In your experience? The world over? Can you tell me your experience. I've been a teacher for a long time. I've worked in the UK, the USA, PNG, and Kenya.
The vast majority of kids in the developed world don't really care about education. A few do, and they get great grades. Most care more about social status, their cliques, or just surviving the jungle that is school.
School is important. It teaches you how to deal with other people. It teaches you how to deal with people in authority. You can't get that at home, in front of a screen. Learning stuff is secondary. I'm sure there are plenty of people here that are not working in whatever they majored at.
School shouldn't be primarily about experiencing social interaction. It's an artificial environment that disappears as soon as you graduate, and which you'll never find again anywhere else in society. You can learn social interaction in plenty of other settings, most of which are vastly more efficient and realistic. Admittedly, none of them function as daycare...
School should be (and used to be) about learning to learn, building mental discipline and a base of knowledge sufficient to bootstrap whatever other studies appeal to the student, even more so than memorizing a particular list of facts. But it seems that that position has been largely abandoned.
In any case, we homeschool.
I haven't really considered how to improve schooling at scale (particularly in an affordable way), but my proposal would be to introduce a _lot_ more granularity to schooling by eliminating the idea of grades and classes and focusing more on individual assessment.
Obviously this is likely cost prohibitive, but perhaps promoting and subsidizing homeschooling and homeschool co-ops is a good start in that direction, and could give rise to more cost-effective solutions over time. Not all parents are equipped to homeschool, but homeschooling does make use of resources which could be improved and which others could leverage as well.
In any case, the problematic schooling model that persists to this day was introduced around the time of the Industrial Revolution, which predates your references.
You could read more in my book: https://www.wyclifsdust.com.
Student A: Went to College X and majored in Y. Finished all XXX number of credits and graduated with Bachelor's Degree
Student B: Went to same College X and majored in same Y. Finished all XXX-1 number of credits so is 1 credit short and never got a degree.
Student B is worthless even though she/he learned exactly the same thing as Student A. School (especially in USA) never was and never will be about learning ...
In your example, I would argue you haven't taken my position to its required logical extent. I don't believe in the value of college degrees at all, the way things are currently structured, and I would discourage my kids from going to college unless they had a very specific career path in mind for which the degree is required. The measurement of learning has become the goal of learning, unfortunately.
What settings are those?
Notably, this is largely an American problem, since America is built around cars, which given the capitalist nature of American society proves to be antithetical to establishing local communities.
European and other countries, whose layouts and culture were established in pedestrian days, are much better off in this regard.
I would say it's quite similar.
For my own kids, you really see the differences at 11 to become more profound in their classroom, where some are running behind while others excel. So I saw that 12 is indeed the age where a split is necessary.
You don't have that?
Edit: After some Wikipeding, I see you really don't have that. Wow, that is crazy in my opinion. I have no clue how you could ever organize those differences among students. Here is the system of Belgium: https://en.m.wikipedia.org/wiki/Education_in_Belgium.
For example my daughter is 12 and she is in a class "STEM and moderns languages". Very focussed on programming, science, math, and they also get Dutch, French and English. Some of her classmates at the end of the schooyear had to switch because their grades weren't good enough.
So in Belgium, there are even different schools for different tracks.
Let's divide it into kids that like to learn vs kids that like to work with their hands. The 2nd group would learn how to work with metal, wood, .... Way more practical stuff, very little theory. The other group is the reverse of course.
At 16, some kids are really tired of sitting in a classroom. For example plumber track would have these 16 year olds already doing an internship with real plumbers. At 18 they can start their own company already.
It's also no secret that a 16 year old in Belgium learns math that in US you would only see at higher education.
I think it works great, and what I saw with my 2 oldest is that last year when they are all still together at age 11, the learning differences really start to show. It's neither fun for the smart ones nor for the slower ones.
The same person as a student, gets tons of chances before maybe having to leave. Depending on what they’re doing, you could just be stuck with them for north of a decade. No escape.
I mean, we can joke about how actually such people still exist at work, but it’s a far less widespread problem and manifests differently.
You can look for other jobs if you want out of a bad work environment. Probably, you’ll be able to find somewhere else to go. Getting out of a bad class is way harder.
