I have a real issue dividing kids up along these lines. I've found that virtually all young kids love to explore and learn things, and if anything schooling can extinguish this innate desire when it becomes a source of stress.
This is a very bold claim. I don't think most kids are curious about the multiplication tables
https://news.ycombinator.com/item?id=48395840
and ultimately this about a successful experiment in other approaches to maths:
I think sibling comments are taking issue with `learn multiplication tables` versus `memorize multiplication tables`. I find no value in the latter in kids but incredible value in the former.
What I'm teaching my homeschoolers is to instead be able to quickly derive the table from the "easy" ones. Everyone practices counting by twos, fives, and tens at an earlier stage of math. So when multiplication tables come around, if you can fill 2s,5s, and 10s out easily, then any other thing you need is (usually) just one simple addition or subtraction operation away.
I do it this way for the same reason I'm against learning "tricks" like FOIL ( first-outer-inner-last) for binomial multiplication. You end up learning the narrow-scoped trick or you end up learning the table, and not a framework by which to solve problems of a broad class.
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I've seen entirely too many kids who memorize the table up to 10x10 and then are totally stunlocked at 11x11.
A better analogy would be "why stop memorising long works now we can read things instead". No one memorises epic poems anymore but we read novel instead.
A multiplication table is just a single-digit multiplication vocabulary.
Kids will learn anything that gives them social standing or self-worth in another way, whatever it takes to be a cool kid.
"nerds" would disagree with you. I think the point that OP was trying to make is the three groups are dynamic based on the topic. So the groups are not the same for biology, maths and for literature.
It’s exceptionally rare to encounter any person, adult or otherwise, that genuinely holds no value in any opinion of another. And even those people hold to their own self evaluations which do not spawn from pure noise.
Which is exactly why they stopped teaching them in US curriculum under No Child Left Behind.
https://www.thewellnews.com/opinions/california-removes-memo...
When rubber hits the road with a learning objective, I think the two most important axis are: how much does the student want to learn (this), and how easy is it for the student to learn (this)?
Both can depend on a variety of factors... For example a masters student paying their own way mid career maybe really wants to learn as much as they can, but a specific research report assigned during a busy work week, and some family emergency, etc. may mean they treat the assignment as "I just need to get this done" instead of "I want to get as much as I can out of this", and one way that can show up is how much they depend on an LLM to do the work for them...
In any case, people who wanted to learn were easy to deal with. The other two motivations could be used to coax the person to learn, but they required different approaches.
There is no stress, they just don’t want to “explore” things they see as non-urgent.. basically everything you need like writing, reading and calculating properly.
No amount of coaxing, gamification or whatever works consistently. The only thing that got my smartest kid through anything is by force. Not too much, but still, they need some amount of coercion no question about it. Anyone that denies this I find very, very hard to take seriously.
Interestingly the slightly less cerebral one is easier to guide through gamification. I guess the smarter you are the easier you see through BS. It’s easier to just learn to suck it up and Do The Thing instead of “learning is fun”. It isn’t and it doesn’t matter.
I've found that the people who are more optimistic about kids tend to live in a particular category of socioneconomic bubble.
The kids that study and apply themselves, I don't think it's so much that they can see they understand the benefits of linear algebra at the time, it's that their parents and the social network they're a part of sends them signals that this is what they should do to be successful and they're rewarded for doing well in school.
The other argument about teaching "advanced math" is the same as why Cristiano Ronaldo spends a significant part of his training in the gym lifting weights? Ever seen Ronaldo take out a barbell and start doing squats during a game? One should reflect on this.
In short, math is a powerhouse tool for carrying society forward.
Art, while cool to look at and experience, has a pretty low efficacy in terms of "motivating people to do work, or removing obstacles, to carry society forward"
In short, starving artists.
There is also the whole thing where art is an abstract concept with a subjective definition, and a solar cell sporting new tech with 33% efficiency objectively being better than one with 24% efficiency.
There were humans for tens of thousands of years before there was high technology. But there were hardly any humans around before there was art.
Idk, the soviets didn't invest in socialist realism propaganda for nothing.
Less sarcastically, art has had an outsized influence on society and culture. Take any social movement you want, and there was probably some novel or work of art that galvanized it.
10,000 artists in, one $20k work of art out.
Whereas something like the engineer is closer to
5 engineers in, $500k of work out (and even that is pretty conservative)
Also i'd point out the selection bias of not counting people who fail out of engineering school but still counting every unsuccessful artist.
