11 ms·

Whatever Happened to New Math? (1990)

42 points by rfreytag 6y ago

hluska 6y ago
This is controversial (and shouldn’t be) but what if instead of spending so much time wondering why ‘Johnny’ can’t add, we spent that money and effort on making sure that Johnny was fed properly?? Countries with as much child poverty as Canada and the United States shouldn’t be surprised when their testing results don’t improve. This is pretty fucking basic science yet I’ve been fighting this battle for over twenty years and quite literally nobody in power gives enough of a fuck to fix it.
- jmt_ 6y ago
  This reminds me of Maslow's pyramid: https://en.wikipedia.org/wiki/Maslow%27s_hierarchy_of_needs https://en.wikipedia.org/wiki/Maslow%27s_hierarchy_of_needs If a child is struggling at the basic needs level of this pyramid then hitting the self fulfillment bit at the top is excruciatingly difficult
  - TT3351 6y ago
    Of course I can't find it now no matter how hard I look, but there was an excellent blog post on here many months ago explaining how the pyramid of needs has become somewhat of a lazy shortcut people like to see on PowerPoint slides, which doesn't actually communicate useful information. It made its way into the wider discourse via educators, who were actually using the model incorrectly in the first place according to a few quotes from Maslow himself in the blog. It's a shame I couldn't find the article. Basically, it's an abstraction of needs that is just too good/simple to be true.
- buzzy_hacker 6y ago
  There’s hope yet: “The reduction in child poverty would be larger still, from 13.7 percent to 3.6 percent. Only about a quarter as many children would remain in poverty after the policy package’s adoption.” https://www.vox.com/future-perfect/21456242/joe-biden-poverty-checks-kamala-harris https://www.vox.com/future-perfect/21456242/joe-biden-povert...
  - hluska 6y ago
    I’m very hopeful about that program, but if you’re interested, I’d love to show you a myriad of Canadian plans to end child poverty by certain dates in the past. I have a lot of hope for the United States now but if my own country’s difficulty is a guide, this will be a tough slog!
- kemiller2002 6y ago
  My cousin and her late husband are dentists. They spent years helping the Native Americans with dental work. During frequent discussions, she mentioned that it's sad that they have bad dental hygiene. Ultimately what she said was, "It's really difficult to convince someone they should focus on brushing their teeth, when really the sole idea occupying their mind is if they are going to get to eat the next day." So many things could be solved so effortlessly, by us spending so little money on basic things.
- Minor49er 6y ago
  Schools in the US serve nearly 12 million free breakfasts and over 20 million free lunches to children every day: https://schoolnutrition.org/AboutSchoolMeals/SchoolMealTrendsStats/ https://schoolnutrition.org/AboutSchoolMeals/SchoolMealTrend...
  - hluska 6y ago
    That’s a wicked program but as of 2018, children were still the poorest age group in the United States. We have an incredibly long ways to go and while that program is a start, it’s barely a drop in the bucket.
    - harperlee 6y ago
      > children were still the poorest age group What... does that mean? I see how someone who cannot (legally) work yet can be poorer than other age groups, but I am sure that’s not what is meant. But is a child somehow deemed poorer than its caregivers? Or perhaps is the child as poor as its poorest caregiver? Or how does that fact appear?
      - jhardy54 6y ago
        I'm curious about this too. My best guess is that they're measuring household income and there are a lot of kids with low household incomes (more than adults with low household incomes, especially when you have more kids than adults in a household). /shrug
        emteycz 6y ago
        Poor households tend to have many kids, and the parent/s are often very young, sometimes even under 18. It's not unseen to have 32-year old parents living with their 16-year old daughter and her two babies, a 14-year old child and another ~12-year old child. Of course these are extremely poor compared to even most of low income households. Perhaps that's what was meant by the comment.
        hluska 6y ago
- deleted 6y ago
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- Chris2048 6y ago
  Is it not the "teach a man to fish" problem? Sometimes, welfare can cause more problems than it creates. So what should "people in power" do? Setup welfare programs, and in turn welfare dependence? Education was seen a cure for poverty, which in turn is why Johnny isn't fed.
  - hluska 6y ago
    The shortest answer is that it’s far cheaper to feed two families than to incarcerate one adult. The longer answer is that you don’t necessarily need welfare programs to help people out of poverty. Rather, a more efficient system would have ‘welfare’ programs for people in crisis that lead into a series of help up services that eventually lead to full independence. Edit - Also, fuck no, it’s not a teach a man to fish argument. We’re talking about child poverty.
    - Chris2048 6y ago
