I know only two people who can readily recite the quadratic formula. My wife is one. She’s always been a whiz at school, but, as a choir teacher, she has absolutely no use for the equation (other than as an occasional party trick). The other person is my brother, who works with electron-beam technology as a mechanical engineer. He’s in the minority of people who actually use advanced math daily.
For most of us, the formula was one of many alphabet soup combinations crammed into our heads in high school long enough to pass a math test, then promptly forgotten. I’m queasy all over again just thinking about it. As a functioning adult in society, I have no use for imaginary numbers or the Pythagorean theorem. I’ve never needed to determine the height of a flagpole by measuring its shadow and the angle of the sun.
Only 22 percent of the nation’s workers use any math more advanced than fractions, and they typically occupy technical or skilled positions. That means more than three-fourths of the population spends painful years in school futzing with numbers when they could be learning something more useful.
I’m talking about applied logic. This branch of philosophy grows from the same mental tree as algebra and geometry but lacks the distracting foliage of numbers and formulas. Call it the art of thinking clearly. We need this urgently in this era of disinformation, in which politicians and media personalities play on our emotions and fears.
Logic teaches us how to trace a claim back to its underlying premises and to test each link in a chain of thought for unsupported assumptions or fallacies. People trained in logic are better able to spot the deceptions and misdirection that politicians so often employ. They also have a better appreciation for different points of view because they understand the thought processes that produce multiple legitimate conclusions concerning the same set of facts. They are comfortable with spirited dialogue about what’s best for our society.
I once asked my pre-calculus teacher whether I would ever use the information she taught in real life. Her answer was surprisingly frank: I probably wouldn’t. The reason to take the class was to score well on the advanced placement test, which would give me a leg up on the math requirements in college. In other words, numbers for the sake of numbers.
Math advocates claim to be teaching complex problem solving, mental discipline and a better understanding of our world. Logic teaches the same things more directly. Geometry can’t teach me when an argument is manipulating my emotions, but logic can. Calculus doesn’t help me solve moral dilemmas, but philosophy does.
Admittedly, all students need to master the basic math of everyday life so they can manage money, compare prices, find the center of a wall to hang a picture and so on. And some students, like my brother, will fall in love with math. That’s a good thing, because they will use it to make bridges safe, to predict the weather, to land spacecraft on the moon and Mars — you get the idea.
It’s reasonable to suggest that public schools all provide a standardized core curriculum. But what makes up a fundamental education? America has not thought through this question in a national conversation since the 1983 release of “A Nation At Risk.” The product of a presidential commission on education, this report warned of declining achievement in the country’s schools and diagnosed “the urgent need for improvement.” Among its recommendations were a minimum of three years of math for all high school graduates.
Since that time, the digital revolution has placed massive computational power in the palm of every student’s hand. Should the need for a cube root arise in someone’ life, Siri is available 24/7 to provide the answer. That same revolution has given us a crisis of conspiracy theories and a polluted public discourse. What’s at risk now is our ability to reason together as citizens. Skills such as these might not be able to solve for X, but they could go a long way in the pursuit of happiness and the health of America. You can’t punch those things into a calculator.
The need to solve problems is eternal, but many of life’s weightiest problems don’t boil down to numbers. Prioritizing higher-level numeracy over other forms of logical reasoning is not turning us into a nation of engineers and physicists. It’s letting us become a nation that can’t think straight.
America’s Founders knew it would take educated citizens for this democratic republic to succeed. But nowhere did they mention the quadratic formula.
Math has a place but I do think it's overtaught. Advanced algebra bullshit should stay as a college requirement for degrees in which it's relevant, I cannot think of any reason I would ever need to understand what a polynomial is, the quadratic formula, or that the square root of -1 is imaginary.
The whole entire point of math is to teach you how to analyze problems in to their simplest parts and synthesize a solution based on previous knowledge, inside and out of the realm of math. If anything, math is taught so poorly in the American education system that people don't see this and it's why there are so many retards that are allowed to pretend they are functional human beings in the first place. I'm not even saying you have to do anything more serious than calculus and basic proofs so much as I'm saying if you can't do basic math, you are not really fit to live in a civilized society.
