Nah. I was labeled a dumb kid in high school because I had to work 40 hours a week. I went back to college as an adult and now have a masters in mech Eng.
Went to my high school reunion and the smart kids were largely abject failures. They never really struggled until college, then mostly failed out. I felt bad for them, but not too bad since most of them bullied me.
Sounds like maybe there weren't the true smart kids. You finished high-school while working a full time job. You were capable and adaptable. Fuck them :)
As one of the resident smart kids who went into CompSci and now works as a software engineer, I haven't touched any of this for a hot minute. I mainly use it for 3D print designs once in a blue moon.
Of course it depends, but for example, it CSS esing functions are based on polinomial or sin waves. If you ever want to understand or perhaps implement and easing function, trigonometry has your back.
I was thinking this myself. sin, cos, tan. Have not used. I have use euler coordinates so thats something but really solve for x is the most advanced thing I have used outside of school. mmmm actually I guess some statistics like stadard deviation.
I recently had to do a two variable equation because I was using a recipe that called for a specific milk fat percentage by mixing cream and milk, and my cream was heavier than what it needed. That was really stretching the limits of what math I remember.
Programmer for 25 years. Only time I have ever used math more complicated than simple multiply/divide was... actually never.
That one time when I copy/pasted a formula for linear interpolation, was still just multiplication and division. And I still have no idea how it works.
I've even done OpenGL and graphics programming and still haven't needed any algebra/trig/etc, although I don't do complex 3D rendering or physics or anything like that.
I wish I knew how to do cool programming stuff like draw circles and waves and stuff though, but I've never seen a tutorial that didn't go WAY over my head immediately.
Drawing a circle is actually pretty simple! Say we want to draw one with:
radius r=5
center C=(0,0)
1000 points
The logic would be:
for (let i = 0; i < 1000; i++) {
// full circle is made up of 2 * PI angles -> calculate current loop angle
const angle = (2 * Math.PI) * (i / 1000)
const x = r * Math.cos(angle)
const y = r * Math.sin(angle)
drawPixel(x, y)
}
The circle starts being drawn at (5, 0). As y approaches -5, x gets smaller until it hits 0. Then x approaches -5 and y approaches 0, and so on.
It's just meant to be a simple example. If someone says other tutorials quickly go over their head, it's not a good idea to introduce unnecessary concepts to start with.
And then I had to write some software that needed to visualise a rotary milking platform which is a circle, divided into segments, with different parts of each segment showing different things at different times.
Oh, and since it's rotary, the circle had to be animated and rotate in sync with the actual milking platform.
Oh and different clients had different numbers of bays in their platforms so I couldn't hardcode anything, it had to dynamically draw the platform, animate it and respond to events like window size change.
Suffice to say I had to drag highschool geometry out from the graveyard of my brain
Check out 3d graphics related stuff, there's a ton of geometry used there, whether you're ray tracing or using 2d projection.
A ray tracer is basically made up of:
ray caster algorithm to map pixels to rays and puts them into an image
data structures to contain scene data (like geometry, lighting, materials)
algorithm that represents a ray as a line and determines which parts of the scene geometry that line intersects with, selecting the one nearest and in front of the eye (or wherever the front is culled)
same algorithm used to determine if a ray from that intersection point to each light has anything between the point and light
also need to get the angle to the light for each ray that isn't blocked
a shading algorithm that uses the lights, materials, and angles (and maybe more info) to determine the colour of that ray
some code that does something with the resulting image, like display it or save to a file
And that's basically it. It will be slow without optimizations but it's cool af seeing your renders. And you can improve on it from there if you want. Though a warning: you might get obsessed with analysing different visual phenomena and thinking about how to render something like that for a while after doing this, which might also lead to gaining a critical eye for where 3d engines fail to be accurate.
I do almost everyday as a mechanical engineer. I even do the common angles in my head, which came in handy several times in situations where I’m sailing and something breaks underway etc
I hated all math classes before it, but I had a great teacher and something about the real-life usefulness (triangulation, navigation, etc) of trig clicked for me and I enjoyed it and made an A.
I fucking failed the shit out of statistics, and hilariously that's the most related to my real life job, where I'm dealing with gigantic data sets daily looking for outliers/trends.
Stats is intuitive but you need a pure math degree to even get started on the foundations (measure theory). Unintuitiveness arises in any subject where they refuse to explain how it works and just give you a bunch of magic formulas to calculate with. Stats just happens to be the most egregious example of this because it requires far more background than most people applying it actually want.
