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Ultimately the solution is better STEM foundation at the very very early ages. Universal pre school would probably be very useful. Empirically [edit: n = 1 or 2

Ultimately the solution is better STEM foundation at the very very early ages. Universal pre school would probably be very useful. Empirically [edit: n = 1 or 2], it seems that drilling basic arithmetic and then multiplication tables early in pre K and earlier elementary will give students a better intuitive math foundation to do algebra very well. That would enable everyone to go into more advanced classes at the same time (earlier) rather than these policies which want everyone to go in at the same time (later).

FredPret 4y ago
I wish we did probability with equal gusto as kids. I very occasionally multiply 7 and 6 in my head, but have to reason with probabilities and statistics all day long.
- texaslonghorn5 4y ago
  Agree. I think getting really good at addition subtraction and multiplication and then division/fractions is the way to go though. Have really strong math fundamentals and then learn algebra and then everything else is far easier to pick up.
  - FredPret 4y ago
    Fair point. My first introduction to stats was at second year in uni though, far too late. By that time I had already done a lot of calculus, which while important, hasn’t exactly been critical in my daily life.
- Jensson 4y ago
  Arithmetics is absolutely the most important topic to learn, since it is the basis for all other quantitative reasoning. For example, it is really important to understand that 1 / 3 chance is the same thing as 3 / 9 chance. It is obvious to you now since you have done so much arithmetic's, but to someone who never properly learned it they wouldn't be able to properly compare those two and could think that one is a very different number than the other. Without basic understanding about quantities all other quantitative skills become worthless.
- Wohlf 4y ago
  Statistics is the only reason I was able to get over my math struggles in college.
chadash 4y ago
Pre-K (4 year olds) seems a bit young for teaching multiplication tables.
- frostburg 4y ago
  They do not require abstraction, I don't know if it is necessary but it is practical to teach them.
  - chadash 4y ago
    What's the point of teaching kids to memorize something that they can't apply? When I was a kid, schools taught multiplication tables in 2nd grade, when most kids are 7 years old. The difference in cognition between a 4 year old and 7 year old is insane. I'd be surprised if there were any countries where multiplication was formally taught to pre-K students as part of the standard curriculum, but i'd love to be proven wrong.
    - texaslonghorn5 4y ago
      I don't know if there are countries. I believe that if there actually was a unified accelerated math framework that was really emphasized starting age 4/5 then kids would be absolutely fantastic at math. > What's the point ... ? Paraphrasing what I said a comment above, you drill addition and subtraction until everyone is good at it, then you drill multiplication, then you do basic division, then you start introducing basic one variable algebra with "move plus to the other side to get minus" etc. The application is using algebra for word problems; formalism can come later.
- texaslonghorn5 4y ago
  In context I meant get really good at addition/subtraction starting pre K and then multiplication once +/- is mastered. Though empirically, I don't know about age 4 but kindergarten is definitely not too young for learning up to 12*12. And once you figure out multiplication and eventually mental division, it's not too big of a leap to have one variable algebra with "move a plus to the other side to become minus" etc. The formalism can come later but it's fantastic to have some exposure to moving numbers and symbols around from an early age.
BitwiseFool 4y ago
>"drilling basic arithmetic and then multiplication tables" I get the sense that such rote methods are no longer encouraged and a lot of the "new math" in Common Core is aimed at approximation and reckoning so that students won't rely on memorization.
- frostburg 4y ago
  If you want to teach people methods to solve equations, limits, integrals etc. speed with basic algebraic operations is necessary. Facility with those methods is then necessary to be able to adequately follow important proofs and gain understanding of more advanced concepts. I don't know how you would teach people important results in their fields (physics, computer science etc., I'm not talking about actual mathematicians) without those skills.
  - RangerScience 4y ago
    TL;DR: algebra != arithmetic AKA real math doesn't use numbers I'm only good at _arithmetic_ because of making Warhammer 40k armies (true story bro). I'm good at _algebra_ because I was taught well, on top of a knack. Speed with basic algebraic operations was very helpful in many places but speed with arithmetic operations has only been helpful in board games. I don't think anyone here would disagree with your point about algebra, but I think a lot of people such as myself would disagree that pre-K memorization of arithmetic helps with algebra later.
    - frostburg 4y ago
      Performing a bunch of calculations for tabletop wargaming is basically the same as learning multiplication tables and solving related problem sets. It should help every time that for example you have to simplify a polynomial involving fractions and similar operations. As I stated in another post, I don't know when it is neurologically ideal to learn arithmetics, it seems something that would be important to study carefully (personally I learnt before grade school, when I was 3-4 years old, but I didn't learn to read until I was 6, something that is often taught earlier).
    - 4y ago
civilized 4y ago
More and more earlier and earlier doesn't comport well with child development and can backfire by making students feel incompetent. We need better teachers, probably by paying more so more talented people join the profession.
- zozbot234 4y ago
  Other countries do a lot of "pre-algebra" in the later grades of primary education, when the kids are quite ready for it; "drill and kill" rote methods are generally focused on in very early grades, since they help build familiarity with the sort of rigorous, algorithmic thinking that's required for good math proficiency. This is what Russian Math, French Math, Singapore Math, etc. are built on, and the approach has stood the test of time indeed. The fuzzy "Common Core" approach pushes abstract content way too early, and ends up confusing kids as a result.
  - civilized 4y ago
    I wholeheartedly endorse Singapore Math, Russian Math, Canadian Math (this is a thing, check out John Mighton's fantastic JUMP program). ANYTHING but US math.
- joebob42 4y ago
  I think we could pay more, but only if we could actually get better teachers. So many teachers are bad and not worth even what they get paid (personal experience from a nominally quite good school district). My concern with paying more before figuring out how to weed out bad ones is that it would just be a waste.
wardedVibe 4y ago
As a math PhD with dyscalcula, I'm very skeptical. I was nearly held back as a child because of poor arithmetic performance, and really only started to be above average when we started on algebra. Poor arithmetic isn't that uncommon among the mathematicians I know.
- texaslonghorn5 4y ago
  Interesting. I do not know much about dyscalcula. At an early age do word problems make it worse or better?
  - wardedVibe 4y ago
    I don't think they make much difference either way, as it's specifically the processing of numbers.
- NegativeLatency 4y ago
  Poor arithmetic actually drove me to learn how to program calculators and caused me to be interested in being a software engineer
- zozbot234 4y ago
  Did that dyscalculia prevent you from learning and attaining familiarity with the standard algorithms? That's the sensible goal of "drill and kill" in early grades, not doing routine arithmetic with high amounts of significant digits.
  - wardedVibe 4y ago
    Nope, its literally recalling the times tables that I choke on. There were timed segments, and I couldn't keep up
- chadash 4y ago
  I love this. On a similar note, I have a friend who majored in math at Harvard. He once told me that he came into Harvard being arrogant because in high school he was always at the top of his class in math. He enrolls in his first college level math course thinking he's got this, but he soon realizes that "higher math", which is largely proof-based, is a completely different subject than what he learned in high school. A month in he bombs the first exam. He went to the professor, who is originally from Italy, and explained his situation and how he was a star in high school. He responds in a thick Italian accent "that was not math, that was computation. In this course I teach math". The math you typically learn in high school is very important, but I wish that we did a better job of explaining to high school students that what they are learning is completely different from what "real mathematicians" study (although I do think that computation is quite important in engineering, for example).
usaar333 4y ago
There is little evidence universal preschool would reduce academic variance later on. On cognitive measures (though not necessarily social/emotional), randomized trials of such programs tend to show fade-out (no difference between control and treatment groups) within several years.

