carrying out arithmetical or algebraic procedures — Tarskian

Trains the mind in the significance, functions and manipulation of numbers, of quantitative relationships and proportions.

memorizing proofs — Tarskian

It's not the memorizing that matters; it's the understanding of how they were derived and why they are valid.
While everyone needs arithmetic to navigate life successfully, few people need mathematics. But they won't know who they are until after they're introduced to the concepts. Therefore, every secondary school students should be given a basic education in maths and science.

Trains the mind in the significance, functions and manipulation of numbers, of quantitative relationships and proportions. — Vera Mont

Learning to formalize a real-world problem into a mathematical model is indeed more meaningful. Next, you can give it to a computation engine to solve. However, that is not mathematics. That is an activity downstream from mathematics. As soon as the problem has any real-world semantics, it is not mathematics but something else:

In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings (alphanumeric sequences of symbols, usually as equations) using established manipulation rules. A central idea of formalism "is that mathematics is not a body of propositions representing an abstract sector of reality.

According to formalism, the truths expressed in logic and mathematics are not about numbers, sets, or triangles or any other coextensive subject matter — in fact, they aren't "about" anything at all. — Mathematical formalism

There is nothing wrong with training people in using a spreadsheet or other computation engines. However, that is not an exercise in mathematics in any shape or fashion. It could be one in accounting, or engineering, or any other downstream discipline, but not one in mathematics.

In fact, you do not learn to use mathematics by studying mathematics. You must learn that elsewhere.

It's not the memorizing that matters; it's the understanding of how they were derived and why they are valid. — Vera Mont

And this is tested by the education system by asking the student to repeat the proof from memory. That does not require understanding. That merely requires rote memorization.

While everyone needs arithmetic to navigate life successfully, few people need mathematics. But they won't know who they are until after they're introduced to the concepts. — Vera Mont

They won't know who they are until they are confronted with a real-life problem that they need to solve and that requires them. Hence, only exposure to real-life problems will make people learn what they need. Therefore, the legitimate starting point is not the concepts or the tools. The legitimate starting point is a problem that you need to solve. no matter what. Next, you try to figure out what concepts and tools could help you doing that. It is of no use to learn concepts or tools unless you are going to actually use them. This can only be guaranteed when you start from the problem to solve and not from arbitrary tools that could possible be useful in solving some future nondescript problem.

Therefore, every secondary school students should be given a basic education in maths and science. — Vera Mont

I don't think so. In practice, it merely leads to memorizing concepts that the student will never use. In my opinion, it is a waste of time. If you some day you really need it, you can learn it then and there. Employers do not value it either. If they did, youth unemployment would not be a thing.

This waste of time is not without consequences. Around the globe, hundreds of millions of young people graduate from secondary schools every year. There is no job that they will be hired for that requires anything they have learned in high school. Starbucks will hire them, but they will also happily hire someone who did not graduate from high school at all. For most of them, it would even be better to get something like a truck driving license instead of a high school diploma, which only takes a month or two, instead of six years. Still, they will much more easily find a job and make a much better living that their high-school peers.

Learning something that you may possibly some day need, has turned out to be a losing strategy. Instead, get straight into a professional environment, and try to solve the problem at hand. Only then, learn what you need to solve it.

Okay. Let's dispense with education altogether. On their sixth birthday, give every child a laptop and put them to work on real life problems.

Neither activity is meaningful in any shape or fashion. — Tarskian

*sigh*

Okay. Let's dispense with education altogether and puts kids right to work on real-life problems as soon as they turn six. — Vera Mont

They used to start working at around fourteen.

Back then, there was no problem of youth unemployment. Employers were perfectly fine to hire apprentices. Nowadays, it is illegal. Around the globe, child labor laws prevent teenagers from working. It proves again that there is no problem in the world that the government won't make worse.

If someone is interested in academic subjects, he will undoubtedly find his way to youtube and start viewing introductory material. If they are not interested, then why would they have to learn it?