As a first order approximation the "price" of art (as distinct from its value) is a function of branding not asthetics.
Secondly most artists get paid, not from doing fine art, but from adjacent careers that require good color, balance, composition, and so on. Industrial designers (think Jonny Ive), interior design, food presentation, magazine layout, web design, architecture and so on. Art skills are all around us. In the same way engineering is around us.
Put another way, engineers build ugly (think beige PC boxes). It took an artist to give us the iMac. And it was a marketing genius (yet another important skillset) to bring the artist and engineer together.
Teaching math goes far beyond creating mathematicians. Teaching art goes far beyond teaching artists. Societies that drop art because it is unproductive get ugliness permeating everywhere.
Applies to art, fashion, media.
Most practical (including engineering) successes are much less externally attractive but do make decent money for everybody involved.
Further, judging the value of art to society by how much it costs is ridiculous and an asinine comparison.
It grew out of a time where basic artistic skills were expensive to learn, and could be a real class differentiator (and had some employment benefits).
That's now a fair bit less true; but still continues to prevent these things becoming the sole domain of private schools.
Did do writing although a lot was extracurricular.
the number of adults i've met who cannot add two fractions together is depressing.
at some point each of them had decided "i'm just bad with numbers, hahaha" and they gave themselves permission to stop trying math. worse, society gives you a pass at not knowing math. we need to apply the same constant social pressure to mathematics skills that we do for learning to read.
An inability to understand compound interest is classic.
I think we're more talking about algebra or, really, anything "higher" in maths than arithmetic. Does a solid knowledge of, e,g, Set Theory, give any benefit later in life?
And also, if we think that basic financial management is a good thing for kids to learn, why don't we teach that?
If you bought 6 liters of soda for £3/2-liter bottle with 8% consumption tax, how much should it cost?
You have to shape that all into a series of operations for your calculator. The calculator can't do it by itself. Even basic arithmetic takes some education before the calculator can be useful.
I would disagree. How to minimize a function, how to calculate interest, first derrivative are all pretty useful in finance, and a bit beyond basic arithmatic.
> I think we're more talking about algebra
"Algebra" as a term covers a lot. Being able to solve for x is a very useful skill and often what people mean by algebra.
If you mean understanding groups, rings, fields, or whatever, then sure that is probably not very useful to the average person's day to day. However i dont think that is usually tought in high school.
> Does a solid knowledge of, e,g, Set Theory, give any benefit later in life?
Pretty sure nobody in high school is getting a solid understanding of set theory. That is more university level.
> And also, if we think that basic financial management is a good thing for kids to learn, why don't we teach that?
I guess it depends on where you live, but i had to take a class on that in high school.
These are college graduates.
> Does a solid knowledge of, e,g, Set Theory, give any benefit later in life?
Knowledge of statistics will help a person a lot.
Another example. I wanted to put an elliptical brick patio in my yard. The contractor gave a square footage and I signed a deal with the charge per square foot. He staked it out.
It looked a bit peculiar to me. So I measured the major and minor axes and computed the area of the ellipse. It was 1/3 smaller than the contracted amount. The pallet of bricks was sitting in the driveway. I multiplied xyz to get the square footage of the bricks, and walla, it matched the area staked out.
I.e. I was being cheated. The contractor evidently was used to math challenged customers, and discovered how much he could cheat before being noticed. I pointed out the "error" (hahahaha) and the contractor reduced the bill by a third.
> why don't we teach that?
Exactly!
I'll add that math isn't really just about that sort of practicality though. It's also about a fundamental understanding of numbers and what they mean.
For example, inflation is in the news a lot. It's high, or low. Most people (the US president included) think that if inflation was 0% prices would come down. But that'd be a profound misunderstanding of the topic.
A grounding in numbers, in this case percentages, makes for a better understanding.
Any business owner needs to know fundamental truths to survive. Cost price, markup, margin, selling price, fixed expenses versus variable expenses and so on. All are grounded in basic math. Without that you can't do basic accounting. Without that you can't effectively run a business.
Anti-vax arguments are built on very bad math, and people bad at math fall for it.
We all use math all the time. People bad at math are at a major disadvantage. Populations bad at math are easily manipulated.
Is there any benefit to being able to distinguish logical entailments from non sequiturs?
The things that are taught under the label "set theory" are taught elsewhere under the label "basic logic". The most primitive symbols are intentionally matched: in logic, "and" is ∧ and "or" is ∨, while in set theory, "and" is ⋂ and "or" is ⋃.