No probability and stats? Maybe it's because I often work with money and forecasting, but I think a solid understanding of stats opens up an understanding to the world. It's not that uncommon to have, say, three chances at something to succeed and perhaps you want to figure out what the overall chance of success is.
I also use basic algebra and the general concepts of variables in my day to day job, but I often work with datasets.
The other thing they should definitely teach is the time value of money equations, so you can compare a 4% return over 12 months with an 8% return over 24 months, figure out what $x in 5 years is worth in today's dollars, understand how much extra they're paying at x APR, etc.
If it's not relevant to your path of study then it is indeed a waste of time and a barrier o f entry. College math requirements for non math using majors wastes the student's time and money.
Actually it's not; it makes sure you aren't a drooling retard, because college is supposed to be for people who aren't drooling retards. These colleges have a vested interest in you not dropping/failing out, regardless of your subject. Advanced Math acts a bit like an IQ test in this regard.
Even the trades need math to some extent -- although a lot of tradies just end up memorizing "rules of thumb" as a substitute (14awg for lighting, 12awg for outlets, etc.).
If you can't find a first derivative after 13 years of math education, consider ditch digging or burger slinging, because whatever else you were bound to do, you'll probably do it badly.
"50% of kids should go to university" was beyond retarded. The correct figure is around 2 to 3%. Everyone else can go to the public library and become halfwit autodidacts there. It will save them a lot of money.
We used to have inherited trades. If your dad was the best carpenter of the city, people expected you learned the trade from him as well. Or inherited businessv if your family owned a bakery, you inherited that, and probably took a few management courses to be able to manage it better, but that's it. You didn't need to learn yourself, but your family educated you.
Not only economy killed that, college did too. Since kids were told they should "follow their dreams!", we assumed every kid who enjoyed watching Toy Story not only wanted to be an astronaut, they had the skill for it and he would be more useful to society doing "science" than keeping the family business. He went to college, the family shut down the bakery, and since then, all kids start from zero and needing a degree.
We used to have inherited trades. If your dad was the best carpenter of the city, people expected you learned the trade from him as well. Or inherited businessv if your family owned a bakery, you inherited that, and probably took a few management courses to be able to manage it better, but that's it. You didn't need to learn yourself, but your family educated you.
Not only economy killed that, college did too. Since kids were told they should "follow their dreams!", we assumed every kid who enjoyed watching Toy Story not only wanted to be an astronaut, they had the skill for it and he would be more useful to society doing "science" than keeping the family business. He went to college, the family shut down the bakery, and since then, all kids start from zero and needing a degree.
Best left in the past. What they leave out is all of the generational poverty that has been caused by failing or financially insolvent family businesses that kids inherit, that are liabilities much more than they are assets.
The dustbowl in the 1930s was largely caused by incompetent artisan farming families that had no fucking clue what they were doing and depleted the soil across huge tracts of the midwest.
Philosophy is an interesting subject, but no, it's not remotely a replacement for math.
The problem with philosophy is that you can't be fact checked. It's all opinions and word bending. Only the most dedicated philosophy students (at least on the high school level) actually become more thoughtful and objective after a philosophy class. The rest just learn fancier words to insult their rhetorical enemies.
Math teaches humility; it teaches you that sometimes in life there are genuine right or wrong answers and sometimes you might be in the wrong. Someone who can't admit when they're wrong won't be successful in math or business or engineering or anything important in the world that matters.
I'd maybe consider classes in logic to be an acceptable replacement for math if they required all their essays to be accompanied by an implementation of their argument in Prolog.
Philosophy professors are more likely to be socialists than even lawyers, so there's a case to be made that modern university philosophy makes you far more likely to be detached from reality and rationalize stupid ideas. Ideally, a university philosophy course should teach you philosophers whose ideas led to modern science, like Aristotle and Descartes, and if you go further, idiots like Marx should be ripped to shreds.
