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Well that's stupid. If anything they should introduce it sooner. There's tons of research that show the sooner it's introduced the better they are able to diges

Well that's stupid. If anything they should introduce it sooner. There's tons of research that show the sooner it's introduced the better they are able to digest that (as in it becomes more second nature and are later able to reason with it and build off that knowledge better).

zozbot234 5y ago
It's hard to introduce Algebra much earlier than 8th grade - the students just don't have the mathematical maturity for it. What you can do though is challenge and expose them to slightly more complex applications of ordinary math (often stated via increasingly elaborate "word problems") that make the introduction of algebra a lot more natural when the students are finally up for it. You tend to see this approach in the various "Singapore Math", "Russian Math", what have you.
- Manuel_D 5y ago
  My elementary school was introducing algebra in 4th and 5th grade. Questions like "7 * ? = 21" aren't explicitly teaching algebra - student's aren't being taught the multiplicative property of equality, they're just remembering their times tables - but it's laying the foundation.
- soperj 5y ago
  I introduced my kid to Algebra in gr.2 during that first stretch of covid last year. He's not particularly adept at Math(doesn't struggle with it - it was gr.2 though so simple + and -), but it really didn't take much.
- pineconewarrior 5y ago
  Seems entirely arbitrary (if not false?). I was taught the basics of algebra and even trig (at least, how pi and radians work) in the 4th and 5th grade
  - zozbot234 5y ago
    Yes, but I'm talking about what works well for the average student, not just math whizs who post on HN.
    - OccamsMirror 5y ago
      Maybe he's a math whiz because he was taught algebra at a young age, not the other way around.
    - kelnos 5y ago
      You shouldn't optimize for the average student; you should stratify instruction so students of different levels are pushed to their limits and beyond. Sure, some students will not be able to handle algebra as early as others. That doesn't mean you hold back the students who can. That's disastrous public policy, at the very least.
      - csa 5y ago
        > You shouldn't optimize for the average student; you should stratify instruction so students of different levels are pushed to their limits and beyond. While I personally agree with your point, I think your statement makes the case for the folks who developed this policy. The “problem” that these policymakers see is that students, when stratified, are not stratified across certain groups in a proportion that is similar to the population. For folks who focus on equality of outcome, this is a problem. For folks who focus on equality of opportunity, it is not a problem.
      - mlyle 5y ago
        I agree, but stratifying too early can be harmful. I believe what's likely to be best for everyone is: * Keep everyone on the same track through early elementary, but we need to work hard on making the classrooms encourage everyone to be curious and stretch themselves. Games and puzzles are the answer here. * In upper elementary, start to offer differentiated instruction within a classroom. * In middle school and beyond, have true stratified tracks (which this article recommends not doing).
    - 5y ago
- antognini 5y ago
  > the students just don't have the mathematical maturity for it. Doesn't this get at the root of the problem though? Some students have the mathematical maturity for it. Others don't. The arguments seem to be between "we should present these concepts early for the benefit of the students who are ready for it" vs "we should delay these concepts until all students are ready." But different students have different levels of mathematical maturity. the problem seems to stem from working in a paradigm where everyone at a particular age has to learn the same thing. It seems we should be moving in the direction of more personalization rather than less.