      Sure, but only short-term. And if you only care short-term, because you are a politician with a short term, then fine (for you). But that's a different plan from "the government" in general. > a more efficient system would have ‘welfare’ programs for people in crisis that lead into a series of help up services that eventually lead to full independence. You are describing "safety-net" welfare, but how do you ensure any form of welfare remains a safety-net, and doesn't become a norm? welfare for those not in poverty is much more likely to work this way. If you specifically set out to tackle poverty, the most important thing are educational programs, and limited welfare programs. I'm not against welfare in any case, but I see it as a double-edged sword that is too often seen as a "throw money at the problem" solution. > Also, fuck no It's a metaphor, the difference between men and children aren't relevant. The abstract meaning is dependence vs self-dependence. Giving a child food solves their food, but not their poverty. The way it was originally stated: what if instead of spending so much time wondering why ‘Johnny’ can’t add, we spent that money and effort on making sure that Johnny was fed properly I could just as well say "what if instead of spending so much time wondering why a man can't fish, we spent that money and effort on making sure that man is fed properly", and the answer is the same: because then they will be dependant on us (the government) to provide food. This doesn't mean we shouldn't provide food, but that both are required, since the original post post specifically proposed providing food should displace education i.e. we spend money elsewhere. In fact, what we spend on food is a problem in itself, but unrelated to what we spend on education, we should not cannibalise one in favour of the other as if they are competing solutions - they are both solutions to the same problem, but do not compete because they have different scope: one long term (poverty) the other short (hunger).
deleted 6y ago
[deleted]
ableal 6y ago
It wasn't just the USA. Even in the conservative Portugal of the 1960s/70s a small wave of "modern math" (as it was called here) washed over the high-schools. I believe it was more of an experimental thing, with partial adoption - i.e. only one of the math teachers would use the new syllabus on their students, with classes six days a week (yep, back then there was Saturday morning school). All I remember now is a bit of bafflement at the set theory paraphernalia, rings and groups etc.
MaxBarraclough 6y ago
Is there any way out of that site's pagination? Even the print button doesn't help.
- kencausey 6y ago
  It seems like if you only load the HTML then use Reader mode that it does OK. I use μMatrix and have it only load HTML for sites where I have not explicitly allowed additional content.
  - cyxxon 6y ago
    Firefox native Reader mode works great here (although I have uBlock installed, not sure how much annoyances it filters out).
    - MaxBarraclough 6y ago
      Doesn't work for me. Firefox Reader Mode just shows the first page. (I have uBlock Origin installed, but I suspect it doesn't matter.) red_admiral's suggestion worked for me though.
- red_admiral 6y ago
  Blocking JS on the site works for me.
  - MaxBarraclough 6y ago
    That works, thanks. Pairs well with Firefox's Reader Mode.
WalterBright 6y ago
Fashions, programs, rhetoric, task forces, agendas, etc., come and go in the public schools. The only constant is no change in results. It's actually kinda funny. There's an endless search for an effortless way to learn math. There is no such thing. Learning math requires work. Just like there is no way to get strong without hard work.
- brazzy 6y ago
  > There's an endless search for an effortless way to learn math. Nonsense. There is a search for more effective ways to teach math. And there most definitely are differences in effectiveness, so no reason to believe that any given way is optimal. > Just like there is no way to get strong without hard work. There are, however, lots of ways to spend a lot of hard work for little gain.
  - username90 6y ago
    If we were finding better way to teach then kids scores would improve, but they aren't improving.
    - harimau777 6y ago
      You may very well be correct; however, I can see some other possibilities: - The scores don't effectively measure learning. - The need to prepare students for tests undermines the ability to try different teaching approaches. - Scores don't change overall but the distribution of scores change. - The distribution of scores don't change but the demographics of the students in a given part of the distribution change. - There are confounding factors such as budget or classroom size.
      - WalterBright 6y ago
        I don't understand how someone can learn math, yet be unable to solve math problems on a test. In my 16 years of education, I saw a consistent 1:1 correlation with learning the material and doing correspondingly well on the tests. That consistency included myself - when I learned the material, I'd ace the test. When I didn't learn it, I failed the test. There wasn't any magical "learned but didn't test well" going on.
hansbo 6y ago
Tom Lehrer did a funny song about New Math: https://www.youtube.com/watch?v=UIKGV2cTgqA https://www.youtube.com/watch?v=UIKGV2cTgqA
rjsw 6y ago
I was taught this when I started school in the UK. It seemed fine to me but I wasn't really thinking about alternative teaching methods at age 4.