Dumb people are not capable of doing puzzles. An IQ test is just a sequence of increasingly difficult puzzles that you do until you fail. People with low IQs start failing on relatively simple puzzles, and people with high IQs don't start failing until the very difficult ones. One thing smart people who spend far too much time around other smart people lose sight of is that dumb people are just...dumb. Their brains don't make these connections. They kind of fuzz out when they are pushed to. You can't teach them to be smart.
The same people yelling that we need to get rid of math and they never use math are the same ones bitching that the schools never taught them to balance a checkbook, compute the interest on their credit cards or mortgage, or taught them how to do their taxes.
They were taught, they're just too fucking stupid to understand that they were taught.
I too think that we need a logic course in high school.
A real logic course, integrated into the math curriculum, featuring all the math that's normally featured in a computer science major's Discrete Math course. It will cover formal symbolic logic and basic proof writing. Maybe we could throw some logic gates in there too and have students make simple digital circuits.
No one shall graduate high school until they have shown that they can read and write inductive proofs of basic theorems from number theory.
If anything, that's reason to teach more algebra, geometry, and trigonometry. Anyone that builds stuff for a living needs to know at least how to put it in a calculator. I have watched plumbers make 45° offsets by cutting the pipe long and trimming it 4-5 times to make it fit. It makes me want to scream. Offset distance times 1.414.
Agreed, basic geometry (much of which has already been thrown out of the curriculum) is profoundly useful stuff if you're ever doing any sort of work with your hands. Declaring geometry and trigonometry "advanced and useless" is an implicit confession that you've either never had to build anything non-trivial or that you think trial and error is an acceptable way to measure materials when building things.
Maybe the most practical math course, one that would teach real understanding and not memorization, would be forcing everyone to take woodshop and metalshop and do some machining. Force them to calculate needed sizes and tolerances by hand.
Aside: I've recently encountered a fascinating book called Polynomials, Dynamics, and Choice which is about group theory and symmetry breaking in the mathematical sense. The starting point is the +/- sign in the quadratic formula but carries you to pretty far off places in Math.
Good choice in literature. I haven't heard of the book before, but the description mentions the following:
In a recent breakthrough, Doyle and McMullen devised a solution to the fifth-degree equation that uses geometry, algebra, and dynamics to exploit icosahedral symmetry.
Doyle and McMullen's original paper, "Solving the quintic by iteration" (see here) is a beautiful piece of mathematics. Sadly I haven't fully understood it yet and lack the time to learn the background material for the parts I don't understand. If I ever end up unemployed I'm putting all that time into learning higher math.
Until the back quarter of the 20th century, learning classical, early Renaissance, and Enlightenment philosophy was considered foundational knowledge. Then we had the revolt against "dead white males." Granted, before then, Marx was taken far more seriously than he should have been, but still. Everything is completely off the rails now.
If you can't find a first derivative after 13 years of math education, consider ditch digging or burger slinging, because whatever else you were bound to do, you'll probably do it badly.
The same people yelling that we need to get rid of math and they never use math are the same ones bitching that the schools never taught them to balance a checkbook, compute the interest on their credit cards or mortgage, or taught them how to do their taxes.
They were taught, they're just too fucking stupid to understand that they were taught.
Unless you're in a STEM career, I disagree. You have to learn the dunce-level stuff before you can grasp the Stephen Hawking-level stuff.
I also think there needs to be more visual aids and focus on applied mathematics. I, for one, don't retain the information if it's too abstract. Rote memory can only get you so far.
Alas, all of this goes deeper than just math. The rot is at the heart of our education system. It's not geared towards making people more versatile, adaptable citizens; it's the Rockefeller Model, which is designed to pidgeonhole you and get you on the wageslave hamster wheel as quickly as possible.
It's why your high school advisory class tells you, "you will be a failure unless you decide what you wanna do for the rest of your life RIGHT THIS INSTANT!" Seemingly forgetting that 15-year-olds seldom think beyond lunchtime.