Diff EQ just turns into TOO MUCH FUCKING ALGEBRA at the end though. It’s never that it doesn’t make conceptual sense, it’s just they throw obnoxious integration by parts and fucking fraction decomp.
You never mess up because you didn’t understand the problem/what you were supposed to do. You mess up because you’re supposed to accept that 1/194737 is a perfectly acceptable coefficient to have and there’s no way of telling if you dropped a sign 10 steps ago.
I had an idiot-savant professor that could do Diff EQ in his head, and didn’t understand why all of us couldn’t do it. We would all get D’s and F’s on every test. If was passed down that people have to go to the dean to curve the final grade every semester, and ever semester he would get angry at not being able to fail almost the entire class.
I just had to do some “find the angle” geometry this week to quantify some physical stuff that was going on in addition to what the software was causing.
And by “do,” I mean scribbling some triangles to figure out what I was calculating, then throwing the numbers into an online calculator!
Math teachers, as a population, are abject failures. Every school day they do incalculable harm to the wellbeing of our society by taking everything in the fundamentals of instruction and doing the exact opposite. They not only fail to cause students to develop a functional understanding of the subject, they instill a pride in their students of that ignorance.
College math professors are no better and possibly worse. We call them "professors" because "teacher" is an incorrect descriptor. Very little teaching goes on in college classrooms.
If I taught flight school the way the typical high school math teacher teaches algebra, I'd be in prison for manslaughter at the very least. None of my students leave my classroom bragging about never needing the training I gave them.
It can honestly be fun. I was never a math person and my school put me in the moron track in high school. After my time in the army, decided to see if they were right.
Now I have a masters in Mech Eng and a few patents. Turns out my math teachers were shit and only taught to the kids who got it quickly, and never bothered with the rest of us.
(Stick with me on this) The joy from spending months to years developing, iterating, designing, and testing something that eventually not only works but works well is an amazing experience.
During Covid, my engineering group also made several ad hoc solutions that could be used for people that didn’t need a ventilator but also were having breathing issues. It saved thousands of lives. Was a nice feeling.
There's a lot of math to flying airplanes, quite a lot of it you'd recognize from high school physics class.
Pilots are required to calculate the weight and balance of the aircraft before flight, making sure the plane is not only below maximum gross weight so that the airplane can safely carry the load, but that the center of gravity falls within an acceptable envelope so that it remains controllable.. This is done by weighing everything including the airplane itself, and noting their location from a datum point. Multiply the weight of each item by their location aft (or sometimes forward but the datum is usually somewhere near the front of the plane) and you get a "moment arm" of that item. Add the weights and moments up, then divide the total moment by the total weight to find the location of the CG. Weight * Arm = Moment.
Often you do this with everything but fuel to calculate how much fuel in pounds you can carry given your intended load of passengers and baggage. Avgas is usually handled in gallons not pounds, so convert from weight to volume. Then look up your fuel consumption rate for not only the cruise portion of flight but startup, taxi, takeoff and climb to altitude. That will tell you your endurance plus the legally mandated 30 minute reserve (45 minutes at night). Determine how long you can be in the air without running out of fuel.
From there, you'll need to plot your course on a sectional chart, measure the true courses, then correct for magnetic variation and compass deviation, then get the winds aloft forecast and do the trigonometry to find the wind correction angle to calculate your compass heading and your ground speed, and then given the distance of each leg and your ground speed during those legs you can compute your time aloft. This information will be used on the ground to make sure you can make the intended flight within your earlier calculated endurance, "will we make it without running out of fuel," plus you will turn to the computed compass heading to not get blown off course and get lost.
Then there's my favorite aviation equation, I found this in the Pilot's Handbook of Aeronautical Knowledge: An airplane tire will hydroplane at a speed in knots equal to the square root of the tire pressure in PSI. The reason the government published that equation was so pilots could calculate whether they can use full braking for short field landings if there is standing water on the runway. For example, the main tires of a Cessna 172 are inflated to 35 PSI, let's round that to 36 to make the math easy, the square root of 36 is 6, 6 times 9 is 54, a Cessna 172 will hydroplane at 54 knots. The VS0 of this plane is 44 knots, a touchdown speed of 1.2VS0 comes out to be about 53 knots, so if you manage your energy well on approach you will just barely have full braking available immediately after touchdown even with standing water on the runway. There's a more fun off-label use for this info though: if you have fairly low pressure tires, like big balloon tundra tires on a bush plane, you can set down on a lake and hydroplane well below your VS0 then just water ski up to the shore, set the tail down and stop to get in and out of somewhere where you don't have room to land on solid ground.