rlvesco7 6y ago
Within home schooling communities, Singaporean style math has quite a following. Singapore also tends to score quite high on international exams. Basically, they focus on fewer topic more deeply. They also teach from concrete to abstract. I wish American schools would adopt this. https://en.wikipedia.org/wiki/Singapore_math https://en.wikipedia.org/wiki/Singapore_math
- red_admiral 6y ago
  That was how I was taught, in Europe, decades ago. We didn't call it Singapore Math, we just called it Maths. And we used Cuisenaire Rods instead of bar charts.
  - deleted 6y ago
    [deleted]
- mkoubaa 6y ago
  “I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times.” -Bruce Lee
- ivan_ah 6y ago
  There is another project called JUMP math which has shown some great results, and is now getting adopted widely in Canada. Essentially the approach is to present concepts as bite-sized chunks (more scaffolded) and make students gradually work their way up to tougher problems. If you think about it, it makes sense: if the problem in math is people get stuck at some foundational step where they are required to "get" something, and start to think they "suck at math" because they are missing this piece, then making the steps VERY small will make sure everyone can make those steps, thus making everyone "good at math." Similar to Singapore math, it's not based on a "textbook" that you read but an "exercise book" that you write and solve exercises in. I don't have personal experience with teaching using this approach, but I have heard many good things. books: https://www.amazon.com/s?k=jump+math https://www.amazon.com/s?k=jump+math (non free) samples: https://jumpmath.org/jump/en/learn https://jumpmath.org/jump/en/learn podcast: https://www.cbc.ca/listen/live-radio/1-63-the-current/clip/15756534-john-mighton-on-math https://www.cbc.ca/listen/live-radio/1-63-the-current/clip/1...
thrower123 6y ago
The biggest problem seems to be that they spend a helluva lot of time on math instruction, but not very much time actually doing the math. For anything through AP calculus, you'd be better served going down the volume and spaced repetition route that math programs like Saxon use. Do things over, and over, and over, and over again until they are second nature. There's no magic bullet to get around that work that you have to do to master something.
mathgenius 6y ago
My grade two teacher demonstrated "venn diagrams" one day, it absolutely blew my mind. She had a bunch of coloured shapes scattered on the floor, then put one hoop over the triangles, another hoop over the red shapes, and then, what to do with the red triangles? My six-year-old brain loved it when she put one hoop overlapping the other one. And yet to this day I refuse to memorize the multiplication table. Rote learning is easier for the teacher: easier to teach, easier to mark. It's not just mathematics, it's all the subjects in school. Many of the "geniuses" merely survive school, nothing more.
- soVeryTired 6y ago
  I found myself thinking about multiplication tables in the shower today. I think you can get away with knowing the tables for 2, 3, and 7 really well. The rest is just tricks: 4: 2x twice 5: add a zero and divide by 2 6: a 3x followed by a 2x 8: 2x three times 9: 3x twice Beyond that, it’s repetition of those tricks, plus the distributive property of multiplication over addition.
  - TeMPOraL 6y ago
    Nice, though I still prefer the trick for 9 that I was taught: 9: 10x, then subtract once.
    - jjk166 6y ago
      Another: for X from 1 to 10, the digits of 9x will add to 9, and the leading digit will be x-1. You can do this visually by putting up all your fingers and putting down the Xth one - this splits your fingers into two groups, the first is the tens place digit while the second is the ones place digit.
      - jmlundberg 6y ago
        They keep adding to nine. 137×9 = 1233 . 34457×9=310113. When it breaks down: 99x9=891 sums to 18, sums to 9.
hprotagonist 6y ago
it’s so simple/so very simple/that only a child can do it! (and remember kids, base 8 is just like base 10, really — if you’re missing two fingers) https://www.youtube.com/watch?v=UIKGV2cTgqA https://www.youtube.com/watch?v=UIKGV2cTgqA
monoideism 6y ago
I still believe New Maths is a great idea. The main problem was that most teachers didn't get it, and so couldn't teach it. And parents were angry their kids were learning math that they couldn't understand. So it was an implementation issue. The concept was sound.
- BearOso 6y ago
  The problem with abstract thinking is that there’s often more than one way to represent an answer, so that means the teacher has to actually understand the problems, not just match to an answer sheet. I’m reminded of a widely circulated common core math problem to draw a series of dots showing 4 x 8 or something. The kid drew 4 rows of 8 dots, and the teacher marked it “NO!” and drew 8 rows of 4.
  - the_only_law 6y ago
    Maybe a dumb question, but if a non-insignificant number of teachers are simply matching answer sheets why do you need a degree and certification to do it. Doesn’t that indicate that a number are incompetent at at least one very large aspect of the job. Or perhaps, that’s as intended?
cafard 6y ago