The symbols stop matching quite that well after that - compare logical ⟶ and ¬ to set-theoretic ⊆ and ᶜ - but they continue to consist of the same material.
Ha Ha Ha! Cute you think society cares about reading abilities!
I mean, OK, you are expected to be able to do basic level reading. But, say, reading something independently to learn something? Even when I was in university 20 years ago it was a struggle to get people to read.
Could you clarify what do you mean by 'kids' and 'advanced math' here?
I personally believe we should stop believing advanced math is meaningful for everyone. Especially stop trying to push them down to high school curriculum.
When I say advanced math I mean anything involved with "what exactly is a ___ (vector space, real number, group, set, etc)".
I know full well that languages are necessary and useful ... and were. I still found learning languages the most boring thing in the world. I liked abstract math despite thinking it is not necessary useful - I did not cared. I could go on, but relation between interesting and useful was never all that straight forward.
When I was just a bit younger, I detested what I'm about to say, but now know as the "reality".
Your argument is focused on rationalism. You're trying to give kids/teenagers real world reasons to learn something.
People are rarely motivated by reason. They are motivated by emotions.
If you look, you'll find plenty of examples of very "rational" adults (college professors included) who clearly know something to be true, will admit to it, but will still go the emotional route.
As a parent, I looked into the research on changing/shaping children's behavior. And the key things that stood out:
1. If you know enough adults who do equivalently bad things even while they know the harm in it, don't expect kids to behave based on reason.
2. Focus on (positive) emotions. Give kids incentives. They shouldn't clean up the table because it will keep the house clean. They should clean it up because they'll get a (short term) positive reward.
3. Focus on building the ritual as a habit, and separate it from any semblance of morality. The brain needs to get accustomed to the actual behavior. The rationale can be added (now or when older), but if you focus too much on rationale without the habit, you'll get someone like me, who realizes a lot of behaviors are good for me, but won't do them because "my brain isn't wired for it".
Getting back to kids learning algebra, or whatever: Their lack of incentive isn't because they can't connect to practical skills in life.[1] The reason they don't want to do it is because it is not a valued skill amongst their peers. And it's also not a valued skill in American society.
That's why high school kids in Eastern Europe or East Asia tend to know this a lot better. If you can't multiply two numbers on paper, you're an idiot. Everyone will know you're an idiot. As much an idiot as not being able to read properly. So you learn it because you know that it's just a baseline intelligence marker you should have by a certain age. You don't whine about it any more than you'd whine about how to properly eat food without spilling it. Sure, once they're older and reflect back, they may say "I never needed algebra", but it doesn't bother them. Knowing it is merely part of being cultured.[2]
Now being motivated by shame is really not a great way to get people to do something, and that's not what I'm encouraging. The point is that it's a broader societal problem. Why should they learn it if they see no one else values it?
I wrote more about this about a month ago: https://news.ycombinator.com/item?id=48065640
[1] Think about all the useless things kids can be good at. Did they have to rationalize why they should learn them?
[2] This is why California, in particular, had a strong push back regarding calculus not being taught in high schools. There's a strong and relatively wealthy Asian/immigrant community in those places, and they've tried to maintain the value of being decent at math. (All the stuff about impacting university education is fluff. I used to work at a university, and they had remedial programs for incoming students who didn't know algebra/pre-calculus. It adds to the time to graduate, but by and large is successful - it's OK if you go into engineering without being exposed to calculus).
'It's fun' is a pretty compelling reason for both kids and adults to learn certain things, but you can't just decide what's fun and what isn't. Maths rarely gets to have that reason (and when it does, it applies to people for whom this entire problem isn't relevant).
I taught at an English-immersion high school in Shanghai.
It's worth remarking that the boy at the top of the class in each grade was dating the girl at the top of the class.
I can believe it, but I don't know if it's true. Obviously not true in the US.
That's also why all the examples of math's usefulness become ridiculous stories like: "imagine yourself getting stuck on an uninhabited island and having to calculate the triple integral to find the volume of a barrel of water".
No. The real use of school-level math/physics/chemistry/language is in laying the _foundation_ and training the brain.
And it doesn't really matter what exactly you want to use for mental training. Every structured activity is fine, as long as it engages the brain.
Even pointless tasks like memorizing scriptures help. There are studies that show that religious students who spent a lot of time on rote memorization, and later switch to other disciplines, in the end do quite well with their studies.