There are not that many jobs in the modern world that are suitable for children between six and fourteen. In the past, they could help out with subsistence farming, but that option is not available for most families. But then again, even today there are still lots of jobs could be done by a fourteen-year old.

Everybody will automatically learn how to use the simplest version of the computer, which is the mobile phone. In fact, children learn by themselves how to use it, long before they graduate from primary school. That is also how most jobs will end up using computers (by using apps on a mobile phone).

I teach elementary, and memorization certainly is part of math teaching, but since Common Core, there's been a shift towards conceptual understanding of math, instead of just rote memorization.

That being said, I don't think math should be taught for more than a half hour a day. Advanced maths also should not be required in high school. They should be electives. There really is no point anymore in forcing the average student to learn algebra and geometry.

Okay. Let's dispense with education altogether. On their sixth birthday, give every child a laptop and put them to work on real life problems. — Vera Mont

What about having HS students take an "intro to maths" class, where the textbook covers "consumer math" (fraction, decimals, percents, etc.) and briefly touches on more advanced concepts. After that, they're done with math requirements. If the student wants to, they can take advanced math as an elective. I would rather require philosophy classes in this day and age than math. Too many people can't think.

there's been a shift towards conceptually understanding of math concepts, instead of just rote memorization. — RogueAI

What strikes me, is that they still test students while imposing the following conditions:

- you cannot use a calculator
- you cannot use your books
- you cannot use google search

Students learn exactly the opposite of what makes you productive in a professional environment.

If you can find a solution by using a piece of software (such as a calculator) or by using a search engine, but you don't, you are considered to be highly unproductive. You won't be able to compete with people who are good at doing exactly the opposite.

In that sense, schools mostly teach students how to be unproductive in a professional environment. The students do not learn concepts, especially not the concept of doing whatever it reasonably takes to figure out the solution, because in fact, this is not allowed.

But then again, if the students are simply allowed to use a tool such as wolfram alpha, then it would become patently clear that they are not learning concepts at all. They are in fact not learning anything that a machine cannot do better than them. On the contrary, all they are learning is to try to be the machine, but miserably fail. That is the main reason why a high school diploma is completely worthless in the labor market. University degrees are rapidly going in the same direction, for exactly the same reasons.

That is the main reason why a high school diploma is completely worthless in the labor market. — Tarskian

If you are competing for a job with another person, and the other person isn't an HS graduate and you are, isn't that going to be a significant advantage for you?

What about having HS students take an "intro to maths" class, where the textbook covers "consumer math" (fraction, decimals, percents, etc.) and briefly touches on more advanced concepts. — RogueAI

I'm okay with that. I'm actually a huge fan of a rounded education, rather than one aimed at a 'career path' (which in my experience is a futile enterprise, often as not, because things change and keep changing.) I would be grateful if you could also squeeze in a bit of history and geography, but for pity's aske,* don't stint on sciences!

There are not that many jobs in the modern world that are suitable for children between six and fourteen. — Tarskian

Oh, really? And here I thought I was being facetious. Pretty soon, with increasing automation, there won't be (m)any jobs for adults, either. The 'modern world' is a fragile and volatile thing. Why assume it will continue as it is?

Students learn exactly the opposite of what makes you productive in a professional environment. — Tarskian

Right up until the power grid and internet break down. After that, when there are no professional environments, it's the ones who don't rely on devices who will have to solve the real life problems.

Ed *or keyboarding skills!