FredPret 4y ago

I wish we did probability with equal gusto as kids. I very occasionally multiply 7 and 6 in my head, but have to reason with probabilities and statistics all day long.

texaslonghorn5 4y ago
Agree. I think getting really good at addition subtraction and multiplication and then division/fractions is the way to go though. Have really strong math fundamentals and then learn algebra and then everything else is far easier to pick up.
- FredPret 4y ago
  Fair point. My first introduction to stats was at second year in uni though, far too late. By that time I had already done a lot of calculus, which while important, hasn’t exactly been critical in my daily life.
Jensson 4y ago
Arithmetics is absolutely the most important topic to learn, since it is the basis for all other quantitative reasoning. For example, it is really important to understand that 1 / 3 chance is the same thing as 3 / 9 chance. It is obvious to you now since you have done so much arithmetic's, but to someone who never properly learned it they wouldn't be able to properly compare those two and could think that one is a very different number than the other. Without basic understanding about quantities all other quantitative skills become worthless.
Wohlf 4y ago
Statistics is the only reason I was able to get over my math struggles in college.

chadash 4y ago

Pre-K (4 year olds) seems a bit young for teaching multiplication tables.

frostburg 4y ago
They do not require abstraction, I don't know if it is necessary but it is practical to teach them.
- chadash 4y ago
  What's the point of teaching kids to memorize something that they can't apply? When I was a kid, schools taught multiplication tables in 2nd grade, when most kids are 7 years old. The difference in cognition between a 4 year old and 7 year old is insane. I'd be surprised if there were any countries where multiplication was formally taught to pre-K students as part of the standard curriculum, but i'd love to be proven wrong.
  - texaslonghorn5 4y ago
    I don't know if there are countries. I believe that if there actually was a unified accelerated math framework that was really emphasized starting age 4/5 then kids would be absolutely fantastic at math. > What's the point ... ? Paraphrasing what I said a comment above, you drill addition and subtraction until everyone is good at it, then you drill multiplication, then you do basic division, then you start introducing basic one variable algebra with "move plus to the other side to get minus" etc. The application is using algebra for word problems; formalism can come later.
texaslonghorn5 4y ago
In context I meant get really good at addition/subtraction starting pre K and then multiplication once +/- is mastered. Though empirically, I don't know about age 4 but kindergarten is definitely not too young for learning up to 12*12. And once you figure out multiplication and eventually mental division, it's not too big of a leap to have one variable algebra with "move a plus to the other side to become minus" etc. The formalism can come later but it's fantastic to have some exposure to moving numbers and symbols around from an early age.

