[if_by_whisky]

Something feels off about this whole debate. I took algebra in 7th grade, so I naturally lean towards the "push it earlier, not later" camp. But the more I think about it, the more I'm convinced that the way we group mathematical concepts together in grade school is fundamentally boring for students. It seems like nit-picking to fall hard on one side of this "8th vs 9th" dichotomy when I actually suspect the whole math cirriculum could use a revamp from the ground up. Maybe we should consider basic discrete math in elementary school. Maybe basic calc in 6th grade. How can we get substantive, critical thinking skills earlier into the curriculum so we don't have to just assure students: "trust us, math will get interesting if you can just stick with it through calculus and linear algebra".

[ams6110]

I agree. I hated math up until 8th grade. My 7th grade math teacher suggested I take algebra, which was the "advanced" option for 8th grade math. I have no idea why, because my math grades were very average, but he must have seen something or had a hunch.

It was like a light bulb went on. Math went from being rote drudgery to something that I could see had some useful purpose. I enjoyed math from that point on.

[bluedino]

I enjoyed math. I loved it.

What I hated was doing 50 homework problems for every type of whatever it was we were learning that day. Even if the answers to have odd-numbered ones were in the back of the book.

Once an equation or soomething 'clicked', I got it. There was no point of doing 50 of them, each slightly different than the last.

[darkwizard42]

I'd argue that you are in the minority here. Most people (especially children) require repetition and depth of work to master a skill / understand a strategy.

In my experience (having watched a LOT of my friends go through varying degrees of good/bad public schools in NJ) most kids really do need the repetition. Without it they don't hammer in why something like adding 2x to each side of an equation cancels out -2x on one side, even if the last problem had you balancing an equation by adding 4x+5 to each side. These concepts might seem absolutely trivial to us now, but as a person first approaching them I think they can be pretty complex.

[peteradio]

How many times did you make a mistake on those questions and learn a new pitfall regardless of whether you new the equation?

[Izkata]

As someone else who was in the same situation: In a way that additional problems would help, almost never. All my mistakes at that point were the equivalent of typos, things like dropping a sign from one line to the next.

[dr_dshiv]

In my school, the more advanced math classes had less homework. Calculus had none. Talk about incentives to succeed!!

[jon_dahl]

Yes - this discussion is kind of ridiculous. If San Francisco had announced that they were removing elective CS from the High School curriculum, Hacker News would be saying "How can anyone expect to succeed in a STEM world without High School CS?"

I was one of the advanced math kids and took calculus in 11th grade. Then I went on to Calc 2 in college, and it was a different league entirely. I would have been better off building a stronger foundation throughout High School and then doing Calc 1 in college.

...which is exactly what the new curriculum aims to do. I have a 6th grade daughter in SF, and the strength of the new curriculum is that they spend a lot more time making math more intuitive. Instead of learning one approach to long division, they learn multiple approaches. In theory at least, this pays off in the long run for a lot of kids.

What American schools need isn't more acceleration (Algebra at age 14 instead of 15) - it's a better understanding of what mathematics actually is and why it matters.

[alistairSH]

What American schools need isn't more acceleration (Algebra at age 14 instead of 15) - it's a better understanding of what mathematics actually is and why it matters.

While I agree with this sentiment, my problem is with the one-size-fits-all approach taken in San Fran. Lumping gifted children in a class with everybody else does them a huge disservice...

My personal experience in 7th grade (pre-algebra) was horrible. My school decided to experiment by placing gifted students in math with the rest of the kids, with the idea being that we'd magically bring up the average performance. Instead what happened was the nerds sat in the back bored out of our minds and lost a year of math education (and this was with an extra teaching aide in the class - the two teachers simply couldn't keep the non-gifted kids on track AND provide us any extra attention). This left us all behind when we entered Algebra in 8th grade.

I hate to be "that parent" - but gifted kids have different needs than normal students and deserve the opportunity to excel without waiting around for everybody else to figure out 2+2.