If you are competing for a job with another person, and the other person isn't an HS graduate and you are, isn't that going to be a significant advantage for you? — RogueAI

Only if that is the only requirement (which it never is because a HS diploma does not reflect any ability to solve any particular problem). Ok, let's take an example and let's look at the following job:

https://www.indeed.com/q-react-js-jobs.html?vjk=5d7f26153585e268

REQUIRED KNOWLEDGE & SKILL SETS

5+ years of experience in Software Programming or Engineering
Proficient with software programming languages such as JavaScript, Java, Python, C++, or Node.js
Experience with full stack development, deployment, and support of web and mobile applications
Experienced with native, react native, hybrid, PWA, and/or mobile-responsive apps
Experienced with development and implementation of APIs, microservice contracts, data structures and interfaces, along with other relevant tools and technologies
Knowledge of Jira, Confluence, and other ALM tools
Comfort and confident in ambiguity, is resourceful, and willing to problem solve around the ‘how’ of execution work
Understanding of how to deliver work iteratively and push goals to the finish line using agile methodologies
Works collaboratively across internal and external product, design, development and QA teams

EDUCATION and/or EXPERIENCE

Bachelor's degree (B.A. or B.S.) in IT, Software Engineering, Computer Science, or related fields preferred; and/or 5 years related experience in demonstrated mobile application, web application and/or software development.

First remark: you don't learn any of the following in high school:

- development and implementation of APIs, microservice contracts, data structures and interfaces, along with other relevant tools and technologies
- native, react native, hybrid, PWA, and/or mobile-responsive apps
- development and implementation of APIs, microservice contracts, data structures and interfaces, along with other relevant tools and technologies

You do not even learn this at university. Universities don't teach it. They would not even be able to teach it. So, a candidate can have a masters degree from MIT or Stanford or even a Ph.D, but he will still not qualify for the job. Seriously, this company won't hire that candidate. Hence, you won't be competing with any graduate from any level, because they are simply not qualified for the job.

So, how do you learn it?

Well, I always had to learn this kind of things by googling for something like "tutorial react native", and then start from there. I've had to do that a lot of times in my career.

The people who would compete with someone like me for this job, are people who have used these technologies in their previous job. They actually stand a much better chance at getting the job, but they are probably not applying for the job, because they get called by recruitment companies who offer them jobs, just like they used to call me when I was still working. So, they do not have to look for jobs. So, they are unlikely to apply.

Does this employer really care about your university degree? Probably not. Almost surely not.

I have a degree, but nobody has ever asked me about it. I am semi-retired now. So, nowadays I don't need to deal with this kind of things anymore, but I can guarantee to you that you are better off with a 3-month bootcamp in "react native" than with a Ph.D in computer science:

https://www.udemy.com/course/complete-react-native-mobile-development-zero-to-mastery-with-hooks/

Complete React Native Bootcamp (with Hooks) Master React Native for iOS and Android Mobile App Development using JavaScript. Build a modern e-commerce mobile app!

So, no, in my experience, having a high school degree won't make any difference. You are not competing on that basis. You really don't need one. You are competing in the area of having practical hands-on experience in a subject that no school has ever taught or will ever teach.

By the way, "react native" may be popular today, but I can guarantee that a few years from now, it will be something else.

While it is true that most things that are taught to students are completely unnecessary for them to know, schools don’t always attempt to teach a student everything they will ever learn in a particular topic. Education is an attempt to teach students the basics of how things work so that the student can continue in many paths, expanding on their knowledge until they can offer new, helpful insights and be productive members of society.

While math knowledge isn’t important for people who won’t use it, and people who will use it probably still don’t need the knowledge (although it is helpful to have a baseline knowledge in case common tools fail to perform a specific task), it is really for the people making the tools. While most people will not use it, the people that will make a huge impact, and progress as a species depends of some group knowing these things.

You might ask “why teach everyone, then?” It is true that this is inefficient, and if it was feasible to offer students only the education they need, I’m sure we would.

This idea has failed because of two problems.
One: the resources required. You can’t have a specialized path for every student, so you end up grouping students in large groups based on what you think they will end up doing, which we already do, to an extent.
Two: It’s hard to know what a person will do, and you can’t have everyone decide at an early age, when education starts. Therefore, it’s necessary to teach a baseline in many topics and then later allow options for specialized learning.
Current education does this fine.
I’m sure there could be more efficient ways to do this, but there always are.