BitwiseFool 4y ago

>"drilling basic arithmetic and then multiplication tables" I get the sense that such rote methods are no longer encouraged and a lot of the "new math" in Common Core is aimed at approximation and reckoning so that students won't rely on memorization.

frostburg 4y ago
If you want to teach people methods to solve equations, limits, integrals etc. speed with basic algebraic operations is necessary. Facility with those methods is then necessary to be able to adequately follow important proofs and gain understanding of more advanced concepts. I don't know how you would teach people important results in their fields (physics, computer science etc., I'm not talking about actual mathematicians) without those skills.
- RangerScience 4y ago
  TL;DR: algebra != arithmetic AKA real math doesn't use numbers I'm only good at _arithmetic_ because of making Warhammer 40k armies (true story bro). I'm good at _algebra_ because I was taught well, on top of a knack. Speed with basic algebraic operations was very helpful in many places but speed with arithmetic operations has only been helpful in board games. I don't think anyone here would disagree with your point about algebra, but I think a lot of people such as myself would disagree that pre-K memorization of arithmetic helps with algebra later.
  - frostburg 4y ago
    Performing a bunch of calculations for tabletop wargaming is basically the same as learning multiplication tables and solving related problem sets. It should help every time that for example you have to simplify a polynomial involving fractions and similar operations. As I stated in another post, I don't know when it is neurologically ideal to learn arithmetics, it seems something that would be important to study carefully (personally I learnt before grade school, when I was 3-4 years old, but I didn't learn to read until I was 6, something that is often taught earlier).
  - 4y ago

civilized 4y ago

More and more earlier and earlier doesn't comport well with child development and can backfire by making students feel incompetent. We need better teachers, probably by paying more so more talented people join the profession.

zozbot234 4y ago
Other countries do a lot of "pre-algebra" in the later grades of primary education, when the kids are quite ready for it; "drill and kill" rote methods are generally focused on in very early grades, since they help build familiarity with the sort of rigorous, algorithmic thinking that's required for good math proficiency. This is what Russian Math, French Math, Singapore Math, etc. are built on, and the approach has stood the test of time indeed. The fuzzy "Common Core" approach pushes abstract content way too early, and ends up confusing kids as a result.
- civilized 4y ago
  I wholeheartedly endorse Singapore Math, Russian Math, Canadian Math (this is a thing, check out John Mighton's fantastic JUMP program). ANYTHING but US math.
joebob42 4y ago
I think we could pay more, but only if we could actually get better teachers. So many teachers are bad and not worth even what they get paid (personal experience from a nominally quite good school district). My concern with paying more before figuring out how to weed out bad ones is that it would just be a waste.

wardedVibe 4y ago

As a math PhD with dyscalcula, I'm very skeptical. I was nearly held back as a child because of poor arithmetic performance, and really only started to be above average when we started on algebra. Poor arithmetic isn't that uncommon among the mathematicians I know.

texaslonghorn5 4y ago
Interesting. I do not know much about dyscalcula. At an early age do word problems make it worse or better?
- wardedVibe 4y ago
  I don't think they make much difference either way, as it's specifically the processing of numbers.
NegativeLatency 4y ago
Poor arithmetic actually drove me to learn how to program calculators and caused me to be interested in being a software engineer
zozbot234 4y ago
Did that dyscalculia prevent you from learning and attaining familiarity with the standard algorithms? That's the sensible goal of "drill and kill" in early grades, not doing routine arithmetic with high amounts of significant digits.
- wardedVibe 4y ago
  Nope, its literally recalling the times tables that I choke on. There were timed segments, and I couldn't keep up
chadash 4y ago
I love this. On a similar note, I have a friend who majored in math at Harvard. He once told me that he came into Harvard being arrogant because in high school he was always at the top of his class in math. He enrolls in his first college level math course thinking he's got this, but he soon realizes that "higher math", which is largely proof-based, is a completely different subject than what he learned in high school. A month in he bombs the first exam. He went to the professor, who is originally from Italy, and explained his situation and how he was a star in high school. He responds in a thick Italian accent "that was not math, that was computation. In this course I teach math". The math you typically learn in high school is very important, but I wish that we did a better job of explaining to high school students that what they are learning is completely different from what "real mathematicians" study (although I do think that computation is quite important in engineering, for example).

usaar333 4y ago

There is little evidence universal preschool would reduce academic variance later on. On cognitive measures (though not necessarily social/emotional), randomized trials of such programs tend to show fade-out (no difference between control and treatment groups) within several years.