Edit - I don't care if the advanced math offering in 8th grade is called Algebra or something else, as long as there is an advanced offering. The linked article made it sound like there was not such a class.

[jelliclesfarm]

I think a solution could be to have classes based on age groups..giving kids 5 years to finish 5 years worth of curriculum so they can finish at their own pace and then grade them at the end of the five year term.

This way, if something is easy or interesting...or tough or boring, kids can choose how they want to tackle it. Having many different ages in the same class without the pressure to finish everything crammed within one year should help. Here is where maybe bright kids can teach kids that need help..or older kids can help younger ones.

Example: ages 5-10 study together in huge single room schoolhouses ..each one on whatever they want to learn. Ages 11-15 is another group etc. amongst them, they can be in sub groups according to interest or ability. A class can have 4-5 teachers who can tackle all of the subjects. Volunteer parents.

Test and grade them at the end of five years. Only test them every year or semester.

[magic_beans]

This sounds like a social nightmare. The needs and behaviors of a 5 year-old vs a 10 y/o and an 11 y/o vs a 15 y/o are astronomically different.

[jelliclesfarm]

They should eventually be able to form groups...and work as peers. Is there really a difference between a 12y/o and a 13y/o...as adults, we don’t always consort with those born within the same solar year. Why wouldn’t it work for kids?

[bzbarsky]

> Is there really a difference between a 12y/o and a 13y/o

There can be huge differences in social development there, and not even strictly tied to age. The variance is rather large.

But even if you just look at averages, as far as I can tell the average 13 y/o girl and the average 12 y/o boy are quite far apart in terms of their social interactions, starting with basics like "are you thinking about dating yet?"

All that said, getting 12- and 13- year olds to work as peers is a much simpler problem than the originally posed one of getting 5- and 10- year olds to work as peers. In _that_ context there are a bunch of problems, ranging from difference in attention spans to the basic issue that most 5-year-olds don't know how to read yet, and most 10-year-olds do, and so conveying information to both together in a way that's not frustrating to one or the other can be quite difficulty.

Now if we want to group students by ability (5-year-old who can read, great, let them work with that 8-year-old if they have an interest in common) instead of age, that might work much better than any sort of age-based grouping. Of course that can exacerbate the social aspects, but there are in fact ways of making this work well. Having the older student partially teach the younger one, for example, is a good way for the older student to significantly improver their own understanding of the material.

[em-bee]

5 year age difference may be a bit much but beyond that, montessori is doing exactly that. they group children in ranges of 3 years: 0-3,3-6,6-9,9-12,12-15,15-18

[em-bee]

we can probably argue about the exact age ranges (maybe follow the schools age-ranges: preschool/kindergarten, primary school, middle school, high school all sound like good age groupings).

but the concept is good. younger kids can learn from older ones. older kids internalize the material by helping younger ones.

and it turns out that this model is already proven too: it's applied in montessori, and it's practiced in scouting as well.

[WillPostForFood]

America doesn't need more acceleration, but nor does it need more deceleration, which is what this policy does. What they got rid of was: some kids are ready for Algebra in 8th grade, and they can take it. New policy is: everyone takes the same class, regardless of skill or preparation.

[linuxftw]

Everyone gets the same 'x' regardless of individual circumstances. Easy policy to prescribe if one holds certain political beliefs.

Unintended consequences: Wealthy and middle class kids will still have access to the same quality of education as they did before, those that rely solely on public education will have access to lower quality.

Inevitably, students from CA will be less prepared for college entrance exams. CA will have to institute a 'statewide college entrance examination' and, maybe they'll pass a law prohibiting using any other entrance exam in an admission process (because they're racist or something or other).

[WillPostForFood]

100% agree - the real intent here is to reduce the achievement gap, and the real effect is to increase it. High achieving wealthy parents make sure their kids get math outside of school. The kids who lose are the smart, poorer kids who would have thrived and advanced given the challenge.