This is a side topic to the main post, so I’ll summarize the relevant point here: the knowledge of basic math must be taught to make students, to assure that the people who would make advancements in fields that require math have basic knowledge to build upon in order to eventually make contributions.

Pretty soon, with increasing automation, there won't be (m)any jobs for adults, either. The 'modern world' is a fragile and volatile thing. Why assume it will continue as it is? — Vera Mont

After a few decades of making money by writing software, I can guarantee to you that the claim that "AI will replace all jobs" is complete bullshit. I really don't know why the mainstream media are pushing that stupid narrative. Maybe because some people will believe it anyway?

Actually, I usually do understand why the media push a particular bullshit narrative. There are so many, and their motivation is usually very transparent. In the case of the AI nonsense, however, I do not even see what they are trying to achieve by making people believe it !?

Education is an attempt to teach students the basics of how things work — Igitur

No, it doesn't. For example, if you want to figure out how to write a mobile app, no school will ever help you. I don't say that anybody should learn this, though. But then again, take whatever real-life example of how something works, and you will quickly understand that the school is totally ignorant of how it works. So, how can they teach it?

You can’t have a specialized path for every student — Igitur

Not true. You definitely can.

For example, the best way to get into software engineering, is to do a 3-month bootcamp. There is no need for 6 years like in high school. I would say that the only way to get people started in their career is a specialized path for every student. It is possible and it is being done already.

It takes two months to train a truck driver and to get the license, if that is what the student wants to do.

It’s hard to know what a person will do, and you can’t have everyone decide at an early age, when education starts. — Igitur

Well, he still has to start somewhere. Not having any starting point at all, is not the solution either.

Therefore, it’s necessary to teach a baseline in many topics and then later allow options for specialized learning. — Igitur

Not true. Baseline generalities do not prepare for anything at all. We already know that. That is why youth unemployment is a reality nowadays.

Current education does this fine. — Igitur

No, current education is pretty much a complete failure. I am surprised that any graduate finds any job at all. If it goes on like this, they will all end up slinging coffee at Starbucks. That is the true career for which they are being prepared.

the knowledge of basic math must be taught — Igitur

No, because Starbucks et alii do not require it. The cash till can perfectly handle all arithmetic. The cash till is a computer. Starbucks will not allow its staff to do any math. Again, either you build the machine, or else you use the machine, because in all other cases, you are trying to be the machine.

Yes.

No, current education is pretty much a complete failure. I am surprised that any graduate finds any job at all. — Tarskian

We might still need a few doctors and architects....

For example, the best way to get into software engineering, is to do a 3-month bootcamp. — Tarskian

Good. So that's where all the 34 million 14-year-olds dropouts should be heading. (Except those two dozen football players, five rappers and one stand-up comic.)

No, it doesn't. For example, if you want to figure out how to write a mobile app, no school will ever help you. — Tarskian

I said it was an attempt, not that it was completely successful. Also, teaching someone how to make an app wouldn’t be the same as teaching them how apps work. I wasn’t saying that it teaches general information about everything, that’s obviously not true, but instead that it teaches a set of basics that people think are necessary.

I would say that the only way to get people started in their career is a specialized path for every student. It is possible and it is being done already. — Tarskian

I’m not talking about programs that teach more specialized subjects, but instead specialized paths built into public education systems. Totally agree with this though, just not that some organization could create separate paths for every student in a largeish country.

Not having any starting point at all, is not the solution either. — Tarskian

True. I was mainly talking about public education systems, and how they usually don’t have that many options to fully commit to a certain path because younger students aren’t trusted to make good decisions for themselves. The “starting point” would be higher education.

Baseline generalities do not prepare for anything at all. We already know that. That is why youth unemployment is a reality nowadays. — Tarskian

Maybe. I was mainly saying the baseline education
was necessary for students who wish to go into jobs that have to do with them. Kind of like a way of introducing a lot of jobs that need to be done, but otherwise might not. (Like math related ones.)
Are you saying we need to shift the baseline to something more applicable for the majority of students’ likely future careers, or just get rid of baseline education altogether?