A really small number of disruptive kids will destroy the learning of the entire middle. The top kids will figure it out at home and survive, or their parents will separate them through brute-force - a few borderline high achievers will probably be brought down too.
In the poorer neighborhoods around me the school performance is actually shameful and the kids are being subjected to the worst of their peers constantly, destroying their ability to succeed. Many will (hopefully) drop out/get arrested by late middle/early high school but the damage they do to their entire neighborhood along the way is massive.
Cohorting the highs and the well-behaved middle would probably work out just fine but unless you can eliminate the disruptive and the very-behind it's just the worst of all worlds.
Arithmetic, Algebra, and Statistics are different classes should be taught separately.
"Please wake up and take your headphones off and answer my question even though you don't plan on passing any of your classes" and History are different classes with different types of students. Trying to conduct both classes at the same time using the same teacher is folly. You will be forced to abandon one or both of the students. You might argue that you should abandon them it turns every other day so they both get something out of the class. But that means they will each get half or less out of the class than they would have if you separated the classes. It is highly likely that you will frustrate both students to the point of impediment.
It shouldn't be. The research overwhelming says its a good practice. The type of people who say this type of thing are the exact type of ideologically motivated people who are destroying school systems in blue districts. Ironically this group both hates private schools and creates the environment that pushes parents to pay for private schools. I've personally seen the bad consequences of schools that do this and I know people who aren't here anymore because of it. So please, for the love of god, stop talking about topics you know nothing about.
The upshot for this is that the benefit is as much for the student doing the teaching as the one doing the learning. Teaching has a much greater effect on _retention_ than listening reading or even doing, which is the majority determinant underlying the primary school curriculum.
There are a whole host of secondary benefits to this (as well as lots of logistical challenges): the students are doing something useful, teaching, and we pay teachers if you wanted to expend budget there I suspect it would have great effect, as would any other form of ~~bribery~~, I mean, incentivisation; socialising, especially if you have the teaching being done across different classes (which you would want to do because you want the teacher to know more than the student).
Projectors, videos, computers, tablets, calculators, are all completely useless in teaching math.
I have a great deal of respect for you. Your math skills are much greater than my own. But you have stretched your statement too far. Flash cards can be very helpful in teaching math. Timed tests for math facts can be very helpful. Both of these can be facilitated with computers or tablets. Animations can be a very useful instructional tool. Even taking a picture of the chalk on the blackboard and putting it online can help students (and possibly helpful parents) review the in-class lecture from home while they do their homework.
I don't dismiss your overall point, but don't be too flippant. A video of the lecture can be very helpful.
What works:
1. having a lecture on a chalkboard
2. taking notes by hand. Yes, by hand. Something about the act of writing it by hand fixes it in my brain
3. using pencil and paper to do the problems.
4. and what really works is giving an in-person lecture on how to do it
What doesn't work:
1. everything else
I've watched many instructional videos. Poof, none of it sticks. I've audited classes. Poof, none of it sticks, because I didn't do the homework.
I've never known anyone who learned arithmetic from a calculator.
It's like wanting to be strong. You have to do the work to get strong. There is no substitute.
There are visual learners out there. Being a visual learner doesn't mean you don't need to do the work, it means you typically need some visualization for things to click, and then you practice applying it like everyone else. Some people can even manage with just lectures.
This causes some students trouble in school because their needs may not be met by every teacher. It's especially worse if the student hasn't learned what their learning style is yet.
Learning Styles: VAK Doesn't Exist (Here's What Research Actually Shows)
https://www.structural-learning.com/post/learning-styles-myt...
Belief in Learning Styles Myth May Be Detrimental (by American Psychological Association)
https://www.apa.org/news/press/releases/2019/05/learning-sty...
I have difficulty believing that my learning style is uncommon. Consider trying to build muscle. There are techniques that are proven to work best. There are no individual "muscle building styles" that work better, unless the person has a disability.
And I don't believe that in general the kids in classes are mentally disabled.
Yes, I know about ADHD, autism, and dyslexia.
I think it's more of a motivation problem. Not all students are eager to learn. They may not be interested in the subject for whatever reason. It's hard to teach someone who isn't open to it. Learning styles can help bring some of those barriers down by shifting the material into a form that they are more open to.
The same applies to building muscle. Not everyone is self-motivated to do it. There are different ways to motivate people to work out. But in the end they all need to do the work/practice.
You have to do the exercises. But it might be beyond your ability to start doing them straight from the textbook. Crafted didactic material can walk you through initial exercises to the point where you have a theory of where to begin on another one. Or it can let you investigate a structure until you have an idea.
