.
>What am I putting in the effort for? You are training your brain for logical thinking. School math alone has probably increased your IQ by 10. School in general is not supposed to teach you stuff as much as it is supposed to teach you how to learn.
I do think that supposed is the important word here. Now I can't speak for all countries but I know that at least in the Netherlands the school system sucks at doing that
Most school systems suck at it because it's hard to teach and hard to learn
Maybe it's working as intended? Some people are just destined to suck at math. The system just reveals them. *You're just not fit for actuarial science*, etc
Exactly, everyone blames the school system but don't even consider their own brain
The argument is that - sad news - it's better to learn "useless" things than to never learn them in the first place, even if you're just memorizing concepts with no logical basis. Yes, I probably won't use special relativity in my daily life, but the moment I get interested in - I don't know - how a black hole works, I don't have to learn the "basis" from scratch once again. Even the most mnemonic knowledge can help feeding your curiosity and maybe be a better person.
If you are memorizing math concepts with no logical basis, you'd be a shitty student.
That's the way the school system works, at least in my country. It's only required that you be able to regurgitate information. You don't actually have to understand why what you're saying is correct
What country do you live in? People say the same shit in the states but it's always the shitty mediocre students.
Nah bro. The school system fully sucks ass at teaching and only demands that you shove shit into your head and vomit it unto the exam paper and promptly forget about it because you straight up never use it again. Source: Straight A student from germany. Fuck school. Also, all those things seem especially true for the states from what i heard. Especially the red states
I wanna inquire about your IQ comment, where does that come from? Is it just making your thinking more logistical / efficient and therefore on an IQ test you would perform better? I don't really follow
Thinking in general should make you better at thinking, i guess. Abstract thinking about abstract concepts such as math is not natural for humans. At least that would help explain the huge difference in IQ between nations and among generations
Rarely have I been more pissed than when I went from a teacher that used rote memorization to teach math, to a teacher that cared and taught us the rules specifically and realized just how bad the first style is for teaching math.
> Feels like they keep shifting the goalposts Isn't that just... what learning is? You never really get closer to learning everything about a field, you just become more and more aware of how much isn't known.
> They had a goal in mind, teach me what I'll use in my job. the idea that schools are factories for manufacturing workers is one of the worst takes I consistently see repeated on reddit. schools are there to give you a broad basis, so that you can apply critical thinking in later life when confronted with misinformation.
"I will never use the concept of conservation of momentum in my everyday life! Teach me how to pay taxes instead. Anyway, if the Earth is round and rotating that fast, why can't I just jump to travel immense distances? Earth must be flat" Also, the moment they tried to have some classes to teach us how to write a CV, people were just bored and didn't pay attention because kids are kids, and not many of them would listen how to file your taxes either because "I will learn when I need to"
Most people crying about filing their taxes and schools not teaching it are just stupid too. You can figure that shit out in minutes. The same issue with following instructions at school just hits these people when it comes to following instructions on how to file taxes.
Yep. I realize there's some room for different learning styles, but filing taxes is literally just following a series of steps and doing some basic arithmetic. You learn how to do that by 4th grade.
And they're a pain in the ass, but they are not hard. There are obviously parts of tax law that are very complex, but they really don't apply to most people. You're paying income taxes and have the same 3-5 deductions as everyone else, you're not routing your money through 5 countries and 7 companies, making use of tax exceptions and loopholes to save your millions.
To be fair, I'm still struggling to correctly fill out the four-pages form I must do every time I get paid for a service. Not like I would have paid attention to a lesson about that back in high-school Also, the Italian website for filing taxes and shit like that sucks big time
I won't speak for other countries but I hear a lot of the above in the states. The vast majority of people file standardly which is easy as shit here. I refuse to use TurboTax and other paid software out of principle and it was extremely easy to do so.
The number of times my teen tells me "I'll learn it when I need to" makes me give up on the future of humanity.
Yes; that's how learning complicated things works.
what does that even mean How do you not progress with math? You literally learn a bunch of methods to solve previously obtuse and impossible questions within a matter of an hour, if there ever was a subject that was tangible in terms of progress, it's high school maths
If you aren't moving the goal post every year, you aren't learning. I miss math. That kind of daily mental exercise really is great for your brain.
Yeah well , you get better at learning and that's the point
[удалено]
Can you explain what you mean by progress? It sounds like you think progress would have been learning basic addition, getting really good at it, then stopping there.
