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New Math was a response to the Soviet lead in the space race. It was thought that introducing more abstract concepts, like different bases and set theory, would

New Math was a response to the Soviet lead in the space race. It was thought that introducing more abstract concepts, like different bases and set theory, would help kids grok math more. It was a fool's game. Just like every other "innovation" in mathematics education since, up to and including Common Core (one of which you probably encountered). At the elementary school level, the only way to increase math proficiency is drilling. Drill the basic math facts and standard algorithms until the kid knows them by heart and can do problems as easily as breathing. Only then will they be ready for the higher level, conceptual stuff. The Soviets were ahead in math and science because they drilled their kids harder. Any kid who didn't want to drill was a traitor to the working class. (Were I a right-wing conspiracy theorist, I'd say New Math and its successors were Soviet psyops designed to sabotage math education in order to weaken the west. Instead I think it's more likely a psyop by the bourgeoisie to make us more compliant and exploitable slaves through mass innumeracy.) No surprise, then, that today, when Americans really want their kids to learn math, they use the curriculum from a country where they cane you for minor infractions. They use Singapore Math. Math is hard, and hard things can only be mastered through discipline.

jrockway 2y ago
I think I'm too old for common core (39). It was "Chicago Math" or something like that. We did multiplication by making a 2x2 grid with diagonal lines and whatnot? I didn't really understand the simplification that much; my parents taught me the old way well before I encountered this in school.
aebtebeten 2y ago
To be fair, New Math is a perfect intro to graduate-level* maths; it's just a poor fit for people who (because they don't have calculators? or even slide rules?) would like their children's maths courses to cover arithmetic. (I had a geometry teacher who had been excited because his daughter wanted him to sign something saying she'd be allowed to take "Sets Education". Imagine, finally sets being introduced at the Jr High level! ... and then he realised he'd misheard: there was an "x" at the end of the first word) Lagniappe: https://www.smbc-comics.com/comic/why-i-couldn39t-be-a-math-teacher https://www.smbc-comics.com/comic/why-i-couldn39t-be-a-math-... * or undergraduate discrete maths, of the sort you'd want for any halfway decent CS programme. I'm glad I got a cheap'n'cheerful intro to lattices in 5th grade.
- CuriousCosmic 2y ago
  New math was actually pretty successful at the lower grades. The issue was that when it came to rolling it out to middle and high schools, they just kind of said "here's the textbook, figure it out" instead of going through a coordinated process of teaching the teachers while helping them develop their new curricula (which they did for elementary school). So you had this really ugly failure of teachers not really necessarily being prepared to teach the material combined with the rush to roll out the curriculum across the board instead of expanding it year by year so there wouldn't be a sudden change in expected education.
  - InfiniteRand 2y ago
    I have a theory that the enthusiasm of teachers teaching the material is a far bigger factor in the effectiveness of learning than the methods. So much so that any advantage from better methods gets quickly nullified without teacher buy in
    - 082349872349872 2y ago
      I have an anecdotal theory that most people who came prepared to a STEM programme in the States last century did so despite, not due to, the modal 7-12 teaching. (if true, I hope it no longer is?)
      - bluGill 2y ago
        Most teachers in the states did poorly in math, and never loved it. They in turn can't pass a love of math on. They are good enough at math to pass the tests, but that isn't why they are teaching.
    - BeFlatXIII 2y ago
      That's why the US can get stuck in such educational ruts. There are too many teachers who don't have the in-depth understanding to alter their teaching methods to approaches other than the one they memorized in education college.
pdonis 2y ago
I've always thought his description of the principle behind the New Math was priceless: "In the new approach, as you know, the point is to understand what you're doing, rather than to get the right answer."
- jrockway 2y ago
  Is that a bad thing? I don't make a lot of arithmetic errors in M-x calc or whatever.
  - pdonis 2y ago
    > Is that a bad thing? It's a bad thing if you never learn how to actually get the right answer. Which unfortunately seemed to be a common consequence of the New Math as a teaching method.
    - andrepd 2y ago
      Why? The objective is understanding, not getting the rightsl answer, because you will never do a long multiplication in your life since a 3$ chip does it in a tenth of a microsecond
      - ghaff 2y ago
        I’m probably not going to multiply two 5 digit numbers together on paper much less do long division but I certainly do smaller scale mental arithmetic all the time.