No, current education is pretty much a complete failure. I am surprised that any graduate finds any job at all. — Tarskian

This is very pessimistic. As long as there are experts who were able to make progress because of their education (talking mostly about experimental fields of science here), progressing the species (or fulfilling roles like doctors) the education system has not failed completely. While it’s stir that this doesn’t happen to the majority of people, how else do you propose we teach the people who end up being the ones who play important roles in the success of humans as a species?
They may come up anyway, but this education system probably either helps them learn about such subjects or helps more students to explore possibilities that they might not have without education.

No, because Starbucks et alii do not require it. The cash till can perfectly handle all arithmetic. The cash till is a computer. — Tarskian

Not for the people using the computer, but for the people designing new, better computers, eventually making life better for the average worker by automating more things/making current systems work more efficiently.

Good. So that's where all the 14-year-olds should be going when they drop out of school. — Vera Mont

I can only talk from my own experience. It is just one example of how things work in practice. The labor market consists of an almost infinite myriad of different jobs, of which I only know 0.1%.

Personally, I did not learn anything in school between the ages of 14 and 18 that was later on helpful in any way. In fact, I did not learn anything at university either that turned out to be useful. I guess that 14-year-olds instinctively sense this.

Therefore, I can understand why a 14-year-old feels like dropping out. In fact, dropping out is actually not the problem. The real problem is that they need to do something else instead. Something that does make sense.

That is where the system fails, and by design so.

With all the child labor laws, it is illegal to hire a 14-year-old. So, he cannot become an apprentice with someone who can teach him something useful. Society has simply outlawed the solution. The government does not solve problems. Instead, the government pretty much always makes the problem unsolvable.

Before around 1850 (before the school system was introduced), there were no "drop outs". There were no demotivated youngsters who felt useless and lost. At the age of 12, you could join the crew of a sail ship and travel the world. Look for example at the fifth officer of the Titanic, Harold Lowe:

https://en.wikipedia.org/wiki/Harold_Lowe

Harold Lowe was born in Llanrhos, Caernarvonshire, Wales, on 21 November 1882, the fourth of eight children, born to George Edward Lowe and Emma Harriette Quick. His father had ambitions for him to be apprenticed to a successful Liverpool businessman, but Harold Lowe was determined to go to sea. At 14, he ran away from his home in Barmouth where he had attended school and joined the Merchant Navy, serving along the West African Coast. Lowe started as a ship's boy aboard the Welsh coastal schooners as he worked to attain his certifications. In 1906, he passed his certification and gained his second mate's certificate, then in 1908, he attained his first mate's certificate.

This system worked much better. Today, Harold Lowe would be a directionless dropout because nowadays nobody can take him on as an apprentice.

The current system is objectively worse than what they had back then.

We might still need a few doctors and architects — Vera Mont

In practice, there are no "architects". In practice, there are only users of architect software. So, either you build the machine, or else you use the machine, because in all other cases, you are trying to be the machine. The last bit, is what architects learn at university. Employers want users with years of experience with the software that they happen to use, while the people who graduate from universities are trying themselves to be the software. That is why they are unemployed when they graduate.

Concerning doctors, the entire medical industry is actually a gigantic scam. Quite a few people became more aware of that during the past scamdemic. Doctors do not learn at university what to prescribe to the patients. They learn that from the pharmaceutical mafia. It is one of the most regulated professions and therefore the profession that tops the list in terms of mafia behavior. If things go on like this, they will manage to bankrupt every modern western country -- if something else does not bankrupt them first. (There is a long list of situations that are busy bankrupting the West, such as the banking system, and so on).

S0. A nation of innumerate illiterates who can't find North on a compass just need to be trained in which buttons to push. Maybe a chimp can instruct them.
Then they can get jobs.
What more can there possibly to human life?