  - zozbot234 5y ago
    > The arguments seem to be between "we should present these concepts early for the benefit of the students who are ready for it" vs "we should delay these concepts until all students are ready." Yes, I'm saying that the argument should be quite a bit broader than that. There's much that could be improved in how we expose students to more advanced math in early grades, and there's also much to learn from these well-established teaching approaches. If you do it badly, it's less likely to work.
  - mlyle 5y ago
    > Some students have the mathematical maturity for it. I think part of the problem here is definitional. * My oldest son's a few years ahead in mathematical understanding. He understood algebraic concepts very early, as presented in Singapore math and then through enrichment and bantering about various problems with his mathematically-inclined parents. Kids can absolutely get algebra and learn the rules early. * But even if your 4th grader understands all the rules of symbolic manipulation, and the general concepts behind them... that's only part of what is taught in an algebra class aimed to 13 year olds. There's an emphasis on systematic process, checking for mistakes, carefully matching terms that is likely to be unnecessarily frustrating to younger kids. * Many programs for gifted youth go in exactly the wrong direction: emphasizing more rigor for the gifted youth, harder problem sets, etc. He took Algebra I with CTY and the number of opportunities for sign mistakes or mismatching coefficients per problem were dizzying. I believe we should be: * Throwing ideas at primary kids, with small numbers of degrees of freedom to make the problems manageable for a population that developmentally has less discipline. The complexity of the ideas involved can scale based on what the kid knows so far. * Throwing deep process and carefulness at older kids. The complexity of the ideas involved can scale based on what the kid knows so far, but the process and accuracy expectations can scale mostly with age.
- sieabahlpark 5y ago
  No one said earlier than 8th, they're commenting on earlier than 9th. There are going to be some dumb kids coming out of California.
- deleted 5y ago
  [deleted]
- elliekelly 5y ago
  Anecdote: I’ve tutored elementary school kids (in Massachusetts) who are doing basic algebra with shapes and emoji instead of letters. > 5 + $basketEmoji = 7 > What number is hiding in the basket? They have no idea they’re doing algebra or what algebra even is but they’re doing it. And they understand the concept on a fundamental level. I don’t remember anyone explaining a variable to me so explicitly. I just remember showing up one day and having to deal with random letters mixed into my math homework.
  - lordnacho 5y ago
    There's an app called DragonBox that does this and slowly replaces the pictures with letters, then develops ideas like expanding brackets and such.
- moultano 5y ago
  I learned it in 7th since my 7-9 highschool had an option to test into it, and could have learned it in 6th.
- esalman 5y ago
  We were introduced to algebra in 6th grade. Talking about Indian subcontinent in the 90s. I (and a lot other kids) did fine with it. Well there were many that didn't and they switched to humanities or business studies later. But even if lives are not good at math, they should be taught math. Doing otherwise is how they grow up to become conspiracy theorists.
- kelnos 5y ago
  I, along with 30 other kids in my grade, took our first algebra class in 7th grade (early 90s). After a few weeks of struggling, I was entirely fine with it. I really think you're underestimating what kids can do if taught properly. If students don't have the "mathematical maturity" for algebra until 8th grade, or later, then that just means instruction in prior years was lacking. Not everyone took algebra in 7th grade; those who did not, took it in 8th grade.
- koheripbal 5y ago
  This is nonsense. I do simple algebra with my daughter and she's in 3rd grade. All it takes is a little one-on-one time and some interest. Kids are way smarter that you realize.