[User23]

Plenty of extremely poor Chinese immigrants scrimp and save every penny to pay for top notch tutoring for their children. This isn't really about wealth, it's about culture and ability.

[WillPostForFood]

I half agree. Chinese immigrants strongly value education, and on average, have more inherent ability. So many overcome the disadvantage of being poor. That doesn't mean that the average poor kid isn't at a disadvantage, and that the smart poor kid is hurt by removing advanced math courses. That smart poor kid may not be getting the support at home like a Chinese immigrant, so support at school is all they are going to get.

[linuxftw]

Why not send them to private school then? Or is top-notch tutoring only available outside of a traditional school? In which case, why have a traditional school model at all?

[tlear]

It is not only that, if you parent is a successful engineer, businessman or whatever. Not only they will hire tutors if needed they can often teach kids themselves.

I learned more math from my dad who has PhD in physics then from all of my teachers and tutors combined.

One of the reason home schooling works so well. It is much easier to teach few kids you care about then whole classroom of the ones you don’t.

[PebblesRox]

From the school district’s page justifying the new course sequence:

“Historically, rigor meant doing higher grade-level material at earlier grades, and equity meant providing all students equal access. The CCSS-M require a shift to seeing rigor as depth of understanding and the ability to communicate this understanding, and to seeing equity as providing all students equal success.”

If the goal is equal success for everyone, you have to hold back the high-achievers so the rest of the group can keep up.

http://www.sfusdmath.org/secondary-course-sequence.html

[tropo]

The problem is hinted at here: "equity meant providing all students equal access"

What they are saying is that they refused to keep unqualified students out of the advanced classes. Keeping those students out would have exposed the schools to all sorts of accusations of discrimination, so they didn't do it. Parents insist that low-performing students be in the advanced classes, and the school doesn't say "no", so the class becomes a mess of failure.

[FakeComments]

When you try to understand math education, remember that it’s basically what would happen if foreign language classes were designed and taught by people who only spoke English and had no training in formal language theory.

Of course it’s largely a disaster: it’s taught by people who brag about hating the subject!

Algebra education can (and does) safely begin in first grade, with the introduction of workbooks: “4 + [ ] = 7” is a common exercise, and involves the implicit solving of a basic linear equation, where you solve for the value which goes in the box.

That you can teach algebra to first graders, but math education is so abysmal, only speaks to the complete disregard mathematics is given in education.

But what else would you expect when you leave it up to people who hate math?

[tpurves]

Can confirm! Have a first grader and she actually found learning basic adding/subtraction, and now multiplication more fun by learning it through games played with implicit basic algebra. “I am thinking of a mysetry number, can you guess it? X marks the soot where the number goes... I’ll give you a clue 2 plus x equals 4. Or 9 times x equals 18.” Etc. She’ll laugh and play this game all day, and make up algebra puzzles for us too. Great way to learn her basic math and implicitly algebra too through play rather than by rote, or the plodding pace of the grade school system.

[philwelch]

Heh, this reminds me of a fond story. My eighth grade algebra teacher (who did seem to genuinely love math) once said that mathematics was a game invented by man. I didn’t appreciate this at the time but I wish this was the mentality.

IMO the US math curriculum now is designed to train kids to become pre-PC-era clerks (who only need basic, manual arithmetic) rather than engineers.

[ams6110]

I remember that, and hated it. Why? Because I had real trouble memorizing sums and products. I still have to stop and think to do simple sums in my head. I sometimes still count on my fingers when I add two numbers. And these types of problems were taught as memorization. Four plus what equals seven? You either knew it or you didn't.

If they had taught us how to solve these problems, I think I would have enjoyed it more. "You can take away the four from both sides, and there's the answer" somehow that would have been easier for me to work with.