Also, teaching someone how to make an app wouldn’t be the same as teaching them how apps work. — Igitur

Someone with a degree in swimmology has read a lot of books about swimming, but he does not necessarily swim himself. That does not matter, because he can teach swimmology!

The “starting point” would be higher education. — Igitur

It used to be high school. Now, they delay it to higher education. But then again, if higher education were such a fantastic starting point, then why do so many of its graduates end up slinging coffee at Starbucks? The proof is always in the pudding, isn't it?

I was mainly saying the baseline education
was necessary for students who wish to go into jobs that have to do with them. Kind of like a way of introducing a lot of jobs that need to be done, but otherwise might not. (Like math related ones.) — Igitur

In fact, there are no math-related jobs. There is only math-containing software. There simply is no job where you have to manually compute math results. These students do not learn how to build such software. They also do not learn how to use such software. Instead, they learn how to fail at being themselves the software.

talking mostly about experimental fields of science here — Igitur

That's just another scam. The government spends money on "scientific research". Next, when there is scientific progress somewhere, the government is quick to claim credit for it, and then wants some more money for "scientific research".

There is an interesting German woman, Sabine Hossenfelder, who spent decades in scientific research and who explains in excruciating detail how the scam works. One of her videos:

What's Going Wrong in Particle Physics? (This is why I lost faith in science.)

They may come up anyway, but this education system probably either helps them learn about such subjects or helps more students to explore possibilities that they might not have without education. — Igitur

You cannot make progress inside the system, because that will almost always be shut down. Every innovation is in one way or another a threat to existing interests. That is why all progress is made outside the system. Example: cryptocurrencies. They dangerously threaten the monopoly of the banking system and associated government power and control. That is why they could never have emerged out of the academia or even the corporate world. The powers that be would have immediately nipped it in the bud. Same for the medical industry. Don't cure a disease that currently makes the pharmaceutical mafia billions already by not curing it.

S0. A nation of innumerate illiterates who can't find North on a compass just need to be trained in which buttons to push. Maybe a chimp can instruct them.
I'm just lucky not to have any future! — Vera Mont

Wrong again.

Software needs to be maintained. If nobody knows how it works anymore, the software is simply dead. These people need to know how to do it manually. If you don't know how to do it manually -- excruciatingly and step by step -- you can't touch one line in the software either.

You see, the specialized knowledge is massively important to some people. However, shoving it down the throat of everyone else, is not the solution. They first need to learn how to use the software.

But then again, after using the software for years, there are always people who want to know more, and who want to know how it works and why it works. That is how I spent years developing small toy compilers and interpreters, because I wanted to know what my compiler or script engine was doing under the hood. That allowed me to read the source code of the tools I was using. That brought me to learning the computer-science math with regards to compiler construction.

You see, it is absolutely wrong to start the journey there. Just learn to use the tool first. Only if it truly piques your interest, it makes sense to look under the hood. Computer science graduates may learn some of it, but they learn it at the wrong time in their lives. They learn it at a point at which it simply does not matter to them. That is why they suck at it.

Teach your brats to cook, to grow food, to work wood and metal. And how to get along with the neighbours, which is by having all these useful skills that can help them stay alive. The machines are no longer your friends.

Teach your brats to cook, to grow food, to work wood and metal. And how to get along with the neighbours, which is by having all these useful skills that can help them stay alive. The machines are no longer your friends. — unenlightened

We used to be hunter-gatherers. So, don't grow food. Hunt it instead.

There is just one problem with this view. There was a reason why we started growing food instead of hunting it. This planet was able to support less than a million hunter-gatherers. We are 8 billion now.

Mutatis mutandis, our current head count of 8 billion does not allow us to get rid of the machines. If we do that, we need to get rid of billions of people too. Who volunteers to leave first? Not me.

We used to be hunter-gatherers. So, don't grow food. Hunt it instead. — Tarskian

Look forwards, not backwards.