In your analogy, if you want to be able to bench 150 pounds, at some point you'll have to bench 150 pounds. But a nonconfigurable 150 pound weight isn't the best way to get there. You can have a set of weights that let you start with easier tasks. You can have a set of exercises that aren't bench pressing. Those things are helpful, and generally required.
The real problem beyond all this is that the educational spending goes to the wrong spots. If you ask me, teachers should be empowered to select their own curriculum using a budget and most of the rest of the money should go towards paid tutors, better teacher-student ratios, etc (and probably way fewer administrators). I am firmly convinced that a lot of kids act out because they can’t grasp the material, not in spite of it.
In the USA there are approximately 50 million students aged 5-18. If you paid for each student to get 1:1 attention one day a week, you would need one teacher per five students in schools that meet five days a week. Let's use that number because it reduces 50 million students nicely to 10 million teachers. Let's pay each teacher $70K/year. That would cost $700 billion per year.
The USA military spent $100 billion per year in Afghanistan.
If the USA provided the 1:1 attention only in 1st Grade and 3rd Grade, they could fund it with the same commitment they made in Afghanistan with a lot fewer deaths. The USA persisted in Afghanistan for 20 years. Shall we experiment with education for 10 years and see if we get a better result than we did in Afghanistan?
That 100 billion goes to a bunch of extremely well-connected businesses who fund lobbyists to make sure the USA continues expending munitions in a series of utterly pointless, futile, wars.
Let's say that you have some curriculum C that you think is vital for children to learn, and you want as many children as possible to learn C.
Even ignoring ethics, it's not obvious to me that attempting to coerce all children into learning C is the best way to accomplish your goal!
Why is it obvious that an educator should do their best to teach a student something even when they don't want to learn? Well for one, it's their job, and two... Children especially are not good judges of which knowledge and skills will benefit them later in life.
This. If children knew what was best for them, they wouldn't need teachers or parents.
When I was in college, the courses were laid out for particular majors. Electives were few. I trusted the college that they knew what they were doing in deciding the curricula, because I sure didn't.
This is very context dependent. If you grow up surrounded by a typical western/industrial/post-industrial diet, then yes, it almost certainly does.
But you could also change the food environment.
Hopefully the analogy/metaphor that connects this to schooling is reasonably obvious.
You go do that then. Enjoy your slow death from malaria.
The food choices having nothing to do with the jungle, but rather: regular, significant consumption of highly processed and most significantly sweetened foods. There were plenty of people in the world before the widespread adoption of sugar as cooking ingredient whose dental health would likely not have been improved by brushing, and they didn't live in "the jungle" but places like ... America, and Japan, and India and ... basically the entire planet.
And you need to do that. It trains your brain. If you simply rely on calculators, LLMs, and Google Search, then you likely can forget about doing advanced science.
It doesn't mean that you have to _master_ everything. Far from it. But you need to apply real effort to various subjects to train yourself.
I've been giving chemistry lessons since I was a teenager, and quite early this became my first order of business after that alone was responsible for turning a D student into a B student in one session.
For that first non-mathematically inclined student who was having so much trouble, this had to be accomplished before any of the specific concepts and problems could be properly addressed in the course they were enrolled in.
All that was accomplished in two hours was gradual but progressive reversal of attitude, not unlike what I was accustomed to in ramping up to more advanced subject matter, but we never got around to that during the first session.
The next week they had a very positive attitude and were going to call me later with some challenging equations for some help.
Wasn't necessary, the very next week they got a B on their own initiative, were so excited and passed everything after that with no further problems. It was probably the most thankful student I ever tutored.
And if good habits are not instilled, they will have a difficult life ahead of them. It's far easier to learn those habits when young, than to try to independently course correct as an adult.
Not coercing a child towards correct behaviours, is doing them a great disservice. In some circumstances, it's child abuse to not coerce those bahaviours.
There's a huge difference between a loving parent gently but firmly teaching their kid to clean their teeth every day even though they don't want to, and a brutal schoolteacher beating facts into a class full of miserable kids.
There is in fact little difference between "you have to learn these things" and "brushing your teeth".
Thus to be ethical in your society, usually means you must follow the rules determined by a collective group of your nations ancestors or you will be shunned/jailed/harmed/etc. Which is essentially coercion. "Act this way or be punished."
White collar crime might be illegal but most societies would definitely punish a murderer either legally or illegaly. Social stigma is a MUCH more serious thing than legality of action.