=====
There is a question that high school algebra teachers get asked a lot that I never heard: "Why do we need to learn this?" When I teach the above math, I answer that question myself. I did so in the paragraphs above, I explained why it is important for pilots do to these things. This is an application of the Principle of Readiness as described by Ed Thorndike, which...think about Maslowe's hierarchy of needs. I'm teaching flight school, you're teaching high school algebra. Where do our lessons fall on our students' pyramid of needs? Probably pretty high up, right? Somewhere in the Self Actualization layer? So first of all, you need to make sure all the students' needs that are below that on the pyramid are taken care of so that they're operating at the level of your lessons, and once you achieve that, you MUST establish why and how your lesson will fulfill their needs.
As a flight instructor, that answer almost always boils down to "so you don't crash the plane and get hurt or killed." Algebra, geometry, trigonometry and calculus teachers are THE LITERAL WORST at this, coming up with answers like "This might save your life someday" or "it's required to get your diploma."
The former answer is so vague that it tastes like a lie; it might as well be "just in case you're ever on Jeopardy and the Daily Double is about this topic." The latter is an outright insult. K-12 students are required by law to go to school, and by the time they're in Algebra class they're old enough to understand the social contract allegedly at play here. "All these classes are supposed to prepare me for life as a citizen of this society, to equip me with the knowledge and skill I will need as a functioning adult responsible for earning my own living." And then they drop "We have unilaterally decided to waste your time by requiring that you 'learn' something that I as the subject matter expert acknowledge is fully useless to you. We have officially departed the 'preparing you for life' portion of your education and have now entered the 'how much bullshit can you swallow' portion. Test is on Friday."
I partially blame the approach taken to building mathematics curricula. We start out teaching pre-algebra to 13 year olds as if they're going to grow up to be mathematicians. You're trying to hit hormonal pubertines with shit like "the transitive property of inequality" and expect them to internalize it for dumbass reasons like "someone decided it's mandatory I guess."
This attitude of vindictive joy at proving your old math teacher wrong, "See? I never use this!"...I can only explain it as an abject failure on the part of the teacher/school/state department of education for designing and teaching the curriculum the way they do; not only failing to motivate students to learn, but building in them a pride in their resulting ignorance. Short of physically injuring your students I don't know how you fuck up worse than that as a teacher.
"I said everything about myself without saying a damn thing about the subject!"
You have zero idea of what you are talking about. Which is the sin of 0. So the more you speak, you just increase the times you are wrong. That's called frequency. If you use that, you can adjust the angle that you approach the subject and have more resonance with your audience.
I don't know if you listen to music though. Maybe you just stick to the Internet. Which also uses frequency. But maybe all this went over your head. Like a jet. Or a cell signal.
I've been a flight instructor since 2010, in 14 years not a single one of the pilots I trained has ever come back to me bragging about how they never use something I taught them. Or failed a test I endorsed them for. I'm a damn good teacher of technical subjects, certainly good enough to recognize a piss poor one.
So you're saying that my students pay attention to my lessons because they are important and relevant to them in their lives. And students of math classes don't pay attention because they do not have that same importance to their students.
And somehow I'm being downvoted to hell for pointing out that this means math class is extremely badly designed for its stated purpose, and the people who design and maintain it in the condition that it is in are complete fuckups.
You don't understand how many people do use these functions. Even yourself. You use them and don't even think about it because it's beyond your comprehension. Frequency of anything is trigonometry. Observing and utilizing the efficiency is a bi-product of applied mathematics. There are so many other examples.
Math is the only language that goes through all other dialects. Think about how monumental that is. Every language in the world agrees that math makes sense. But you don't.
this has a lot to do with resources and time. class size and student to teacher ratio will always have a huge impact on student learning. i really want to write that twice. plus in america, capitalism and zero-sum life is introduced in education by way of separating higher and lower scoring students, assigning students to 'gifted' classes. not being able to give enough support for students with disabilities, and separating them as well. and of course stability and support outside of the classroom/school is a big factor.
Granted, teaching 10 well-off adults is easier than 30 poor kids.