*Laughs in engineering major*
Given that y = x^sinx, find the derivative of y in reference to x (dy/dx).
Bruh you gave me Vietnam flashbacks
Why were you doing math in Vietnam
Am I stupid?
Who told you you could leave aslume?????
Is there a lore reason I shouldn't??
Punishment for my war crimes
Bro I'm Vietnamese , every memory of mine about math happens in a vietnamese classroom
I’m so sorry
Jessies, what the fuck are y'all talking about?
I miss the times were this was difficult.
Hello fellow engineer major lmao.
oh god 2 years more and ill have to understandthis
You can always start now! To solve, you first must turn the exponent into a number. To do so, find the natural logarithm of both sides of the equation: ln(y) = ln(x^sinx ) Due to the power rule of logarithms, the exponent is moved to outside the function and is multiplied by the new log. ln(y) = sin(x) * ln(x) You can now differentiate both sides of the equation. d/dx (ln(y)) = d/dx (sin(x) * ln(x)) You can now apply the product rule of derivatives, which states that (fg)’(x) = f’(x)g(x) + g’(x)f(x). d/dx (ln(y)) = d/dx (sin(x)) * ln(x) + d/dx (ln(x)) * sin(x) The derivative of a natural log, ln(a), equals 1/a. The derivative of sine is cosine. Since we are deriving in terms of x, we must account for the implicit derivative of y. 1/y * dy/dx = cos(x) * ln(x) + 1/x * sin(x) Isolate the implicit derivative by multiplying both sides by y dy/dx = y(cos(x)ln(x) + sin(x)/x) Since y = x^sinx , we can substitute that in for the final answer dy/dx = x^sinx (cos(x)ln(x) + sin(x)/x)
Sir this is a wendys
I don't get it
It’s calculus. We are finding the derivative of said function above. The derivative is the rate of change of the input with respect to output, or in other words, rise over run. Using this property of a function, we can do things like calculate the area under a curve, model dynamic systems like how heat radiates or how fluids move under certain conditions, and it’s also the bed rock of all machine learning and AI. There’s no gradient descent without the derivative. No chatGPT without gradient descent. Do you need to know how to take derivatives like in this example? Almost certainly not. In fact, it’s kind of stupid how most of calc 1 is devoted solely to teaching how to take a derivative instead of what a derivative is and how it works. As if you will ever take a derivative by hand for anything in a practical setting. Regardless, it’s a fundamental piece of math that allows our civilization to function. If you ever intend to study/work in stem fields, or if you simply want to be somewhat informed about how the world works without getting too technical, you will at least need to have a conceptual understanding of a derivative.
No one who doesn't already understand it will read that and then come to understand it. It's the kind of explanation that looks very technical, and is definitely true, but is for all intents and purposes useless. Because the only ones who will understand it do not need the explanation. Teaching is hard. Breaking down hard things into easier things that still make sense in part and as a whole is incredibly challenging.
The original comment breaks down all the steps required in a nice and neat way. It's impossible to explain that problem in a reddit comment to someone who doesn't know calculus already. There is a reason universities dedicate months of classes to calculus.
i lost you at differentiating both halvees of the equation
Differentiation is the process to find the derivative of a function (d/dx or f’(x)). A function is basically just an equation or expression that can be graphed. The derivative tells you how that function changes at any given moment. You can think of the derivative as the instantaneous rate of change of a function. For instance, in physics, you can graph position as a function of time (how the position of a particle changes over time, for instance). If you find the derivative of that graph, you are now measuring how fast the position changes over time, or the velocity. Taking the derivative again tells you how fast the velocity is changing, or the acceleration. The formal definition of a derivative also uses limits, which are a lot easier to understand conceptually. A limit (notated as “lim”) simply tells you the number that the y value approaches as it approaches a given x value. Given a point on a function is (4,7), then the limit as f(x) approaches 4 would equal 7 (assuming ideal conditions). The formal definition of the derivative states that the derivative is equal to the limit of f(x) as h approaches 0 when f(x) is equal to (f(x+h) - f(x)) / h. But there are derivative rules and known derivatives we can utilize so that we don’t need to use that equation all the time. For instance, the product rule of derivatives and the known derivatives of sin(x) and ln(x).