I think that I had New Math in sixth grade, and I remember nothing in particular of it but learning about number bases (as Feynman remarked, kind of pointless), and learning the terms commutative and associative--though it was a long time before I grasped the latter.
- mcphage 6y ago
  > learning the terms commutative and associative--though it was a long time before I grasped the latter I think it's kinda interesting—commutativity is so much a more clearer and approachable property than associativity, and it sounds more useful, but the later is far more important.
motohagiography 6y ago
That we get any STEM talent at all is a quirk of selection and survivor bias, which very likely happens in spite of public education methods, not because of it. I have had some truly incredible teachers, but their ability was pareto distributed. Great teachers have nothing in common with the long tail of inadequate ones. The problem they are trying to solve is how to produce citizens with math skills while preserving the system of one generic teacher talking at 30+ kids with increasingly heterogeneous experiences confined in a room and sitting at desks. It's a stupid problem. The concrete math and geometry you learn from things like music, cooking, carpentry, navigation, engine repair, gambling, and building a basic physical experimental apparatus could take a child "up" to differential calculus in less than a couple of years. We have to look at who becomes a teacher and whether they are transmitting their tangible skills to students, or if they are themselves physically helpless talking heads for a received curriculum. Today, I meet ostensibly educated people and their defining characteristic is they have been institutionalized. Whether it was in grad school or prison is just a matter of taste.
- jl2718 6y ago
  I’d being institutionalized bad? PhD is nearly a requirement now to progress beyond mid-level in all top STEM fields, sometimes an entry requirement. I think this is because institutionalized people all think the same way, never too much creativity or questioning what is going on. I would say that this is useful for large organizations only, but the startup community is just as enamored with it, most especially venture capitalists as a group. People that don’t submit fully to some system end up not fitting into any system after enough years.
rfsliva 6y ago
I remember learning about sets in elementary school in the 60's - subsets, unions, intersections (joins) - year after year, and thinking that I would never need this. Now I've been doing data engineering since 1989 (when it was called systems integration) and all I do is work with sets. So glad I had that schooling.
godelzilla 6y ago
Why would we expect teachers to understand math when they're generally not mathematicians? Why would we expect teachers to change the system that created them? Why would we expect a system that was created for sorting people to educate people? Students are trained to serve, not to think. https://poibella.org/papers/indefenseofmath.pdf https://poibella.org/papers/indefenseofmath.pdf
unethical_ban 6y ago
Anecdote: I was an ADD kid in the 90s Undiagnosed, but intelligent and bored and distracted easily. So much so, that during math, one other kid and I were sat outside the classroom in the hallway, and with very little assistance from the teachers, given worksheets on base-5 math. I essentially taught myself what different bases are, what digits represent, and so on. I thought of this the other day as I listened to Radiolab do a thoroughly piss poor job of explaining binary, as part of a larger discussion about computer memory and the relevance of 4096 to a computer error. I mean, they spent a lot of time talking about light bulbs going on and off, and then how, if you represent 2, you flick one bulb off and another on, but if you represent 3, you leave the first bulb on, etc. They did finally mention powers, but not in a generic sense. They didn't ever mention that binary is "just" base 2 math like normal math is base 10. It seemed so contrived. I know they were trying to explain it to the layman, but it seems they actually made it more conceptually difficult. I haven't been able to rant about this and here seems like the best spot.
TT3351 6y ago
Standout passage for me: "The villain, if there is one, might be the country’s penchant for the “quick fix.” Had Sputnik not flown, UICSM, SMSG, the Madison Project, and the other experimental programs might have evolved slowly and carefully into a national curriculum; as it was, they were shoved to center stage, lavishly financed, and told to perform a miracle overnight. They couldn’t, so the country passed on to the next educational fad (“back to basics”), labeled the previous one a failure, and blamed it for low test scores and a decline in skills."
hhas01 6y ago
What happened? Well, it was taught to the kids by all those Old Math teachers, using all of their perfectly-honed and time-proven Old Math techniques, of course. Naturally this was a disaster for both sides, so as soon the correct scapegoats were identified and dispatched, they could safely return to their Old, safe, familiar system which is a disaster for only one. https://fs.blog/2016/07/richard-feynman-teaching-math-kids/ https://fs.blog/2016/07/richard-feynman-teaching-math-kids/ Adding together all the temperatures of red, yellow, green, and blue suns? Kill me now.