This doesn't explain why all math classes everywhere from about 6th grade and up are designed as if we're raising an entire generation of mathematicians. What good does memorizing proofs do? Why do we focus so much on the quadratic equation? Algebra is a useful skill that schools systematically beat a hatred for into the masses...in order to pretend they're doing something academic and scholarly?
I agree with you on the over emphasis of certain topics and the need to shift more to mathematical thinking rather than ending up with kids tending too much on (often short term) memorizing. Many students jump right to the quadratic eqtn because they are told it always works. Even when factoring might be simpler and more elegant. The common core was misunderstood by most folks, me included initially. But that is its goals are more towards mathematical thinking and connections as opposed to memorization and applying algorithms. Even simple ones such s stacked subtraction or multiplication. It's implementation was poorly done, teachers weren't trained and again the testing regime constraints bore down. But it's thinking more towards future though it too may need to speed up with changes.
Joke's on you, I sin every day.
The smarter kids in your class probably do use them.
Jokes on you, I'm in the bourgeois class and let kids from the working class and professional mangerial class do that kind of homework for me
He said smarter, not wealthier. I'm getting the guillotine.
Nah. I was labeled a dumb kid in high school because I had to work 40 hours a week. I went back to college as an adult and now have a masters in mech Eng.
Went to my high school reunion and the smart kids were largely abject failures. They never really struggled until college, then mostly failed out. I felt bad for them, but not too bad since most of them bullied me.
Sounds like maybe there weren't the true smart kids. You finished high-school while working a full time job. You were capable and adaptable. Fuck them :)
Thank you for that.
As one of the resident smart kids who went into CompSci and now works as a software engineer, I haven't touched any of this for a hot minute. I mainly use it for 3D print designs once in a blue moon.
Of course it depends, but for example, it CSS esing functions are based on polinomial or sin waves. If you ever want to understand or perhaps implement and easing function, trigonometry has your back.
But you use things that use them.
like any device that uses graphics
There is at least one smbc for everything
Case in point, there are two!
Sauce
Never really understood people who say they don't use algebra. I use it very regularly.
I was thinking this myself. sin, cos, tan. Have not used. I have use euler coordinates so thats something but really solve for x is the most advanced thing I have used outside of school. mmmm actually I guess some statistics like stadard deviation.
I recently had to do a two variable equation because I was using a recipe that called for a specific milk fat percentage by mixing cream and milk, and my cream was heavier than what it needed. That was really stretching the limits of what math I remember.
Programmer for 25 years. Only time I have ever used math more complicated than simple multiply/divide was... actually never.
That one time when I copy/pasted a formula for linear interpolation, was still just multiplication and division. And I still have no idea how it works.
I've even done OpenGL and graphics programming and still haven't needed any algebra/trig/etc, although I don't do complex 3D rendering or physics or anything like that.
I wish I knew how to do cool programming stuff like draw circles and waves and stuff though, but I've never seen a tutorial that didn't go WAY over my head immediately.
Drawing a circle is actually pretty simple! Say we want to draw one with:
The logic would be:
The circle starts being drawn at (5, 0). As y approaches -5, x gets smaller until it hits 0. Then x approaches -5 and y approaches 0, and so on.
That won't work well ;-) it will draw 1000 pixels whatever the circumference!
A good start though, for sure.
It's just meant to be a simple example. If someone says other tutorials quickly go over their head, it's not a good idea to introduce unnecessary concepts to start with.
I use them every day. Making science is rad as fuck.
As opposed to degree as fuck.
Almost made me do a π
I see what you did there.
K
Sin, Cos and Tan were gifted to us by the gods, and it's solely your fault, if you don't use them daily in your freetime.
Know any good resources for math-ignorant programmers that teaches how to use those in useful ways?
But you do use them everyday, because the Internet would not work without them.
Doesn't it? Have we ever tried to rid humanity of this triangle of evil? Un-tan the internet I say! Grab your pitchforks and cos this sin-er to hell!
Jokes on you, basic arm and leg mechanics involves trig
Sad take.
The non-programmer folks upvote this post. I mean, not that I use it for every app, but I have used it in recent memory. SOH-CAH-TOA, bitches!
Back in my day we had to use sentences to remember it
Sill Old Harry Caught A Herring Trawling Off America
Firmly lodged in place forever
Hey, I’m not a programmer, as a real engineer half of my education was in some way related to trig
Alright, alright, you can sit with us cool nerds. 🤓 But on Wednesdays we wear pink fanny packs.