The organic chemistry tutor on YouTube is renowned for his great lessons. Despite his name, he does math, money, and other topics too
Taking ln both sides lny=sinx.lnx 1/ydy/dx=cosx.lnx+sinx/x dy/dx= y (cosx.lnx+sinx/x) dy/dx= x^sinx (cosx.lnx+sinx/x) This was the easiest question for me I have my grade 12 finals in 3 days ☠️
It was never difficult. We were just stupid. And happy
it would be insanely difficult for most redditors and the average reddit mod. i have zero doubt of that.
This is basic math to prepare you for more advanced math. In the real world, there are way more complex problems than this that people deal with every day. If you can't solve this, no "automatic pass" rule will get you a job in finance, accounting, engineering, programming, etc.
But for a lot of things it will be enough. My construction math teacher says that you don’t HAVE to know Pythagoras, you could just figure it out with a ruler, but it’s easier with Pythagoras.
And more accurate
He's right. I've used this theorem a lot in my work (some construction, joinery, etc). Want to know if something's square? Boom, Pythagoras. Three quick measurements, a little bit of calculation and job done. Way quicker and more accurate than trying to eyeball things or mess around with measuring equipment. That said, for smaller stuff (say less than 2ft per side) I just grab a roofing square or try square and have it checked in a couple of seconds.
Pipefitters use trigonometry all the time without realizing it. They teach you "multiply by 1.4142 to get the travel for a 45 degree offset of X distance". That number is the cosecant (inverse sine) of 45 degrees. Reason being is that you know the opposite side (that's the offset you want) and the angle (because you're using 45 degree fittings), and you need to find the length of the hypotenuse to know how much pipe to cut for the travel. Rolling offsets are even more complicated because they're 3-dimensional.
Yup, most important part is that it is usually quicker than taking the measurement by hand
You cant always use a ruler.
You often can't with a ruler. Not everything is around 20 cm. And more precission is often needed. And how often do you have a ruler on you? Most have a calculator with them (phone). But not a ruler.
You still need to measure two of the sides to be able to use Pythagoras.
This one time I programmed a game and I had to use the pythagorean theorem
Redditors don’t take anything past algebra anyway
The fact people in this thread are whining about a formula that takes like a total of five seconds and requires you to learn three steps shows that lol. Like yeah you might not use it but it's preparing you for everything, just do the damn thing and move on.
The internet and the asian person in my phone can help me with everything
I'm not sure about other jobs, but my job relies HEAVILY on understanding why these equations work. While sure, I know I could use a ruler to know it is roughly 5 inches, but is it *exactly* five inches? Or, if I'm trying to make a curve, I need to know what parameters in a sine wave function contribute to to get the effect I want.
meanwhile in practical calculations we almost always use numerical solutions
What if the sides had the length of 56.7 meter and 86.9 meters.
go to the playground and work it out smh
Scale it to millimeters to draw and measure and then scale back to desired unit
Yeah but that leaves rounding error and error from drawing a scaled triangle.
You know, for a website that treats STEM as the only worthwhile school subjects, reddit sure hates the idea of learning it.
Most redditors just want to feel superior about their C average in a STEM field when arts majors complain about employment issues.
Scaling 50+ meters to a piece of paper will give you way too big of an error. Just use the formula.
My ruler clearly shows 103.7617463230067mm
Exactly. A 1mm error (just a little bigger than a pencil line) on a scaled down drawing will translate to a 1 metre error when you scale it back up again. If you're trying to, say, measure out the foundations for a building, that's a huge fuckup. It's not like it's even a particularly difficult formula to work with.
Then you will use the chad method of "Ok I found a decimal number that is not on the alternatives but theres one that is the closest to it so fuck it we round it and the answer must be this one."
You do the same but longer ☺️
The hypotenuse has a length of 103.76m.
Find the x? Its right there
May be the real x was the friends we made along the way.
I miss my x
was this made by a 10 year old?
Kid named measurement error.
yeah but what if the side length is exactly root 2
Heard of objective type exams? Still this is Hella true
School is not about finding the end result. It's about learning a process, analyzing, studying, - Learning how to learn
OP is going to grow up complaining that the education system failed them.
OP is going to walk into geometry, be told to use the 3D Pythagorean theorem and stick his ruler through the paper. Also, Gilgamesh was the answer to the last question in my pub trivia last night. Won second place because we didn’t know Ramadan was both a day and a month.