There’s a couple huge differences.
And to be honest, I have no idea how you can make the US system work, so I probably agree with you. Come to Belgium and let your kids study here :D.
I wonder if there’s literature analyzing Belgian academic outcomes alongside American academic outcomes.
Just a nitpick that school enforcing memorizing particular list of facts or memorizing poems - is indeed teaching people how to learn, because how else will you explain to a child or an adult "hey you know if you read this thing 10 times and then try to repeat it another 20 times from memory - guess what !!! that is one trick to learn to memorize something."
But if they spend time on finding out how to memorize hand picked for them stuff and how to perform on exams on limited and picked topics - that sounds like they will be able to learn anything but still too many don't realize what the real lesson there is.
Knowing how to memorize is occasionally useful depending on one’s profession, but I don’t think it deserves such a heavy emphasis. People naturally remember what is interesting and useful to them. Force-feeding facts or dates or speeches or poems into memory is not fun and has very little educational value. That time and energy would be much better spent on projects that use and integrate the knowledge.
Whoa there, society functions like a school environment.
You have cliches, bullies, enforcers, popular kids, the weirdos, etc.
What are our political parties other than massive cliches?
Bullies you can meet on the road, in stores, and nearly any other place you go.
Enforcers are police, detention centers, and fines.
Popular kids you need look no further than influencers, movie stares, etc.
The weirdos are anyone that doesn’t fit into our cliches.
Also, Foucault would have a few words with you as society is also an artificial environment.
The drama of daily life that plays out just happens in a larger more chaotic scale, but when we left highschool, highschool never left us.
Also, I think the biggest thing that present in school environments but missing from other environments is the forced segregation by age range, which prevents the more organic tribal self-organizational practices to which humans have adapted over tens or hundreds of thousands of years.
And I would also add that there are degrees of artificiality and what really matters is not so much whether we have constructed our environments so much as whether or not they have stood the test of time, and adapted to us as much as we’ve adapted to them.
It did. You didn't pay attention. You want school to teach media literacy? It did, but you complained the whole time "when are we going to use this?". My school taught us how to interpret a "source", how to write well defended arguments (even if I don't always rise to that level), how to calculate mortgage interest rates and payments etc etc etc.
But people will swear up and down "school doesn't teach anything important"
because they didn't pay attention to what was taught!
The primary problem with education in america today is that a huge proportion of parents do not give a fuck about education, see school as just a thing you have to do instead of a constant opportunity. When a kid sees their parent complaining about education being "Liberal brain washing" every other day, why would they pay attention in class?
Education requires emotional and ideological buy in from parents and students for best results.
It didn't. I specifically remember the hole where my class should've explained what a court case actually determines, how the process runs, because I noticed things were missing / being swept under the carpet (we did some mock jury stuff but without the right context for it to teach us anything).
> You want school to teach media literacy? It did, but you complained the whole time "when are we going to use this?"
Nope. I specifically remember watching movie "making of" videos and my teacher saying "write this down!" about irrelevant technical details that distracted from the more important stuff the director was saying.
> But people will swear up and down "school doesn't teach anything important"
> because they didn't pay attention to what was taught!
Nope. I was an engaged, attentive student (indeed a kind of star pupil). I still learnt more in spite of school than because of it. Indeed some of the stuff that's most important for my education and career is stuff I was actively punished for doing at school (poking at the computers to see how they worked). Schools, at least the standard-ish state school that I went to (which had good official ratings) teach the wrong things and teach them badly.
We mainly teach either boring material or outright lies about how life works. Because we try to put our education on rails, teaching students that that's how life and education works, that's why it's a complete failure. The fact that students in COVID didn't respond to remote lessons is partly because they weren't even engaged prior to COVID.
We don't teach students how to be present, to know nature, how to explore their thoughts and emotions, or how to collaborate.
Montessori schools do. Wish they were more common.
And as a result, your experience is mostly limited to kids who are forced to be where they don't want to be. That's a hugely biased data set.
> School is important. It teaches you how to deal with other people. It teaches you how to deal with people in authority.
And yet it does a worse job at it than those who are home schooled, as most studies show.