[mntmoss]

I was frustrated in this way during my math education, but lately my opinion about memorization has softened a bit.

The trick is that it has to be approached in the same way as in sports: Demonstrate a technique, explain the principles, attempt in live play, then return to drill muscle memory(now that the student has discovered how bad they are at it). Music is very similar - you can play a song badly, then drill scales and arpeggios a while, come back and suddenly you play the song better.

The point of memorizing is, in the end, to make the knowledge closer and more available to you. But there are several ways in which this cycle drops the ball during education and succumbs to rote learning as the sole factor:

* The teacher themselves doesn't understand the principle, and thus is poor both at explaining concepts and grading results. "You get a zero," they will shrug, when the student has misunderstood something and turns in a problem set with wrong answers.

* The principle isn't connected to "live play", making the technique unrelated to existing knowledge. It's the way in which education systemically fails most frequently, and it starts with having classes specialized per subject and limiting the crossover between them. All too often, all that happens is that you do some problem sets, get tested a little later, and that's it - and so all your focus as a student is on passing, not on learning.

* The drill focuses overly much on tricks and "gotchas" and not on developing confidence and long-term retention, making the student uncertain about how to generalize the technique to the tricks. In comparison, when I took judo, we drilled all techniques on one side only, for the entire semester. Is it useful to be able to mirror the techniques? Yes, but that doesn't mean that any study time needs to be allocated to it.

[heavenlyblue]

Yeah, the sum issue seems like a concoction of taking the difference of sets and then taking their lengths.

Explaining sets (buckets of fruit) and then explaining their difference could work better.

[lenticular]

This was true for me. I absolutely hated math in middle and high school. I never studied for it and got mediocre grades. I had a few teachers who really had no enthusiasm or drive to make it interesting. Fortunately, I started taking some community college classes my last couple of years, where I really fell in love with linear algebra. I wound up being a math major in undergrad and a geophysics PhD.

[yostrovs]

This development is part of a ground up movement that aims to change education from an activity in which learning is done to an activity in which the correct opinions are formed. Math, not being an opinion-based matter, gets dumbed down so that other topics can be put forth to the students.

[danbard]

It’s the kill zone competitive strategy applied to education (competitors to your children) instead of big tech. Make sure nothing can develop that threatens your family’s market position.

[ams6110]

Raising kids to think about things on the basis of opinion and emotion makes it easier to get their votes when they are adults.

[mcguire]

Do you have any evidence for your conspiracy theory?

If not, it's not helpful for the discussion.

[tjpnz]

I was bored out of my mind at that point so tuned out. 7 years later I was struggling through the math portions of my CS degree and now with 10 years in the workforce I'm genuinely frustrated about not being allowed to do the shiny stuff (namely ML). The NZ school system at the time basically fucked me when it comes to basic mathematics and now in my early 30s I'm trying to fix this using Khan Academy. It's not easy and I know I'm going to struggle a lot more being significantly older. Maybe things have changed in the intervening years but I still hold genuine scorn towards whoever designed that math curriculum. This stuff is actually important.

[sethammons]

It doesn't need to be harder because you are older. Many young minds lack developed abstract thinking. I recall hearing that many don't develop this until their mid twenties. My first pass in 9th grade of geometry and 11th grade trigonometry were rough. I later self-studied and found the material to be crazy approachable. If you are still struggling, I advise going further back in your studying or getting a good tutor who will help fill holes in your knowledge.

[wDcBKgt66V8WDs]

Anecdata but I definitely developed better abstract thinking at the end of and even after college.

I've always thought I got more patient or maybe the research phase of debugging and programming required me to get better. Maybe I just got older.

[leesec]

IMO do top down ML stuff and learn the math as-needed. This is recommended by Rachel Thomas and Jeremey Howard of fast.ai as well. There are a lot of great resources for the specific kinds of math you'd need for ML. I personally am self-proclaimed terrible at math ( also had very been schooling ) and was able to ML with not much extra work after their courses. Good luck!