      - pdonis 2y ago
        > The objective is understanding, not getting the rightsl answer I would argue that if your "understanding" doesn't actually enable you to get the right answer, you don't really understand. > you will never do a long multiplication in your life since a 3$ chip does it in a tenth of a microsecond And how do you know the chip's answers are accurate? Or what if you want to design the chip? Or what if there's an EMP and all of the chips are fried? More generally, if you're satisfied with just some conceptual-level "understanding" of anything that doesn't actually enable you to tell right answers from wrong, you are setting yourself up to be manipulated, misled, conned, etc. Critical thinking is a valuable life skill, and it requires you to be able to tell right from wrong answers.
XMPPwocky 2y ago
> Math is hard, and hard things can only be mastered through discipline. There are certainly some things you can only learn effectively by doing them a lot. There are also other things that you've sort of got to learn by rote memorization (e.g. times tables, various formulas). I'm not aware of anything you can only learn effectively by the threat of physical violence. For what it's worth, I was taught logic and set theory well before I learned things like long division. Somehow, it made me like math more, and I had no problems with long division either. Maybe it might have helped more if I'd been beaten though- not sure.
- woooooo 2y ago
  You really don't think so? Personally, threats of physical violence are very persuasive. Yeah I'll memorize that multiplication table.
7402 2y ago
I was in elementary school in the early 1960s. We had New Math. We learned set theory and how to do arithmetic in any base from 2 to 10. It was fun for a budding math geek. However I kept failing miserably at the tests of memorization of the multiplication table. I knew how to add, so I didn't see the point of memorizing something that I could simply derive by repeated addition.
petsormeat 2y ago
I have lingering bitterness for the irresponsible New Math experiment in my elementary education. I couldn't tell time on an analog clock until I was 12, thanks to the blithe dismissal of "rote" multiplication tasks.
- dj_mc_merlin 2y ago
  Just out of interest and if it's not too personal, what's your age/generation? I'm in my mid twenties and I don't have any peers that couldn't more or less always read analog clocks as far as they remember. edit: I just googled it and apparently New Math was during the 1950s-1970s. This confuses me even further since reading an analog clock seems even more important in those times?
  - ghaff 2y ago
    I certainly learned New Math in the sixties. And neither myself nor anyone else I knew had any trouble with analog clocks which is most of what existed.
- contrast 2y ago
  I’m fascinated - I’ve never thought of reading the time as a maths skill. How does it depend on learning multiplication? (non-American here, I may be lacking context that makes it obvious)
  - Angostura 2y ago
    I guess the 5 times table for counting minutes?
  - thaumasiotes 2y ago
    It doesn't; multiplication isn't involved at all. The only skill required is remembering that the shorter hand is hours and the longer hand is minutes. https://images.thdstatic.com/productImages/f220d887-1a05-4181-8f94-4df8f6d7fbc7/svn/silver-westclox-wall-clocks-37065-64_1000.jpg https://images.thdstatic.com/productImages/f220d887-1a05-418...
gopher_space 2y ago
Are you involved with studying pedagogy as it relates to math at a graduate level? If so, where and how long ago?
coryrc 2y ago
> Just like every other "innovation" in mathematics education since, up to and including Common Core Have you actually looked into it? I was skeptical too, but then I saw they were trying to teach kids the way I do math. For example, what's 4001 - 3989. The old way would be to borrow and carry three times. But change question to 1+4000-3990+1 and the answer is perfectly simple. Kids I went to school with would literally write out 43-39 with 13-9 and 3-3. Maybe they're just dumb, but you don't have to be a whiz to use these techniques if someone shows you them. I hope they're still doing some times table memorization.
- giantg2 2y ago
  The easy ways work for easy problems. But the harder ways work for all problems. I've used a lot of that shortcut math before it was allowed in class. I probably would have been better off just doing it the regular way, especially so I wouldn't get points off for not showing my work or showing the wrong work.
  - MrJohz 2y ago
    At least in the UK, where we also learned these sorts of arithmetic tricks, we still learned the "harder ways". The point of these techniques wasn't to replace long multiplication or something, but more as shortcuts so we didn't have to do it if we didn't need to, and we could simplify problems if we saw a better way to do them. We also practiced this stuff regularly, and had mental maths quizzes at least once a week. And (at least when we weren't learning a specific technique), it didn't matter how we did the calculations, so if you felt more comfortable with the traditional methods, you could do that, you were usually just slower. (I was one of those slower people very often!) The point isn't to go "here's how you do maths, it's always like this". It's about (a) helping you do arithmetic more quickly, and (b) helping you understand why numbers behave the way they do, in terms of bases and pairs and factors and other things like that.