Most kid athletes are also not self-motivated to run laps, or do boring repetitive drills, when they know from experience that these activities help them win games within the next few months. Usually need a coach to force them to do them. Same for young music players. Practicing scales endlessly does make you a better musician. But they won't do it till forced.
The primary reason kids don't like running laps or playing scales or doing math drills is because they are boring.
The value of such exercises, or any other drill-based curriculum, must be measured with its opportunity cost. If you practise scales for an hour a day, you can indeed reliably expect to be better at your musical instrument, but it could very well be that the same hour spent on improving another skill (sight-reading, articulation etc.) would make you considerably better still at your instrument.
I think it might be more generally useful to say that, in order to develop well-rounded competency in a given field, one should expect to sometimes have to perform boring drills.
I’ve heard that kids in upper middle class circles are totally different in this regard though. Maybe they want to do more on average.
[1] See, most recently, Zambia
For higher education there is charade of education to get jobs. So for office manager job where grade 8 would be enough, we have MBAs now because we all need advanced education to survive in global economy blah..blah.
This would actually be a good business opportunity: hire such "grade 8 educated" people as office managers, but pay them much less than MBAs. If they are nearly as good as MBAs, you save a lot of money on this group of employees, and thus your company has a strong economic advantage.
The trouble is it's performance all the way up and down. In the first place you're only going to get the weirdos / extreme gamblers, and then you'll struggle to attract investors, your clients/suppliers will wonder why your business development folks missed their classical references...
You will (hopefully) nevertheless check whether an applicant has the necessary traits to be a decent office manager. On the other hand, I wouldn't claim that weirdos are necessarily bad office managers.
My opinion differs a lot here. I would not say that I have a good number sense (I guess that people who have to do "numeric calculations" or "back-of-the-envelope calculations" as daily part of their job have a much better number sense than me). On the other hand, I find it rather easy to learn really abstract algebraic concepts (think Grothendieck-style algebraic geometry or similarly abstract mathematical topics), which many people (most of them with much better number sense than me) tend to find insanely difficult.
On the other hand, textbooks about, say, analysis and mathematical physics (both in a broader sense) - which can also be very complicated - have a tendency to demand a lot of (also long, tedious) "routine" calculations from the reader (often to do by his own). For these areas of mathematics your argument surely makes sense.
Textbooks about particular areas, in particular specific topics in physics (including mathematical physics), teach me a lot about number sense (and let me feel that mine is not really good or perhaps badly trained). On the other hand, these very abstract topics feel like a quite different activity to me that is only barely related to number sense.
> People capable of understanding Hartshorne have number sense.
This can also be explained by the hypothesis that people with a strong number sense love to feel themselves challenged - thus they attempt to understand this nontrivial textbook (even though understanding it may in particular require different skills).
Evidence that it's causative? That would be utterly bizarre and I'd love to see a citation, because doing algebra has nothing to do with fractions. I'd think it's far more likely that there's a strong correlation between the two because they're both determined by the ability to understand and follow the rules of an abstraction/notation system, and if you taught people algebra first and then fractions afterwards you'd say that ability to understand fractions was determined by whether they could do algebra.
Doubt. Do you have any evidence at all for this claim?
> It would be bizarre to teach someone how to add rational functions before they can add fractions.
Sure, rational functions obviously sit at the intersection of algebra and fractions and require both. But they're hardly some deep foundational piece of algebra; I'm not sure my classes even covered them.
Only anecdotal evidence. I’ve taught beginning algebra courses at a community college for 23 years. Students who don’t know fractions have a very hard time in algebra. Those who can’t understand that x + 5/3 x is 8/3 x have a hard time understanding that 2xy+ay is (2x + a)y.
Understanding rational functions helps to understand what vertical asymptotes are and as such are a fundamental source of examples when learning limits. They also aid in understanding why tan(x) has vertical asymptotes where cos is 0. Every complete algebra curriculum includes rational functions. I say complete because algebra is usually broken up into 3 courses (2 at the pre-college level).
Sure - but that's just as true in reverse.