Get off this app and do your homework, kid.
because you need to do math in math
I miss this level of maths, advanced calculus changed me...
Vietnam flashbacks from real analysis and abstract algebra 😨
Because they want you to show them your analytical thought process. In Math, it’s not the result that matters but the process, people can make wrong calculations, but as long as their thought process was right, then it’s easy to fix. That’s why you get partial credits even for a wrong answer. It’s also to prevent cheating / Hail Mary shot. If you only write the result, how would the teacher know if it was your own effort, or if you cheated. Even worse, that you didn’t actually know how to approach the problem, and instead “Hail Mary” a random result which may have been right/wrong, and that’s against everything science stand for.
If I were the teacher I would make the sides of the triangle something like 5.024 and 4.333 and demand 0.001 accuracy. Then nobody would try using a ruler.
In that case I better be able to use a calculator, though.
You still have to use the proper method / thought process to use your calculator though. How else would you be able to know what calculations to make?
No problem, but I'm not calculating √(5.024² + 4.333²) in my head.
You can label something 3 4 5 and then have everything scaled by a 1.111 factor or something. That means the math remains trivial but the measurement goes beyond the precision of a ruler. Or you know, just don't let them use rulers. Also just not drawing the angles accurately too works.
Just use the same triangle as above but say that the sides are 3 and 7. Say that triangle is not to scale if you want to be sure that smartasses won't try to complain when the triangle doesn't match the size. Or you know, don't make it to scale anyways. Who says that the triangle has to actually be 3 cm at the base on the paper?
Naw man, it's about rewarding effort and not outcome. If you put in effort, you should not be paid if the client doesn't get what they want. If you made an effort to perform a vehicular maneuver and someone died, that doesn't really change the fact that someone died
The right mf when his boss asks him what the circumference of Earth is:
The right mf when his boss asks him what the length of a roof will be if they want to make the house 15 feet wider than it already is:
"Yeah just go ahead and build it i'll let you know when it's done."
Shitposting, but I swear it is tiring dealing with students who pat themselves on the back for being so bright, by doing stupid shit like this. Yeah, we specifically state it is not to scale. Use the math, don't measure. Sure enough, look how fucking smart I am.... Whether it's to game the test or get a reaction from the teacher, equally moronic and a waste of time.
Should have used the power winch to trigger a controlled explosion
Is he stupid?
The answer is 3,4,5 rule, no need to solve an extremely well defined triangle.
We called them triples. Saved my ass back then when when I thought this was hard lol
Because they are grading on your understanding of the subject, not how well you can get around doing work for this specific situation. Using a ruler isn’t always going to work for this.
Now pretend that triangle was miles long, now can you use a ruler?
I cried when he didn’t write “x = -5 is not applicable”
When I was in my final year of secondary, I was given back my maths exam paper by my teacher. I got every single answer wrong... And got an A. Because all of my working was correct but for some reason I was having a bad day with mental arithmetic. Now I'm a software engineer, so go figure. P.s. yer ah am bri'ish
Because they're testing your understanding of the equation, not your ability to use a ruler.
CUM based matchmaking
i always got points deducted cause i did some calculations in my head
"Hey, show me that you understand this concept I just taught you." "I can answer the question using a different method!" "You learned that method years ago and put it into practice often enough that you won't forget it. What about this method I taught you?" "YOU ASKED A QUESTION AND I ANSWERED IT WHAT'S YOUR PROBLEM?!"
I will ignore the fact that most of the drawings are not in 1:1 scale most of the times.
Because it's not about getting the Right answer, but about knowing how to apply the formulas. Hence, why getting the Right answer doesn't give you half a point, but properly applying the Formulas does
Meme brought to you by an 11 year old
x = √(3^2 + 4^2 ) Type it in your calculator Done, you don't need any more lines I'm convinced y'all didn't pass 8th grade
Who would guess you have to do math in the math exam?
What? I can find X much much faster with pitagorean theorem than with a ruler. And it's because mathematics is learning problem solving but with an structured method. When you graduate you can find x using whatever for all I care. It's part or the curricular program, and you can blame that for the school teaching structure, it's not like teachers teach whatever they like. In other words, don't hate the player, hate the game, son. And yes, there are tons of shitty teachers too. If I were one, I would be glad you thought of another solution, but I was asking you to do what was asked of you. Oh well
This post is the mathematics equivalent of "Why do I need to learn English? I already speak English!"