  - andrepd 2y ago
    They don't have to "work" as in "be an efficient pen and paper algorithm", because the far more efficient algorithms is "use a computer"! They have to be good to build understanding and intuition, and e.g. presenting subtraction as "distance on the real line" is an excellent way to do this. I did not expect this short-sighted way to look at maths education here in this website.
cyberax 2y ago
> The Soviets were ahead in math and science because they drilled their kids harder. Any kid who didn't want to drill was a traitor to the working class. That was not how the Soviet schools worked. There was no corporal punishment, and struggling students were given help. Instead, it was quite competitive. There was a system of academic competitions ("Olympiads") that went all the way up from schools to the international level. Students were encouraged to compete. At the same time, school sports competitions were pretty much absent.
- 082349872349872 2y ago
  One thing that struck me as very different in classroom scenes is that we* were always to avoid giving each other help, but I get the impression soviets were supposed to aid each other. Punchline 1: (little Johnny sent to the principal after making a comment about physical attributes of the teacher instead of Pushkin's next line, says to the visiting teacher evaluators) "Next time, sirs, when you don't know, don't prompt!" Punchline 2: (a former maths prof turned shipbuilder, trying to coast, read literature, and earn some extra cash in "maths for the proletariat" evening school, is stuck at the brownboard having calculated a negative circumference of a circle = -2πr; his classmate helps) "Psst, colleague, swap order of integration!" Lagniappe: https://www.youtube.com/watch?v=VogwWGEO1-c&t=10574s https://www.youtube.com/watch?v=VogwWGEO1-c&t=10574s * I distinctly remember being taught the "right" way to raise hands in 4th grade, and in particular placing one's elbow on the desk and putting a forearm perpendicular to it was "wrong". Imagine my surprise upon discovering, many decades later, that they for sure didn't want us somehow (despite the iron curtain — as if we'd had had a clue anyway) copying soviet classroom protocol.
Angostura 2y ago
Counterpoint: I was bought up before new math and completely bewildered by maths at school. As far as I could tell it was just a set of magical and arbitrary operations that I had to learn by heart, with no inkling as to what was going on. There was nothing there I could understand no framework my brain could hang things on and I completely failed. New math sounds like it would have been idea for me.
andrepd 2y ago
Amazing how this comment is diametrically opposed to the truth :) It's in fact the very contrary! "Drilling maths" into kids is how you get everyone except the most pre-disposed to "hate maths" with a passion. Because they grow up thinking mathematics is deathly boring busy work of repeating the same busy-work ad nauseum. Teaching rote memorization is useless and wastes time that could better be used exploring ideas and concepts and abstractions and all that makes mathematics beautiful. I recommend reading "A Mathematician's Lament" https://maa.org/sites/default/files/pdf/devlin/LockhartsLament.pdf https://maa.org/sites/default/files/pdf/devlin/LockhartsLame...
- vundercind 2y ago
  I am deeply suspicious of this POV because in my actual experience it was precisely when we shifted from “apply this thing” to something more like real math that classmates started to give up on math entirely. They may not have liked it before, but that didn’t mean they were bad at it. The anger and resentment and resistance to math came later, when we were past arithmetic and drilling (which were also by far the most useful parts of our primary and secondary school math education, in actual life, for most people) [edit] my suspicion is because it’s both entirely contrary to my experience, and always seems to come from people who like math so much that they majored in it and started to really love it right around the time the folks I’m thinking of above—a far larger set—have decided not just that they dislike math, but that they can’t do it and also that hardly matters because it seems to be pointless.
  - andrepd 2y ago
    You seem to be extrapolating from very incomplete data. Maybe if you had a better mathematical education you wouldn't? :) /s
- bitwize 2y ago
  I can guarantee you that Lockhart drilled in the basic arithmetic problems until he knew his times tables and such by heart. He couldn't do things like algebra without this fundamental knowledge ingrained into the fiber of his being. You can't play a Chopin sonata, at least not smoothly and beautifully, without having played lots of boring scales and finger exercises. And you can't get to the fun, creative, beautiful bits of mathematics without having drilled in the fundamentals. Not unless you're Gauss or somebody.