If we do that, we need to get rid of billions of people too. Who volunteers to leave first? Not me. — Tarskian

I will be leaving soon enough. So will you. That is going to happen, and the population will reduce to a sustainable level. Because an unsustainable level is "unsustainable". So your fatuous argument is to exclude the proposed middle of an agrarian society because 'no reason' in favour of a complete collapse to an imagined hunt that neglects the accompanying gathering. Or else the machine paradise...

But then again, if higher education were such a fantastic starting point, then why do so many of its graduates end up slinging coffee at Starbucks? The proof is always in the pudding, isn't it? — Tarskian

Maybe true, but it could also be that most people aren’t interested in the jobs that education helps with attaining, and so for the majority it is not that helpful. What would you propose?

There simply is no job where you have to manually compute math results. These students do not learn how to build such software. They also do not learn how to use such software. Instead, they learn how to fail at being themselves the software. — Tarskian

The students aren’t learning how to do math themselves, but how math works. (Which you need to know to know how you increasingly complex science and math work.) While you may need to know how to make software to make a software that does math, you also need to know how to do math, and knowing how to do math is more helpful towards making a software than the other way around.

There are also ways people can learn to make software within public education programs too, they just aren’t ass common (by all means, we should have more though).

That's just another scam. The government spends money on "scientific research". Next, when there is scientific progress somewhere, the government is quick to claim credit for it, and then wants some more money for "scientific research". — Tarskian

There’s scams everywhere. Just because the government wastes money on this doesn’t mean we don’t need scientists to actually make progress.

You cannot make progress inside the system, because that will almost always be shut down. Every innovation is in one way or another a threat to existing interests. That is why all progress is made outside the system — Tarskian

Just because making progress in the system is hard doesn’t mean it doesn’t give students opportunities. I wasn’t talking at all about innovation in the part you responded to.

Maybe true, but it could also be that most people aren’t interested in the jobs that education helps with attaining, and so for the majority it is not that helpful. What would you propose? — Igitur

"Child labor". Like it used to be.

Harold Lowe was one of the officers on the Titanic:

https://en.wikipedia.org/wiki/Harold_Lowe

Harold Lowe was born in Llanrhos, Caernarvonshire, Wales, on 21 November 1882, the fourth of eight children, born to George Edward Lowe and Emma Harriette Quick. His father had ambitions for him to be apprenticed to a successful Liverpool businessman, but Harold Lowe was determined to go to sea. At 14, he ran away from his home in Barmouth where he had attended school and joined the Merchant Navy, serving along the West African Coast. Lowe started as a ship's boy aboard the Welsh coastal schooners as he worked to attain his certifications. In 1906, he passed his certification and gained his second mate's certificate, then in 1908, he attained his first mate's certificate.

Schooling in mathematics spends a lot of time on:

(1) carrying out arithmetical or algebraic procedures that a tool like wolfram alpha can perform automatically.

-> There is no job where you will ever be required to manually carry out procedures that a computer can carry out. — Tarskian

And how can you pick the correct toll, if you don't know the arithmetical and algebraic procedures themselves? By at least learning to do them yourself, you understand them.

Neither activity is meaningful in any shape or fashion. That is, however, what mathematics education is all about. — Tarskian

I disagree. The problem is that there's simply too much math to study at a slow pace. So teachers in school and in the university don't have the time to go really through how some "proof" finally got to be what is now. The pace is so quick it favours memorization and simply those who can use various algorithms quickly.

Wrong again — Tarskian

Inevitably!

You see, the specialized knowledge is massively important to some people. However, shoving it down the throat of everyone else, is not the solution. They first need to learn how to use the software. — Tarskian

Oh, goodie! The six people who still understand some aspect of 'manual' programming can teach it to their children, set up dynasties and rule the world. For the +/-30 years (at the rate it's progressing, probably low end - you're looking at 1-generation dynasties.) it will take AI to generate its own programs.

For all other kinds of work, paid or volunteer, zero education required. O, brave new world!

Sounds as if you are arguing for an intellectually impoverished populace, and I wonder why?