[ThrustVectoring]

>How can we get substantive, critical thinking skills earlier into the curriculum so we don't have to just assure students: "trust us, math will get interesting if you can just stick with it through calculus and linear algebra".

Don't teach math to elementary school students. Seriously. The current system mostly just teaches children to hate mathematics. Talk to some random adults if you doubt me - if you like math, you're in a large minority.

There's a good chunk of math that is nearly impossible to grasp until you've developed sufficiently abstract thought, at which point they're pretty obvious. I remember reading something like "sixth graders who enter with zero prior math exposure are merely a year behind fully educated peers at the end of the year". People are extremely good at picking up the mathematical concepts they need that are within their conceptual grasp. Hell, I know someone who wasn't exposed to algebra until they were taking calculus courses for their mechanical engineering major - they had to put in a ton of work and get help from their greek peers, but they passed their courses.

[Nursie]

I learned basic discrete maths - simple set theory, the notation around it, simple manipulations, at the age of around 10 or 11. IIRC.

This is in the UK, at a private school. Worked for me!

[aphextron]

The American math curriculum is embarassing to even explain to most europeans. An “advanced” high school senior in the US might be taking Calculus 1. Most students graduate barely able to explain what a linear function or a quadratic equation is.

[barry-cotter]

What American math curriculum? Every American state has its own curriculum and every school district has very broad autonomy, right? I’m no expert but most states don’t even have state exams at the end of high school that are exactly comparable. There are many states that have more internal variety in their education system than most European nations.

The closest the US comes to having a national curriculum is the College Board Exams.

[panzagl]

This has changed with Common Core and the pushing of standardized testing to the lower levels (elementary and middle school), though high schools still tend to have more variation.

[dboreham]

I grew up in a European education system (Scotland) and subsequently emigrated to the US. I have two kids in the school here. Although your sentiment was my initial expectation too, it wasn't borne out by some time I spent studying the two curricula (present-day Scotland vs the classes my kids have). What I found was that they pretty much matched up age for age.

[mruts]

I was taking ap calculus bc in 9th grade (calculus I). There were 2 other students in 9th grade with me. 6 were in 10th grade, many were juniors or seniors.

I left high school soon after 10th grade started so I don’t know what track I would have been on. But there are tons of overachievers taking on as much advanced stuff as possible in high school. So I think it’s a little unfair to say an advantages student only might be taking calculus I as a senior, because my personal experience and observations don’t suggest that.

On the other hand, what you are saying might have been true a long time ago. My wife’s father is a professional economist and he only took Calculus in college and he’s pretty smart. So I think education has improved in the US in that time.

[spamizbad]

American schooling is centered around standardized testing, and you can get a perfect score on the SAT Math without knowing the quadratic equation, so of course it's just a footnote in Algebra education.

The other problem with Calculus in American schooling is the number of students who took and aced their AP Calculus classes only to completely flunk their college-level multivariable calculus. I remember it always being recommended that, even if you took AP calc in high school, you should re-take calculus in highschool if you were going into Physics, Engineering, or Computer Science. Is that still the case

[chrisseaton]

Americans seem to make a really massive deal out of calculus. I wonder if that's counter-productive and puts people off.

You give it a special name, you talk about other topics purely in relation to calculus ('pre-calculus') as if calculus is the central big thing, and people talk about dreading it at college.

In the UK we never used the term 'calculus' when we learned it at school - we were just introduced to differentiation one day without any fanfare as part of an ongoing maths course, and then integration later. You didn't get a chance to get apprehensive about it and build up a mental block because you didn't know it was coming and it was no big deal.

[alexhutcheson]

FWIW, prior exposure to calculus is really helpful for tackling introductory undergrad engineering classes. If you can't do derivatives and some basic integrations without thinking, then you will really struggle in the subject-specific engineering classes (e.g. Circuits, Statics, etc.) that you start to take in your 2nd year. Not sure if pre-college calculus experience is as helpful for other fields, though.