Small PL: I work in finance. All I need to know for my particular job is how to add, subtract, multiply, and divide. Most higher education is a rip-off; your first few years of undergrad will be basically reruns of high school.
Full disclosure: I have a PhD in Pure Mathematics and have taught a few university level courses along with tutoring math students in public school. I'm going to try to keep my boiling contempt for people like the author to a minimum, but I can only do so much.
This is a serious problem I have been aware of since I was in high school Chemistry class many many years ago. We were doing equilibrium calculations with ICE tables, and that involves solving very basic quadratics. We had access to graphing calculators, but not the fancy ones with a built-in plug and play quadratic solver; all calculations had to be done using the quadratic forumula, if not completing the square or factoring. This was in the 12th grade, and a majority of students in my class were completely stuck trying to solve these things. These are people who wanted to become nurses, pharmacists, etc. They should have had a grasp on this stuff for at least 3-4 years by that point.
Even simple stuff like rearranging fractions (basic algebra, solve for x) was difficult for them. Something I found that helped when explaining how was suggesting they look at it like a triangle:
Code:
Y
/ \
X — Z
X = Y / Z
Y = X * Z
Z = Y / X
Math classes teach the technically correct approach, which is to multiply/divide both sides to add or remove the denominator. It's important to have this insight, but students often aren't given simple models like what I wrote above so they can quickly calculate these things in their heads. Maybe you won't use quadratics much, sure; you will need to rearrange fractions and basic arithmetic equations like this in daily life though; these students weren't even equipped to do that. People who are bad at basic skills like entry level math avoid having to use such things in their daily lives to avoid problems, but they are heavily restricting their potential by not applying themselves to learn it properly.
For most of us, the formula was one of many alphabet soup combinations crammed into our heads in high school long enough to pass a math test, then promptly forgotten. I’m queasy all over again just thinking about it. As a functioning adult in society, I have no use for imaginary numbers or the Pythagorean theorem. I’ve never needed to determine the height of a flagpole by measuring its shadow and the angle of the sun.
Most people would benefit from taking an intro physics course, like they provide in high schools. The examples may not always seem practical, but the knowledge one gains is very useful. At the very least, having a decent understanding of classical mechanics, rates of change, vectors, and such is very useful. Especially in fields like transportation, cooking, manufacturing, etc. These concepts involve calculus at their core, but high school students are introduced to it using the famous kinematics formulae for stuff like acceleration and velocity w.r.t. time.
Only 22 percent of the nation’s workers use any math more advanced than fractions, and they typically occupy technical or skilled positions. That means more than three-fourths of the population spends painful years in school futzing with numbers when they could be learning something more useful.
I'm skeptical of this statistic. It's based on a survey of workers, many of whom may not consider the odd instances they have to do advanced math interspersed between the thousands of times they have to do basic arithmetic. Plus, I feel like this doesn't account for all of the people who have their math done for them by spreadsheet software and the like.
I’m talking about applied logic. This branch of philosophy grows from the same mental tree as algebra and geometry but lacks the distracting foliage of numbers and formulas. Call it the art of thinking clearly. We need this urgently in this era of disinformation, in which politicians and media personalities play on our emotions and fears. Math advocates claim to be teaching complex problem solving, mental discipline and a better understanding of our world. Logic teaches the same things more directly. Geometry can’t teach me when an argument is manipulating my emotions, but logic can. Calculus doesn’t help me solve moral dilemmas, but philosophy does.
De Morgan's Laws: A ∧ ¬(B ∨ C) ≡ A ∧ ¬B ∧ ¬C ≡ ¬(¬A ∨ B) ∧ ¬C
Contrapositive: (A ⇒ B) ≡ (¬B ⇒ ¬A)
This may just look like a bunch of symbols, but it is merely an algebraic representation of the truthiness of statements. A, B, and C are logical statements, which are either true or false. They could be anything like "A car is a vehicle" or "Liz Fong-Jones is a woman", which would be true and false respectively. The symbols ∧, ∨, ¬, are logical operators (like plus, minus, multiplication, or division signs) that represent a logical AND, OR, and NOT respectively. Like with normal order of operations, we need to handle the operations inside the brackets before we perform operations outside of them. The way we read the first expression (with some brackets for better clarity) is "A AND (NOT (B OR C)) is logically equivalent to (often shortened to "iff" or "if and only if") A AND (NOT B) AND (NOT C) is logically equivalent to NOT ((NOT A) OR B) AND (NOT C)".