Every day, I use them ever damn day.
For determining the right angle to fuck the sharks from?
I use them at least once a week
This was me for years.
And then I had to write some software that needed to visualise a rotary milking platform which is a circle, divided into segments, with different parts of each segment showing different things at different times.
Oh, and since it's rotary, the circle had to be animated and rotate in sync with the actual milking platform.
Oh and different clients had different numbers of bays in their platforms so I couldn't hardcode anything, it had to dynamically draw the platform, animate it and respond to events like window size change.
Suffice to say I had to drag highschool geometry out from the graveyard of my brain
Any code you can share? I'm interested in finally learning how to apply some simple geometry maths to my programming, but I failed math in school.
Check out 3d graphics related stuff, there's a ton of geometry used there, whether you're ray tracing or using 2d projection.
A ray tracer is basically made up of:
And that's basically it. It will be slow without optimizations but it's cool af seeing your renders. And you can improve on it from there if you want. Though a warning: you might get obsessed with analysing different visual phenomena and thinking about how to render something like that for a while after doing this, which might also lead to gaining a critical eye for where 3d engines fail to be accurate.
I do almost everyday as a mechanical engineer. I even do the common angles in my head, which came in handy several times in situations where I’m sailing and something breaks underway etc
I often go on a TANgent when I'm thinking or talking about something. Does that count?
Yeah, cos it's a sin to not use trigonometry.
Niiiiiiccccce ones guys
I love whipping out the low angle approximation at work and looking like a wizard.
I actually really enjoyed trig class.
I hated all math classes before it, but I had a great teacher and something about the real-life usefulness (triangulation, navigation, etc) of trig clicked for me and I enjoyed it and made an A.
I fucking failed the shit out of statistics, and hilariously that's the most related to my real life job, where I'm dealing with gigantic data sets daily looking for outliers/trends.
Stats is the most unintuitive and unpleasant part of math. Trig is a fun problem that nests perfectly into physics
Stats is intuitive but you need a pure math degree to even get started on the foundations (measure theory). Unintuitiveness arises in any subject where they refuse to explain how it works and just give you a bunch of magic formulas to calculate with. Stats just happens to be the most egregious example of this because it requires far more background than most people applying it actually want.
Stats by hand is worse than diff EQ. You are right, it’s so unintuitive. I just let R-Studio decide.
Diff EQ just turns into TOO MUCH FUCKING ALGEBRA at the end though. It’s never that it doesn’t make conceptual sense, it’s just they throw obnoxious integration by parts and fucking fraction decomp.
You never mess up because you didn’t understand the problem/what you were supposed to do. You mess up because you’re supposed to accept that 1/194737 is a perfectly acceptable coefficient to have and there’s no way of telling if you dropped a sign 10 steps ago.
I had an idiot-savant professor that could do Diff EQ in his head, and didn’t understand why all of us couldn’t do it. We would all get D’s and F’s on every test. If was passed down that people have to go to the dean to curve the final grade every semester, and ever semester he would get angry at not being able to fail almost the entire class.
I just had to do some “find the angle” geometry this week to quantify some physical stuff that was going on in addition to what the software was causing.
And by “do,” I mean scribbling some triangles to figure out what I was calculating, then throwing the numbers into an online calculator!
Whenever I implement something based on trigonometry, I try around with the different functions until my tests give the expected results.
I use them roughly monthly.
Haha, well in my case high school geometry drew my interest and hyper focus. I will never forget the basic triangle functions/rules.
Ratio
Weird, I find them rather useful. How else do you calculate angles of things?
To check some flat-earthers I recently calculated the angle between an upright person and some skyscrapers 60 miles away.
How often do you need to calculate angles? If I want to know the angle of something I usually measure it.
That's a lot of circles and curves on your desk bro.
Whenever I'm making a hobby game I use so much half remembered trig.
atan2 my beloved 😍
Yeah to hell with atan, at least from when atan2 came into existence.
Especially tan. Fuck tan.
I hate having to relearn socatoa every couple months to years, at this point I might as well get it tattooed on my arm
I’m just over here occasionally getting to 50…
Day 9,125 of not using it here. 25 years in IT and never had to once use it.
And then there's gamedev, where I barely managed to go 1 week without them
Yeah very much depends on what part of IT you’re in.
Math teachers, as a population, are abject failures. Every school day they do incalculable harm to the wellbeing of our society by taking everything in the fundamentals of instruction and doing the exact opposite. They not only fail to cause students to develop a functional understanding of the subject, they instill a pride in their students of that ignorance.