jrockway 2y ago

I think I'm too old for common core (39). It was "Chicago Math" or something like that. We did multiplication by making a 2x2 grid with diagonal lines and whatnot? I didn't really understand the simplification that much; my parents taught me the old way well before I encountered this in school.

aebtebeten 2y ago

To be fair, New Math is a perfect intro to graduate-level* maths; it's just a poor fit for people who (because they don't have calculators? or even slide rules?) would like their children's maths courses to cover arithmetic. (I had a geometry teacher who had been excited because his daughter wanted him to sign something saying she'd be allowed to take "Sets Education". Imagine, finally sets being introduced at the Jr High level! ... and then he realised he'd misheard: there was an "x" at the end of the first word) Lagniappe: https://www.smbc-comics.com/comic/why-i-couldn39t-be-a-math-teacher https://www.smbc-comics.com/comic/why-i-couldn39t-be-a-math-... * or undergraduate discrete maths, of the sort you'd want for any halfway decent CS programme. I'm glad I got a cheap'n'cheerful intro to lattices in 5th grade.

CuriousCosmic 2y ago
New math was actually pretty successful at the lower grades. The issue was that when it came to rolling it out to middle and high schools, they just kind of said "here's the textbook, figure it out" instead of going through a coordinated process of teaching the teachers while helping them develop their new curricula (which they did for elementary school). So you had this really ugly failure of teachers not really necessarily being prepared to teach the material combined with the rush to roll out the curriculum across the board instead of expanding it year by year so there wouldn't be a sudden change in expected education.
- InfiniteRand 2y ago
  I have a theory that the enthusiasm of teachers teaching the material is a far bigger factor in the effectiveness of learning than the methods. So much so that any advantage from better methods gets quickly nullified without teacher buy in
  - 082349872349872 2y ago
    I have an anecdotal theory that most people who came prepared to a STEM programme in the States last century did so despite, not due to, the modal 7-12 teaching. (if true, I hope it no longer is?)
    - bluGill 2y ago
      Most teachers in the states did poorly in math, and never loved it. They in turn can't pass a love of math on. They are good enough at math to pass the tests, but that isn't why they are teaching.
  - BeFlatXIII 2y ago
    That's why the US can get stuck in such educational ruts. There are too many teachers who don't have the in-depth understanding to alter their teaching methods to approaches other than the one they memorized in education college.

pdonis 2y ago

I've always thought his description of the principle behind the New Math was priceless: "In the new approach, as you know, the point is to understand what you're doing, rather than to get the right answer."

jrockway 2y ago
Is that a bad thing? I don't make a lot of arithmetic errors in M-x calc or whatever.
- pdonis 2y ago
  > Is that a bad thing? It's a bad thing if you never learn how to actually get the right answer. Which unfortunately seemed to be a common consequence of the New Math as a teaching method.
  - andrepd 2y ago
    Why? The objective is understanding, not getting the rightsl answer, because you will never do a long multiplication in your life since a 3$ chip does it in a tenth of a microsecond
    - ghaff 2y ago
      I’m probably not going to multiply two 5 digit numbers together on paper much less do long division but I certainly do smaller scale mental arithmetic all the time.
    - pdonis 2y ago
      > The objective is understanding, not getting the rightsl answer I would argue that if your "understanding" doesn't actually enable you to get the right answer, you don't really understand. > you will never do a long multiplication in your life since a 3$ chip does it in a tenth of a microsecond And how do you know the chip's answers are accurate? Or what if you want to design the chip? Or what if there's an EMP and all of the chips are fried? More generally, if you're satisfied with just some conceptual-level "understanding" of anything that doesn't actually enable you to tell right answers from wrong, you are setting yourself up to be manipulated, misled, conned, etc. Critical thinking is a valuable life skill, and it requires you to be able to tell right from wrong answers.