AND takes 2 statements, and if both statements are true, the result is true. So false ∧ true ≡ false, true ∧ true ≡ true, false ∧ false ≡ false.
OR takes 2 statements, and if one or both statements are true, the result is true. So true ∨ false ≡ true, true ∨ true ≡ true, false ∨ false ≡ false.
NOT takes a single statement and inverts/negates its value. So ¬true ≡ false, ¬false ≡ true.
⇒ is an operator that expresses an "if A, then B" relationship that only works in one direction; "if B, then A" (the converse) is not always true when "if A, then B" is.
So let's try an example where we replace the letters with either true or false:
I encourage you to try assigning your own true and false values to A, B, and C and give it a shot.
Knowing when two or more sets of statements are equivalent is a very powerful tool, since we can reframe how we look at a particular problem. A common example is trying to prove the statement "If x^2 is odd, then x is odd." An easier way to prove this is to use the contrapositive like written above, so we can take the statement and transform it into the equivalent statement "If x is even, then x^2 is even." It's common knowledge that multiplying two even numbers gives an even product (typically, you use placeholder values like 2k or 2k+1 in a formal proof). We have effectively proved the original statement using a similar equivalent statement. Try to think of some more real-world examples of "if A, then B" relationships and how they can be reasoned about in this fashion. If you have a blue car, finding it in a busy parking lot can, for the most part, be boiled down to working with the statements "If it is my car, then it is blue." and "If it is not blue, then it is not my car.", which are contrapositives of each other. Obviously, there's a bit more to it than that, but it's a reliable filter that gets you home quicker.
Notice how I was able to explain these facts mathematically and provide real (admittedly simplistic) examples of how this knowledge can be abstracted and applied in day to day life? I didn't have to push any subjective rhetoric or ideologies like political philosophy is full of. To use a term libtards and media types absolutely love, disinformation is almost always a massive dog whistle for "People believe things that I don't like or agree with." They want to have children be taught what to think, rather than giving children the tools to think for themselves and form their own beliefs. I can tell if my students grasp a concept when they ask insightful questions about the subject matter. Part of learning is figuring out by yourself how you can apply the concepts. Simply believing the concepts aren't important or relevant to most people is intellectually lazy and only does a disservice to those who fall into that flawed line of thinking.
Admittedly, all students need to master the basic math of everyday life so they can manage money, compare prices, find the center of a wall to hang a picture and so on. And some students, like my brother, will fall in love with math. That’s a good thing, because they will use it to make bridges safe, to predict the weather, to land spacecraft on the moon and Mars — you get the idea.
Since that time, the digital revolution has placed massive computational power in the palm of every student’s hand. Should the need for a cube root arise in someone’ life, Siri is available 24/7 to provide the answer. That same revolution has given us a crisis of conspiracy theories and a polluted public discourse. What’s at risk now is our ability to reason together as citizens. Skills such as these might not be able to solve for X, but they could go a long way in the pursuit of happiness and the health of America. You can’t punch those things into a calculator.
We also have a problem in society where no one knows how to do anything anymore. If their phone can't do their thinking for them within a few seconds, they give up and pay someone else to worry about it. Is this what we want in greater society—incompetence?
The need to solve problems is eternal, but many of life’s weightiest problems don’t boil down to numbers. Prioritizing higher-level numeracy over other forms of logical reasoning is not turning us into a nation of engineers and physicists. It’s letting us become a nation that can’t think straight.
America’s Founders knew it would take educated citizens for this democratic republic to succeed. But nowhere did they mention the quadratic formula.