College math professors are no better and possibly worse. We call them "professors" because "teacher" is an incorrect descriptor. Very little teaching goes on in college classrooms.
Careful, don't cut yourself on that edge.
If I taught flight school the way the typical high school math teacher teaches algebra, I'd be in prison for manslaughter at the very least. None of my students leave my classroom bragging about never needing the training I gave them.
If math was as fun as flying airplanes you'd have a very different opinion about math teachers.
It can honestly be fun. I was never a math person and my school put me in the moron track in high school. After my time in the army, decided to see if they were right.
Now I have a masters in Mech Eng and a few patents. Turns out my math teachers were shit and only taught to the kids who got it quickly, and never bothered with the rest of us.
I'm not saying it isn't, but have you tried flying?
I have, and it was enjoyable.
(Stick with me on this) The joy from spending months to years developing, iterating, designing, and testing something that eventually not only works but works well is an amazing experience.
During Covid, my engineering group also made several ad hoc solutions that could be used for people that didn’t need a ventilator but also were having breathing issues. It saved thousands of lives. Was a nice feeling.
There's a lot of math to flying airplanes, quite a lot of it you'd recognize from high school physics class.
Pilots are required to calculate the weight and balance of the aircraft before flight, making sure the plane is not only below maximum gross weight so that the airplane can safely carry the load, but that the center of gravity falls within an acceptable envelope so that it remains controllable.. This is done by weighing everything including the airplane itself, and noting their location from a datum point. Multiply the weight of each item by their location aft (or sometimes forward but the datum is usually somewhere near the front of the plane) and you get a "moment arm" of that item. Add the weights and moments up, then divide the total moment by the total weight to find the location of the CG. Weight * Arm = Moment.
Often you do this with everything but fuel to calculate how much fuel in pounds you can carry given your intended load of passengers and baggage. Avgas is usually handled in gallons not pounds, so convert from weight to volume. Then look up your fuel consumption rate for not only the cruise portion of flight but startup, taxi, takeoff and climb to altitude. That will tell you your endurance plus the legally mandated 30 minute reserve (45 minutes at night). Determine how long you can be in the air without running out of fuel.
From there, you'll need to plot your course on a sectional chart, measure the true courses, then correct for magnetic variation and compass deviation, then get the winds aloft forecast and do the trigonometry to find the wind correction angle to calculate your compass heading and your ground speed, and then given the distance of each leg and your ground speed during those legs you can compute your time aloft. This information will be used on the ground to make sure you can make the intended flight within your earlier calculated endurance, "will we make it without running out of fuel," plus you will turn to the computed compass heading to not get blown off course and get lost.
Then there's my favorite aviation equation, I found this in the Pilot's Handbook of Aeronautical Knowledge: An airplane tire will hydroplane at a speed in knots equal to the square root of the tire pressure in PSI. The reason the government published that equation was so pilots could calculate whether they can use full braking for short field landings if there is standing water on the runway. For example, the main tires of a Cessna 172 are inflated to 35 PSI, let's round that to 36 to make the math easy, the square root of 36 is 6, 6 times 9 is 54, a Cessna 172 will hydroplane at 54 knots. The V
S0of this plane is 44 knots, a touchdown speed of 1.2VS0comes out to be about 53 knots, so if you manage your energy well on approach you will just barely have full braking available immediately after touchdown even with standing water on the runway. There's a more fun off-label use for this info though: if you have fairly low pressure tires, like big balloon tundra tires on a bush plane, you can set down on a lake and hydroplane well below your VS0then just water ski up to the shore, set the tail down and stop to get in and out of somewhere where you don't have room to land on solid ground.=====
There is a question that high school algebra teachers get asked a lot that I never heard: "Why do we need to learn this?" When I teach the above math, I answer that question myself. I did so in the paragraphs above, I explained why it is important for pilots do to these things. This is an application of the Principle of Readiness as described by Ed Thorndike, which...think about Maslowe's hierarchy of needs. I'm teaching flight school, you're teaching high school algebra. Where do our lessons fall on our students' pyramid of needs? Probably pretty high up, right? Somewhere in the Self Actualization layer? So first of all, you need to make sure all the students' needs that are below that on the pyramid are taken care of so that they're operating at the level of your lessons, and once you achieve that, you MUST establish why and how your lesson will fulfill their needs.