42 points by rfreytag 6y ago

This is controversial (and shouldn’t be) but what if instead of spending so much time wondering why ‘Johnny’ can’t add, we spent that money and effort on making sure that Johnny was fed properly?? Countries with as much child poverty as Canada and the United States shouldn’t be surprised when their testing results don’t improve. This is pretty fucking basic science yet I’ve been fighting this battle for over twenty years and quite literally nobody in power gives enough of a fuck to fix it.

jmt_ 6y ago
This reminds me of Maslow's pyramid: https://en.wikipedia.org/wiki/Maslow%27s_hierarchy_of_needs https://en.wikipedia.org/wiki/Maslow%27s_hierarchy_of_needs If a child is struggling at the basic needs level of this pyramid then hitting the self fulfillment bit at the top is excruciatingly difficult
- TT3351 6y ago
  Of course I can't find it now no matter how hard I look, but there was an excellent blog post on here many months ago explaining how the pyramid of needs has become somewhat of a lazy shortcut people like to see on PowerPoint slides, which doesn't actually communicate useful information. It made its way into the wider discourse via educators, who were actually using the model incorrectly in the first place according to a few quotes from Maslow himself in the blog. It's a shame I couldn't find the article. Basically, it's an abstraction of needs that is just too good/simple to be true.
buzzy_hacker 6y ago
There’s hope yet: “The reduction in child poverty would be larger still, from 13.7 percent to 3.6 percent. Only about a quarter as many children would remain in poverty after the policy package’s adoption.” https://www.vox.com/future-perfect/21456242/joe-biden-poverty-checks-kamala-harris https://www.vox.com/future-perfect/21456242/joe-biden-povert...
- hluska 6y ago
  I’m very hopeful about that program, but if you’re interested, I’d love to show you a myriad of Canadian plans to end child poverty by certain dates in the past. I have a lot of hope for the United States now but if my own country’s difficulty is a guide, this will be a tough slog!
kemiller2002 6y ago
My cousin and her late husband are dentists. They spent years helping the Native Americans with dental work. During frequent discussions, she mentioned that it's sad that they have bad dental hygiene. Ultimately what she said was, "It's really difficult to convince someone they should focus on brushing their teeth, when really the sole idea occupying their mind is if they are going to get to eat the next day." So many things could be solved so effortlessly, by us spending so little money on basic things.
Minor49er 6y ago
Schools in the US serve nearly 12 million free breakfasts and over 20 million free lunches to children every day: https://schoolnutrition.org/AboutSchoolMeals/SchoolMealTrendsStats/ https://schoolnutrition.org/AboutSchoolMeals/SchoolMealTrend...
- hluska 6y ago
  That’s a wicked program but as of 2018, children were still the poorest age group in the United States. We have an incredibly long ways to go and while that program is a start, it’s barely a drop in the bucket.
  - harperlee 6y ago
    > children were still the poorest age group What... does that mean? I see how someone who cannot (legally) work yet can be poorer than other age groups, but I am sure that’s not what is meant. But is a child somehow deemed poorer than its caregivers? Or perhaps is the child as poor as its poorest caregiver? Or how does that fact appear?
    - jhardy54 6y ago
      I'm curious about this too. My best guess is that they're measuring household income and there are a lot of kids with low household incomes (more than adults with low household incomes, especially when you have more kids than adults in a household). /shrug
      - emteycz 6y ago
        Poor households tend to have many kids, and the parent/s are often very young, sometimes even under 18. It's not unseen to have 32-year old parents living with their 16-year old daughter and her two babies, a 14-year old child and another ~12-year old child. Of course these are extremely poor compared to even most of low income households. Perhaps that's what was meant by the comment.
      - hluska 6y ago
deleted 6y ago
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Chris2048 6y ago
Is it not the "teach a man to fish" problem? Sometimes, welfare can cause more problems than it creates. So what should "people in power" do? Setup welfare programs, and in turn welfare dependence? Education was seen a cure for poverty, which in turn is why Johnny isn't fed.
- hluska 6y ago
  The shortest answer is that it’s far cheaper to feed two families than to incarcerate one adult. The longer answer is that you don’t necessarily need welfare programs to help people out of poverty. Rather, a more efficient system would have ‘welfare’ programs for people in crisis that lead into a series of help up services that eventually lead to full independence. Edit - Also, fuck no, it’s not a teach a man to fish argument. We’re talking about child poverty.
  - Chris2048 6y ago
    Sure, but only short-term. And if you only care short-term, because you are a politician with a short term, then fine (for you). But that's a different plan from "the government" in general. > a more efficient system would have ‘welfare’ programs for people in crisis that lead into a series of help up services that eventually lead to full independence. You are describing "safety-net" welfare, but how do you ensure any form of welfare remains a safety-net, and doesn't become a norm? welfare for those not in poverty is much more likely to work this way. If you specifically set out to tackle poverty, the most important thing are educational programs, and limited welfare programs. I'm not against welfare in any case, but I see it as a double-edged sword that is too often seen as a "throw money at the problem" solution. > Also, fuck no It's a metaphor, the difference between men and children aren't relevant. The abstract meaning is dependence vs self-dependence. Giving a child food solves their food, but not their poverty. The way it was originally stated: what if instead of spending so much time wondering why ‘Johnny’ can’t add, we spent that money and effort on making sure that Johnny was fed properly I could just as well say "what if instead of spending so much time wondering why a man can't fish, we spent that money and effort on making sure that man is fed properly", and the answer is the same: because then they will be dependant on us (the government) to provide food. This doesn't mean we shouldn't provide food, but that both are required, since the original post post specifically proposed providing food should displace education i.e. we spend money elsewhere. In fact, what we spend on food is a problem in itself, but unrelated to what we spend on education, we should not cannibalise one in favour of the other as if they are competing solutions - they are both solutions to the same problem, but do not compete because they have different scope: one long term (poverty) the other short (hunger).