[PeterisP]

Our high school physics teacher pushed for alignment of math schedule with physics lessons, as basic mechanics is much more intuitive with the understanding of derivatives, and derivatives get a clear illustration (of the principles, and also of the reasons why one might care about derivatives) in these physics lessons, so it makes sense to teach these topics hand-in-hand.

[heavenlyblue]

They explained derivatives to us on the first year of UK university CS degree.

Eastern european curriculum does that on the 10th or 11th year high school.

[bigger_cheese]

Yes this was my experience in Australia as well we did not have separate "Algebra", "Geometry", "Calculus" etc classes it was all just 'Mathematics'.

From memory I think concepts from Calculus were first introduced in year 10/11 via geometry (plotting curves and finding points of inflection) from there derivatives just made a lot of sense - slopes as a rate of change and all that.

[Nursie]

OK so I started calculus at 15, IIRC, but I was in the advanced class at the young end for my year. Most people who are going to do it start it at 16-17, if doing maths at A-level.

Everyone else drops maths at 16, never having encountered calculus.

[chrisseaton]

But your college courses seems to be so high quality. How does a student in the US go from what sounds like quite a limited education in maths at high-school to doing so well in maths at college? What connects the two up?

[barry-cotter]

Individual school districts and occasionally schools have enormous autonomy compared to the norm in Europe. So two schools in the same state can each have a class called Algebra II, with literally zero overlap in the material covered. Yesterday I read about a high school math teacher who decided to teach partial differential equations, normally, I believe what Americans call Calculus II in university, as an elective. There are good schools, but the system is very far from uniform. Partly this is because it wasn’t designed from the ground up to teach nationalism with education fit in around that goal. Puritan New England was the first society with mass literacy. Schools were locally funded, run and organised and that organisation of local rather than state administration persists, possibly in every state, certainly in most. Education came before nationalism so there was never a state system designed from the top down to turn everyone into Americans, nationwide, though many reformers gave it a good try.

[tropo]

No, partial differential equations would be the fourth semester.

Calculus I is differentiation. Calculus II is integration. Calculus III is vector calculus, with stuff like curvature in 3 dimensions. Differential Equations would be the next class.

The AP test covers differentiation and, optionally, integration. It's the first semester or two. This is what a good high school student will do unless the school itself is really bad or really small.

[rmah]

I remember Calc I (1st semester) being limits, differentiation and integration. And Clac II (2nd semester) being partial differential equations. This was in the engineering school though... it may have been different for other schools in the university.

This is the original poster's point. There is no consistency. Even in university. Some schools use quarters, some semesters, some trimesters. Some have letter grades, some percentages. Some are pass/fail freshman year, but are graded in subsequent years (e.g. MIT). What makes up "Calc I" at university varies tremendously.

[scott00]

One thing to keep in mind is that although there are a lot of elementary and high schools that do a bad job teaching math in the US, there's also a lot that do a good job. Kids that struggle in math in high school and/or come from high schools with poor programs mostly don't even try doing it in college. One other observation I've made is that people who do poorly in what I would think of as engineering math (calc 1-3, linear algebra, differential equations, probability and statistics, CS theory classes) often have more trouble doing the algebra error free than doing the "complicated" parts of problems. It's possible spending more time on algebra is actually beneficial to doing well in college level math.

[maxlybbert]

My high school math teacher had spent years teaching remedial math at a university level. We thought she was being a curmudgeon when she complained that universities even offered remedial classes.

Nowadays, I think she was right: university students should be ready for university-level work. Many people aren’t at that level the moment they graduate high school. The US really doesn’t have a place for those people, aside from remedial classes.

But, anyhow, for many people, there’s an intermediate step that doesn’t get talked about.

[nradov]

The US has a place for those students: community college. Universities shouldn't waste resources on remedial courses.