XMPPwocky 2y ago

> Math is hard, and hard things can only be mastered through discipline. There are certainly some things you can only learn effectively by doing them a lot. There are also other things that you've sort of got to learn by rote memorization (e.g. times tables, various formulas). I'm not aware of anything you can only learn effectively by the threat of physical violence. For what it's worth, I was taught logic and set theory well before I learned things like long division. Somehow, it made me like math more, and I had no problems with long division either. Maybe it might have helped more if I'd been beaten though- not sure.

woooooo 2y ago
You really don't think so? Personally, threats of physical violence are very persuasive. Yeah I'll memorize that multiplication table.

7402 2y ago

I was in elementary school in the early 1960s. We had New Math. We learned set theory and how to do arithmetic in any base from 2 to 10. It was fun for a budding math geek. However I kept failing miserably at the tests of memorization of the multiplication table. I knew how to add, so I didn't see the point of memorizing something that I could simply derive by repeated addition.

petsormeat 2y ago

I have lingering bitterness for the irresponsible New Math experiment in my elementary education. I couldn't tell time on an analog clock until I was 12, thanks to the blithe dismissal of "rote" multiplication tasks.

dj_mc_merlin 2y ago
Just out of interest and if it's not too personal, what's your age/generation? I'm in my mid twenties and I don't have any peers that couldn't more or less always read analog clocks as far as they remember. edit: I just googled it and apparently New Math was during the 1950s-1970s. This confuses me even further since reading an analog clock seems even more important in those times?
- ghaff 2y ago
  I certainly learned New Math in the sixties. And neither myself nor anyone else I knew had any trouble with analog clocks which is most of what existed.
contrast 2y ago
I’m fascinated - I’ve never thought of reading the time as a maths skill. How does it depend on learning multiplication? (non-American here, I may be lacking context that makes it obvious)
- Angostura 2y ago
  I guess the 5 times table for counting minutes?
- thaumasiotes 2y ago
  It doesn't; multiplication isn't involved at all. The only skill required is remembering that the shorter hand is hours and the longer hand is minutes. https://images.thdstatic.com/productImages/f220d887-1a05-4181-8f94-4df8f6d7fbc7/svn/silver-westclox-wall-clocks-37065-64_1000.jpg https://images.thdstatic.com/productImages/f220d887-1a05-418...

gopher_space 2y ago

Are you involved with studying pedagogy as it relates to math at a graduate level? If so, where and how long ago?

coryrc 2y ago

> Just like every other "innovation" in mathematics education since, up to and including Common Core Have you actually looked into it? I was skeptical too, but then I saw they were trying to teach kids the way I do math. For example, what's 4001 - 3989. The old way would be to borrow and carry three times. But change question to 1+4000-3990+1 and the answer is perfectly simple. Kids I went to school with would literally write out 43-39 with 13-9 and 3-3. Maybe they're just dumb, but you don't have to be a whiz to use these techniques if someone shows you them. I hope they're still doing some times table memorization.

giantg2 2y ago
The easy ways work for easy problems. But the harder ways work for all problems. I've used a lot of that shortcut math before it was allowed in class. I probably would have been better off just doing it the regular way, especially so I wouldn't get points off for not showing my work or showing the wrong work.
- MrJohz 2y ago
  At least in the UK, where we also learned these sorts of arithmetic tricks, we still learned the "harder ways". The point of these techniques wasn't to replace long multiplication or something, but more as shortcuts so we didn't have to do it if we didn't need to, and we could simplify problems if we saw a better way to do them. We also practiced this stuff regularly, and had mental maths quizzes at least once a week. And (at least when we weren't learning a specific technique), it didn't matter how we did the calculations, so if you felt more comfortable with the traditional methods, you could do that, you were usually just slower. (I was one of those slower people very often!) The point isn't to go "here's how you do maths, it's always like this". It's about (a) helping you do arithmetic more quickly, and (b) helping you understand why numbers behave the way they do, in terms of bases and pairs and factors and other things like that.
- andrepd 2y ago
  They don't have to "work" as in "be an efficient pen and paper algorithm", because the far more efficient algorithms is "use a computer"! They have to be good to build understanding and intuition, and e.g. presenting subtraction as "distance on the real line" is an excellent way to do this. I did not expect this short-sighted way to look at maths education here in this website.

