10 ms·

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 thin

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".

yostrovs 8y ago
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 8y ago
  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.
- mcguire 8y ago
  Do you have any evidence for your conspiracy theory? If not, it's not helpful for the discussion.
- ams6110 8y ago
  Raising kids to think about things on the basis of opinion and emotion makes it easier to get their votes when they are adults.
Nursie 8y ago
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 8y ago
  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.
  - chrisseaton 8y ago
    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 8y ago
      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 8y ago
FakeComments 8y ago
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 8y ago
  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 8y ago
    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 8y ago
  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.
tjpnz 8y ago
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 8y ago
  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 8y ago
    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 8y ago
  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!
ams6110 8y ago
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 8y ago
  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 8y ago
    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 8y ago
    How many times did you make a mistake on those questions and learn a new pitfall regardless of whether you new the equation?
    - Izkata 8y ago
      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.
war1025 8y ago
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 8y ago
  > 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 8y ago
  > Old rules don't apply at all How did that happen?
  - war1025 8y ago
    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.
jon_dahl 8y ago
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.
- WillPostForFood 8y ago
  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 8y ago
    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 8y ago
      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.
ThrustVectoring 8y ago
>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.
AngryData 8y ago
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.
mjevans 8y ago
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 8y ago
  Sounds kind of like the Interactive Math Program that was (is?) used at some US high schools : https://www.mathimp.org/ https://www.mathimp.org/

yostrovs 8y ago

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 8y ago
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.
mcguire 8y ago
Do you have any evidence for your conspiracy theory? If not, it's not helpful for the discussion.
ams6110 8y ago
Raising kids to think about things on the basis of opinion and emotion makes it easier to get their votes when they are adults.

Nursie 8y ago

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 8y ago
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.
- chrisseaton 8y ago
  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 8y ago
    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 8y ago

FakeComments 8y ago

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 8y ago
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 8y ago
  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 8y ago
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.

tjpnz 8y ago

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 8y ago
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 8y ago
  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 8y ago
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!

ams6110 8y ago

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 8y ago
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 8y ago
  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 8y ago
  How many times did you make a mistake on those questions and learn a new pitfall regardless of whether you new the equation?
  - Izkata 8y ago
    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.

war1025 8y ago

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 8y ago
> 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 8y ago
> Old rules don't apply at all How did that happen?
- war1025 8y ago
  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.

jon_dahl 8y ago

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.

WillPostForFood 8y ago
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 8y ago
  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 8y ago
    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.

ThrustVectoring 8y ago

>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.

AngryData 8y ago

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.

mjevans 8y ago

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 8y ago
Sounds kind of like the Interactive Math Program that was (is?) used at some US high schools : https://www.mathimp.org/ https://www.mathimp.org/