zozbot234 5y ago

It's hard to introduce Algebra much earlier than 8th grade - the students just don't have the mathematical maturity for it. What you can do though is challenge and expose them to slightly more complex applications of ordinary math (often stated via increasingly elaborate "word problems") that make the introduction of algebra a lot more natural when the students are finally up for it. You tend to see this approach in the various "Singapore Math", "Russian Math", what have you.

Manuel_D 5y ago
My elementary school was introducing algebra in 4th and 5th grade. Questions like "7 * ? = 21" aren't explicitly teaching algebra - student's aren't being taught the multiplicative property of equality, they're just remembering their times tables - but it's laying the foundation.
soperj 5y ago
I introduced my kid to Algebra in gr.2 during that first stretch of covid last year. He's not particularly adept at Math(doesn't struggle with it - it was gr.2 though so simple + and -), but it really didn't take much.
pineconewarrior 5y ago
Seems entirely arbitrary (if not false?). I was taught the basics of algebra and even trig (at least, how pi and radians work) in the 4th and 5th grade
- zozbot234 5y ago
  Yes, but I'm talking about what works well for the average student, not just math whizs who post on HN.
  - OccamsMirror 5y ago
    Maybe he's a math whiz because he was taught algebra at a young age, not the other way around.
  - kelnos 5y ago
    You shouldn't optimize for the average student; you should stratify instruction so students of different levels are pushed to their limits and beyond. Sure, some students will not be able to handle algebra as early as others. That doesn't mean you hold back the students who can. That's disastrous public policy, at the very least.
    - csa 5y ago
      > You shouldn't optimize for the average student; you should stratify instruction so students of different levels are pushed to their limits and beyond. While I personally agree with your point, I think your statement makes the case for the folks who developed this policy. The “problem” that these policymakers see is that students, when stratified, are not stratified across certain groups in a proportion that is similar to the population. For folks who focus on equality of outcome, this is a problem. For folks who focus on equality of opportunity, it is not a problem.
    - mlyle 5y ago
      I agree, but stratifying too early can be harmful. I believe what's likely to be best for everyone is: * Keep everyone on the same track through early elementary, but we need to work hard on making the classrooms encourage everyone to be curious and stretch themselves. Games and puzzles are the answer here. * In upper elementary, start to offer differentiated instruction within a classroom. * In middle school and beyond, have true stratified tracks (which this article recommends not doing).
  - 5y ago
antognini 5y ago
> the students just don't have the mathematical maturity for it. Doesn't this get at the root of the problem though? Some students have the mathematical maturity for it. Others don't. The arguments seem to be between "we should present these concepts early for the benefit of the students who are ready for it" vs "we should delay these concepts until all students are ready." But different students have different levels of mathematical maturity. the problem seems to stem from working in a paradigm where everyone at a particular age has to learn the same thing. It seems we should be moving in the direction of more personalization rather than less.
- zozbot234 5y ago
  > The arguments seem to be between "we should present these concepts early for the benefit of the students who are ready for it" vs "we should delay these concepts until all students are ready." Yes, I'm saying that the argument should be quite a bit broader than that. There's much that could be improved in how we expose students to more advanced math in early grades, and there's also much to learn from these well-established teaching approaches. If you do it badly, it's less likely to work.
- mlyle 5y ago
  > Some students have the mathematical maturity for it. I think part of the problem here is definitional. * My oldest son's a few years ahead in mathematical understanding. He understood algebraic concepts very early, as presented in Singapore math and then through enrichment and bantering about various problems with his mathematically-inclined parents. Kids can absolutely get algebra and learn the rules early. * But even if your 4th grader understands all the rules of symbolic manipulation, and the general concepts behind them... that's only part of what is taught in an algebra class aimed to 13 year olds. There's an emphasis on systematic process, checking for mistakes, carefully matching terms that is likely to be unnecessarily frustrating to younger kids. * Many programs for gifted youth go in exactly the wrong direction: emphasizing more rigor for the gifted youth, harder problem sets, etc. He took Algebra I with CTY and the number of opportunities for sign mistakes or mismatching coefficients per problem were dizzying. I believe we should be: * Throwing ideas at primary kids, with small numbers of degrees of freedom to make the problems manageable for a population that developmentally has less discipline. The complexity of the ideas involved can scale based on what the kid knows so far. * Throwing deep process and carefulness at older kids. The complexity of the ideas involved can scale based on what the kid knows so far, but the process and accuracy expectations can scale mostly with age.
sieabahlpark 5y ago
No one said earlier than 8th, they're commenting on earlier than 9th. There are going to be some dumb kids coming out of California.
deleted 5y ago
[deleted]
elliekelly 5y ago
Anecdote: I’ve tutored elementary school kids (in Massachusetts) who are doing basic algebra with shapes and emoji instead of letters. > 5 + $basketEmoji = 7 > What number is hiding in the basket? They have no idea they’re doing algebra or what algebra even is but they’re doing it. And they understand the concept on a fundamental level. I don’t remember anyone explaining a variable to me so explicitly. I just remember showing up one day and having to deal with random letters mixed into my math homework.
- lordnacho 5y ago
  There's an app called DragonBox that does this and slowly replaces the pictures with letters, then develops ideas like expanding brackets and such.
moultano 5y ago
I learned it in 7th since my 7-9 highschool had an option to test into it, and could have learned it in 6th.
esalman 5y ago
We were introduced to algebra in 6th grade. Talking about Indian subcontinent in the 90s. I (and a lot other kids) did fine with it. Well there were many that didn't and they switched to humanities or business studies later. But even if lives are not good at math, they should be taught math. Doing otherwise is how they grow up to become conspiracy theorists.
kelnos 5y ago
I, along with 30 other kids in my grade, took our first algebra class in 7th grade (early 90s). After a few weeks of struggling, I was entirely fine with it. I really think you're underestimating what kids can do if taught properly. If students don't have the "mathematical maturity" for algebra until 8th grade, or later, then that just means instruction in prior years was lacking. Not everyone took algebra in 7th grade; those who did not, took it in 8th grade.
koheripbal 5y ago
This is nonsense. I do simple algebra with my daughter and she's in 3rd grade. All it takes is a little one-on-one time and some interest. Kids are way smarter that you realize.