cyberax 2y ago

> The Soviets were ahead in math and science because they drilled their kids harder. Any kid who didn't want to drill was a traitor to the working class. That was not how the Soviet schools worked. There was no corporal punishment, and struggling students were given help. Instead, it was quite competitive. There was a system of academic competitions ("Olympiads") that went all the way up from schools to the international level. Students were encouraged to compete. At the same time, school sports competitions were pretty much absent.

082349872349872 2y ago
One thing that struck me as very different in classroom scenes is that we* were always to avoid giving each other help, but I get the impression soviets were supposed to aid each other. Punchline 1: (little Johnny sent to the principal after making a comment about physical attributes of the teacher instead of Pushkin's next line, says to the visiting teacher evaluators) "Next time, sirs, when you don't know, don't prompt!" Punchline 2: (a former maths prof turned shipbuilder, trying to coast, read literature, and earn some extra cash in "maths for the proletariat" evening school, is stuck at the brownboard having calculated a negative circumference of a circle = -2πr; his classmate helps) "Psst, colleague, swap order of integration!" Lagniappe: https://www.youtube.com/watch?v=VogwWGEO1-c&t=10574s https://www.youtube.com/watch?v=VogwWGEO1-c&t=10574s * I distinctly remember being taught the "right" way to raise hands in 4th grade, and in particular placing one's elbow on the desk and putting a forearm perpendicular to it was "wrong". Imagine my surprise upon discovering, many decades later, that they for sure didn't want us somehow (despite the iron curtain — as if we'd had had a clue anyway) copying soviet classroom protocol.

Angostura 2y ago

Counterpoint: I was bought up before new math and completely bewildered by maths at school. As far as I could tell it was just a set of magical and arbitrary operations that I had to learn by heart, with no inkling as to what was going on. There was nothing there I could understand no framework my brain could hang things on and I completely failed. New math sounds like it would have been idea for me.

andrepd 2y ago

Amazing how this comment is diametrically opposed to the truth :) It's in fact the very contrary! "Drilling maths" into kids is how you get everyone except the most pre-disposed to "hate maths" with a passion. Because they grow up thinking mathematics is deathly boring busy work of repeating the same busy-work ad nauseum. Teaching rote memorization is useless and wastes time that could better be used exploring ideas and concepts and abstractions and all that makes mathematics beautiful. I recommend reading "A Mathematician's Lament" https://maa.org/sites/default/files/pdf/devlin/LockhartsLament.pdf https://maa.org/sites/default/files/pdf/devlin/LockhartsLame...

vundercind 2y ago
I am deeply suspicious of this POV because in my actual experience it was precisely when we shifted from “apply this thing” to something more like real math that classmates started to give up on math entirely. They may not have liked it before, but that didn’t mean they were bad at it. The anger and resentment and resistance to math came later, when we were past arithmetic and drilling (which were also by far the most useful parts of our primary and secondary school math education, in actual life, for most people) [edit] my suspicion is because it’s both entirely contrary to my experience, and always seems to come from people who like math so much that they majored in it and started to really love it right around the time the folks I’m thinking of above—a far larger set—have decided not just that they dislike math, but that they can’t do it and also that hardly matters because it seems to be pointless.
- andrepd 2y ago
  You seem to be extrapolating from very incomplete data. Maybe if you had a better mathematical education you wouldn't? :) /s
bitwize 2y ago
I can guarantee you that Lockhart drilled in the basic arithmetic problems until he knew his times tables and such by heart. He couldn't do things like algebra without this fundamental knowledge ingrained into the fiber of his being. You can't play a Chopin sonata, at least not smoothly and beautifully, without having played lots of boring scales and finger exercises. And you can't get to the fun, creative, beautiful bits of mathematics without having drilled in the fundamentals. Not unless you're Gauss or somebody.