> Understanding rational functions helps to understand what vertical asymptotes are and as such are a fundamental source of examples when learning limits. They also aid in understanding why tan(x) has vertical asymptotes where cos is 0. Every complete algebra curriculum includes rational functions.
Meh. x^-1 is a good example of some things, sure, but I don't remember ever doing addition of rational functions which is what you originally talked about, and I went through an extremely reputable maths degree.
No middle school, and I very much doubt it. Searching I can see them mentioned in a further maths GCSE (which is something most schools including the one I went to don't offer, and rather suggests they're not on the regular maths GCSE, which would match my memory).
> Most students who know that x + 5/3 x is 8/3 x have trouble, initially, with understanding that 2xy+ay is (2x + a)y.
Who know that first or who have been taught it? I genuinely would like to see any actual evidence that the latter is objectively more difficult than the former.
I think you are partially right in that the dryness of much of math teaching hides a lot of the underlying material's applicability to life. I think one thing AI could do is help design rich situational lessons that could are prompted, vetted, and updated by teachers and then taught to the class. It could be trivial to create incremental difficulty of problem materials tailored to each student's progress and goal.
The real real answer is that it probably does, but on a much longer timescale that we generally consider and it is really hard to explain why. Something like better math skills lead to better life outcomes. Maybe due to a better model of the world and sharper thinking, but I am just guessing.
The way to correct this is by imbuing students with the confidence and skills required to learn (according to their style of learning) correctly from the very beginning, so that they build on solid foundations instead.
So you are a teacher?
Upon reaching a certain threshold of technological dependence, the need for rational thought (which includes calculation) is tied to the need for food. The actual yield may be low based on other factors, but it is absolutely necessary for survival.
The alternative you suggest, is where technology no longer advances.
Logically then, population growth hits a malthusian trap, the old crowd out the young since they have the most influence, and then a depopulation occurs as the old naturally die off, and replacement births cannot sustain those dependent systems used to feed the masses.
You get a dragon-king event where everyone its a free for all over food and bare necessities, farming no longer becomes possible (because of looters), and the world order collapses to pre-agrarian levels, assuming the environment isn't destroyed in the chaos (i.e. MAD and Nuclear Fallout).
There are much better ways to calculate than are currently taught in schools, Trachtenberg System and Vedic Maths have worked well in many places.
Mental math has been around for quite some time, and the principles of math are all about finding uncommon knowledge or information that is not immediately apparent (though it becomes so via various mathematical transformations).
The current pedagogy of math is all about sieving and exclusion, and rote-authority based teaching, since it is a requirement for any specialized area of science (and is only taught in relation to mathematical concepts, instead of intuitive approaches). This is why they adopted a burn-the-bridge strategy right around trigonometry at the grade school level (intended to cause PTSD/suffering/torture), to safeguard against disruptive innovators at the source.
Algebra -> Geometry -> Trig
1 -> 2 -> 3
What do you suppose happens when the passing grading criteria in 1 is changed from just following the process (but not correct answer) to 2 (separate unrelated material which is passed) to 3 (correct process and correct answer).
If they fail Trig, and the problems are from Algebra (not something a teacher paid bupkiss will bother to look at), how do they go back if they passed Geometry? The students not knowing why they are failing are simply told, well you maybe you are just not good at math and should consider other paths if you can't do it.
This structure is called burning the bridge because it makes it so you can't go back from a progression standpoint. Ironically, this structure was adopted at the request of representatives from the National Teachers Union in the late 80s/90s, and largely remains the same today.
There are several other progression sieves embedded in academia intended to make it almost impossible for us as a society to develop a large number of creative people who reach einstein-level achievements in math and science (outside-self study, or specific environments/private schools).
This broad push largely started in the 1970s in publishing, and expanded from there.
this seems like a bizarre conclusion. In my experience, most people, the world over, are in fact self motivated. You won't see that if you have a very narrow definition of what is it that they're supposed to be learning
kids aren't motivated to do boring math drills, because they don't see why it matters to their life (the real answer is: it does not, they are not wrong).
I appreciated hearing this echoed by Conrad Wolfram in a recent PIMA episode: https://freakonomics.com/podcast/why-do-we-still-teach-peopl...