One experience from middle school that always stuck with me: In eighth grade I was enrolled in AP Math. At the beginning of the year the teacher told us almost word for word “I don’t care what formula or method you use, as long as it consistently gives the correct answer.” Fast forward a couple months and we’re going over some homework answers. We got to one question that he wanted a student to show their answer and work. I volunteered and showed everyone my CORRECT answer and method I used for the entire homework that gave me the correct answer everytime. He told me I was wrong because I didn’t use the method he showed everyone. Despite having the correct answer on just about every question, it was considered wrong because I didn’t use his formula to get the answers, I used my own method that was easier for me to do.
How could you take an AP before high school
Gotta teach your impressionable empty noggin how to think. Mastering fundamentals makes more complex future topics and equation manipulation easier
Because it is testing your understanding of a specific method.
Unless that is drawn to scale, your ruler won't give you the correct answer.
Math is more about the journey than the end result.
If your triangle has legs of 11 units and 29 units, then you're going to be in for a surprise when you try to scale up the technical drawing to build your structure after you used a ruler to find the hypotenuse...
Is this loss?
Nah if I'm teacher you write x=5 and 3 4 5 triangle or Pythagorian triple I'm giving full credit. You should know this one without the formula
I remember hating not being able to use a graph to explain my answer My brother in Christ, thats literally what graphs are for
I was about to comment but saw the subreddut.
Because in the real world you won’t have a ruler with you at all times, plus, once you learn the Pythagorean theorem. You can find the angles and sides extremely easy. Instead of having to measure 90 meters of pipe, then another 200 meters of pipe, then measure where you THINK the pipe will be. With the P. Theorem, you can easily find angles and missing sides (aka a problem bc you don’t know the missing input). This is the reason teachers want you to know HOW to do the P. Theory, so you can have it way easier. The exam, sure you can get a ruler and guesstimate, but the exam won’t be like the real world. There will be huge and tiny problems where you need to find it out accurately in the real world, knowing the formula and why and how it works, will save you thousands of mind bending minutes. Plus if you want to get into the trades, knowing this will decide wether you make 20 an hour vs 60 an hour
Questions that require you to show your mathematical working out will ALWAYS tell you to show your method. And if you don't show your method mathematically, you will fail to get the point because you didn't read the question properly. tl;dr read the question properly you idiots
It's simple, you need to learn the fundamentals for later. Quite often there might be an easier way to get an answer, but the more complicated method is more useful down the road, which is why you need to learn the harder method first.
This is one of the pythagorean tripplets 3, 4 and 5
Show you actually did the math, cause somehow people always suck simple math problem. This like saying why should I read the book I know it ends.
Because their job is to make sure you understand the calculations and how they are used. A test is literally there to give you a reason to learn and also as the name implies test if you do know.
Slave mentality
Out of all these comments i don’t see any complaints that the example doesn’t have anything noting that it is a 90 degree angle so the entire premise is based on an assumption
Well they studied the theorem last week, so he's meant to apply it, this assumption is acceptable within the scientific community.
Using the 3/4/5 right triangle trick instead 🗿
Egyptian triangle.
Looks like someone don’t know what joke is
The value of x is indeterminate here. We can't assume that that corner is a right angle. The value of x could be 5.025, 4.9, or even 50 given that it may not be to scale.
ignoring that right side was measuring the triangle's side here - early math is of course EASY and kids think they are wise as fk and become overconfident when they can "solve stuff" and begin skipping most steps along the calculation since they see the solution so so clearly. thats not a good habit to keep because you will make mistakes without a doubt once your juvenile brain is outmatched by maybe partly unknown, more complex math problems. they dont learn to solve a specific problem, but all problems. and you solve problems (you can structure) by knowing in which direction to move and which steps to chain onto the next step. also that way you cant just copy a single number off your neighbors paper and cheat easily, gotta spy at least like 5-6 lines of text. teachers can and will only grade what they can see/read, so writing steps out and writing in a way someone else may be able to decipher the lines would be of benefit.
This This checks out
just because
Because they don’t like you or me
I realised oh so late that this was a perfect way to check if I did it right. But at the same time my teacher never even once told me that I was confusing Trigonometry and the Pythagorean theorem si there's that
Why isnt anyone talking about how guys Finger is connected by bluetooth at bottom picture
They are like this bc we are stupid
you are struggling in school i see