[cat199]

for the US student:

they went to private schools or, alternatively, they went to the wealthier public schools which teach these sort of courses, although usually on a 'tracking' system which segregates the 'smart' from the 'not so smart' at around 12/13.

for the US university (at least the more elite ones):

the above, in combination of the fact that a big chunk of the of the students are international students.

[xvector]

Selection bias - self-motivated kids, or kids with good teachers, will take some of the amazing STEM courses our colleges have to offer.

The rest don't even bother, if they go to college at all.

[scott_s]

An advanced high school senior in the US will take Calculus 1. An advanced high school senior in the US might take Calculus 2. (Yes, I am intentionally implying that taking calculus is what defines a student as advanced.)

[ams6110]

My high school don't go beyond Calculus 1 (edit to add: this was two semesters and covered differentiation and integration).

That was years ago (pre-internet) and if a student wanted to take other college-level math they were released to take it at the local university campus. Today, I guess online classes are an option.

[lordnacho]

What's the difference between 1 and 2?

[ls612]

Calc 1 (Calc AB) is basic derivatives and integration without too many frills. Calc 2 (Calc BC) adds advanced integration (by parts, partial fractions, etc), L’Hopital’s rule and indeterminate forms, coordinate transforms, and basic Taylor Series.

[agent008t]

But the US seems to consistently do well in maths olympiads?

[lordnacho]

There's 300M people there, you're bound to find 6 who are pretty good at it. And there's definitely resources somewhere to teach them stuff, it's the richest big country in the world.

The question is more how does the system work for average kids.

[FakeComments]

The US has extreme outliers, but it’s mean and median are below other nations.

[mruts]

Maybe you can’t have both? I don’t know, but that sounds possible?

An example is putting stupid kids with smart kids in the same class. The stupid kids probably benefit but the smart kids are probably hurt.

[FakeComments]

The US not only separates smart kids into different classes, eg AP and IB programs and early admission to community colleges, they separate the elites into whole other schools, eg private boarding schools, magnet schools, and technical schools.

This is ignoring the huge baseline variance in quality, due to funding and cultural variations.

[ams6110]

Yes, I recall that very basic sets topics (e.g. unions and intersections),might have been introduced in 3rd or 4th grade? Definitely was in there somewhere before middle school.

[mjevans]

The entire concept of grades is what's broken; as well as isolating and refining everything to the point that it looses meaning and ties to anything useful in the real world.

It would be better if there were projects that everyone were mentored on. Projects that had sub-assignments related to doctrines of focus and mentors (teachers) ready to help and to upgrade to high levels of detail and quality.

Even more ideally the work would be anything that currently qualifies as a government or civil need (double checking work by full time employees), re-enacting historical work with period engineering constraints (sort of steam-punk-ish) to teach live history, or otherwise maintaining the commons. (Infrastructure projects in software, analysis of actual civil infrastructure, conducting studies and tabulating results; with the interesting ones actually checked in more depth.)

[bgorman]

Sounds kind of like the Interactive Math Program that was (is?) used at some US high schools : https://www.mathimp.org/

[AngryData]

At my school they started introducing algebra in 5th grade with legit algebra classes in 6th grade. I think that is a good time to start, although at least half the kids could have started a year earlier even.

[war1025]

Calculus was an absolute mind-fuck for my algebra centered mind when I got to college. Took me probably two full months before it clicked and I basically settled on "this is still math, but it's completely different rules and the old rules don't apply at all."

[lordnacho]

> Took me probably two full months before it clicked

That doesn't actually sound like very long. I can easily image it taking more than two months to learn a new programming language, or how to build your own radio. Pretty much any nerd activity will take some time to get into.

[EnFinlay]

> Old rules don't apply at all

How did that happen?

[war1025]

I meant it as "Don't try to apply Algebra rules to Calculus." Doing so was a major hangup that took me a while to get past.