I do think, and have expressed on other threads here, that trying to rely on the heckin soyence and flawed statistical models for everything has caused a lot of problems that we face today. Humans are terrible at reasoning with large numbers, so most people (myself included) are terrible at working with and understanding statistics. When we make essential things in life something only a select few academics can fully understand and reason about, we outsource our thinking to retards like the economists who said printing all of that pandemic money wouldn't cause inflation, and many mock, deplatform, and censor those who ask questions about such things. We need more people to think for themselves again.
I don't understand the failure rates behind ochem. Shit makes sense. It' s a puzzle. A difficult one, and OC II makes it difficult by throwing too many pieces at you and not enough time to memorize their function, but the pieces all fit together like math.
Biochem though. Fuck biochem. I will never need to know that shit in order to do surgery. Who the fuck needs to know what an oxyanion hole does to cut into someone? Why do I have to memorize all this shit??? View attachment 5709772
My undergrad degree is in more biological field, the research I was roped into was more physics based. All my graduate classes eventually lead me to Mr. Dirac and relativistic physics.
The point of the current education system was to give children access to more than what their parents had. Universities being open to the middle and lower classes were so that the baseline of intelligence and education would eventually rise. Math is an amazing tool because from it you can derive ways to make life a lot easier.
I think a problem is that a lot of “advanced math” is easy when you have proper integration of how it works in other classes. Woodshop and making certain things used to integrate math and physics. You could see the application of why Geometry works and why you give a shit. Know where are those classes? Defunct because why would you need to learn how to handle that in a service economy? Most high schools now aren’t agricultural, industrial, or pre-training, but daycare. Schools used to prepare a citizenry that was self-sufficient.
I thing my beginning with mathematics was shit, but I retook classes in college until I got it. I’m probably gonna retake linear equations and other shit over the Summer because I need to know it. Not everyone needs to know what bullshit I got into, but treating basic math like it’s Quantum Mechanics is retarded. You’ll eventually end up in a dirty nigger town society where no one can do basic division.
There should be mandatory classes on financial literacy. Just stuff like balancing a checkbook, making a budget, and how to rent an apartment/buy a car/how credit cards work. It would definitely cut down on a lot of early adulthood pain, and lots of people don't learn this stuff at home. Break the cycle of debt slavery!
deriving the formula through Completing the Square or such like, so you had to rely on rote. I'm sorry that your Math teachers failed you but it doesn't follow that quadratic formula is a "useless Math requirement'.
The same people yelling that we need to get rid of math and they never use math are the same ones bitching that the schools never taught them to balance a checkbook, compute the interest on their credit cards or mortgage, or taught them how to do their taxes.
yeah, interest rates are covered in algebra and algebra 2. And taxes are complex and can change yearly, so good luck with that. The basics can be taught at home.
The rot is at the heart of our education system. It's not geared towards making people more versatile, adaptable citizens; it's the Rockefeller Model, which is designed to pidgeonhole you and get you on the wageslave hamster wheel as quickly as possible.
It's why your high school advisory class tells you, "you will be a failure unless you decide what you wanna do for the rest of your life RIGHT THIS INSTANT!" Seemingly forgetting that 15-year-olds seldom think beyond lunchtime.
And it doesn't even pigeonhole well either. We rip on illegal immigrants taking all the fast food and construction jobs, but the reason why is because a serious business never wants to take the chance of dealing with surly teenagers. High school is also a profoundly distorted world unto itself with completely different social mores and incentive structures. For you Boomers and Gen Xers that thought Head of the Class was realistic, your average high school today is more like Class of '09. Due to truancy laws, schools do not want students to be working part-time which significantly narrows the vision students can have in school. Academic skill is secondary to socialization skill, so the goal of a student that wants to be popular is the one that can throw the best house party with easy access to drugs and alcohol. The result is also manifest in college where being skilled is not as important as being liked, which is why competency crisis is even a thing. Since school life is a 15 year old's entire life, they can't conceptualize the life of a professional anything because their entire life up to that point is going to classes according to a bell for no pay and for skills that are not valued in the real world either, hence the college scam.