As a flight instructor, that answer almost always boils down to "so you don't crash the plane and get hurt or killed." Algebra, geometry, trigonometry and calculus teachers are THE LITERAL WORST at this, coming up with answers like "This might save your life someday" or "it's required to get your diploma."
The former answer is so vague that it tastes like a lie; it might as well be "just in case you're ever on Jeopardy and the Daily Double is about this topic." The latter is an outright insult. K-12 students are required by law to go to school, and by the time they're in Algebra class they're old enough to understand the social contract allegedly at play here. "All these classes are supposed to prepare me for life as a citizen of this society, to equip me with the knowledge and skill I will need as a functioning adult responsible for earning my own living." And then they drop "We have unilaterally decided to waste your time by requiring that you 'learn' something that I as the subject matter expert acknowledge is fully useless to you. We have officially departed the 'preparing you for life' portion of your education and have now entered the 'how much bullshit can you swallow' portion. Test is on Friday."
I partially blame the approach taken to building mathematics curricula. We start out teaching pre-algebra to 13 year olds as if they're going to grow up to be mathematicians. You're trying to hit hormonal pubertines with shit like "the transitive property of inequality" and expect them to internalize it for dumbass reasons like "someone decided it's mandatory I guess."
This attitude of vindictive joy at proving your old math teacher wrong, "See? I never use this!"...I can only explain it as an abject failure on the part of the teacher/school/state department of education for designing and teaching the curriculum the way they do; not only failing to motivate students to learn, but building in them a pride in their resulting ignorance. Short of physically injuring your students I don't know how you fuck up worse than that as a teacher.
Your high school had physics?! My god man. I couldn't even pass algebra.
"I said everything about myself without saying a damn thing about the subject!"
You have zero idea of what you are talking about. Which is the sin of 0. So the more you speak, you just increase the times you are wrong. That's called frequency. If you use that, you can adjust the angle that you approach the subject and have more resonance with your audience.
I don't know if you listen to music though. Maybe you just stick to the Internet. Which also uses frequency. But maybe all this went over your head. Like a jet. Or a cell signal.
I've been a flight instructor since 2010, in 14 years not a single one of the pilots I trained has ever come back to me bragging about how they never use something I taught them. Or failed a test I endorsed them for. I'm a damn good teacher of technical subjects, certainly good enough to recognize a piss poor one.
Yea. That's because if they failed they died. The epitome of cognitive dissonance.
So you're saying that my students pay attention to my lessons because they are important and relevant to them in their lives. And students of math classes don't pay attention because they do not have that same importance to their students.
And somehow I'm being downvoted to hell for pointing out that this means math class is extremely badly designed for its stated purpose, and the people who design and maintain it in the condition that it is in are complete fuckups.
You don't understand how many people do use these functions. Even yourself. You use them and don't even think about it because it's beyond your comprehension. Frequency of anything is trigonometry. Observing and utilizing the efficiency is a bi-product of applied mathematics. There are so many other examples.
Math is the only language that goes through all other dialects. Think about how monumental that is. Every language in the world agrees that math makes sense. But you don't.
this has a lot to do with resources and time. class size and student to teacher ratio will always have a huge impact on student learning. i really want to write that twice. plus in america, capitalism and zero-sum life is introduced in education by way of separating higher and lower scoring students, assigning students to 'gifted' classes. not being able to give enough support for students with disabilities, and separating them as well. and of course stability and support outside of the classroom/school is a big factor.
Granted, teaching 10 well-off adults is easier than 30 poor kids.
This doesn't explain why all math classes everywhere from about 6th grade and up are designed as if we're raising an entire generation of mathematicians. What good does memorizing proofs do? Why do we focus so much on the quadratic equation? Algebra is a useful skill that schools systematically beat a hatred for into the masses...in order to pretend they're doing something academic and scholarly?
I agree with you on the over emphasis of certain topics and the need to shift more to mathematical thinking rather than ending up with kids tending too much on (often short term) memorizing. Many students jump right to the quadratic eqtn because they are told it always works. Even when factoring might be simpler and more elegant. The common core was misunderstood by most folks, me included initially. But
that isits goals are more towards mathematical thinking and connections as opposed to memorization and applying algorithms. Even simple ones such s stacked subtraction or multiplication. It's implementation was poorly done, teachers weren't trained and again the testing regime constraints bore down. But it's thinking more towards future though it too may need to speed up with changes.