deleted 6y ago

[deleted]

ableal 6y ago

It wasn't just the USA. Even in the conservative Portugal of the 1960s/70s a small wave of "modern math" (as it was called here) washed over the high-schools. I believe it was more of an experimental thing, with partial adoption - i.e. only one of the math teachers would use the new syllabus on their students, with classes six days a week (yep, back then there was Saturday morning school). All I remember now is a bit of bafflement at the set theory paraphernalia, rings and groups etc.

MaxBarraclough 6y ago

Is there any way out of that site's pagination? Even the print button doesn't help.

kencausey 6y ago
It seems like if you only load the HTML then use Reader mode that it does OK. I use μMatrix and have it only load HTML for sites where I have not explicitly allowed additional content.
- cyxxon 6y ago
  Firefox native Reader mode works great here (although I have uBlock installed, not sure how much annoyances it filters out).
  - MaxBarraclough 6y ago
    Doesn't work for me. Firefox Reader Mode just shows the first page. (I have uBlock Origin installed, but I suspect it doesn't matter.) red_admiral's suggestion worked for me though.
red_admiral 6y ago
Blocking JS on the site works for me.
- MaxBarraclough 6y ago
  That works, thanks. Pairs well with Firefox's Reader Mode.

WalterBright 6y ago

Fashions, programs, rhetoric, task forces, agendas, etc., come and go in the public schools. The only constant is no change in results. It's actually kinda funny. There's an endless search for an effortless way to learn math. There is no such thing. Learning math requires work. Just like there is no way to get strong without hard work.

brazzy 6y ago
> There's an endless search for an effortless way to learn math. Nonsense. There is a search for more effective ways to teach math. And there most definitely are differences in effectiveness, so no reason to believe that any given way is optimal. > Just like there is no way to get strong without hard work. There are, however, lots of ways to spend a lot of hard work for little gain.
- username90 6y ago
  If we were finding better way to teach then kids scores would improve, but they aren't improving.
  - harimau777 6y ago
    You may very well be correct; however, I can see some other possibilities: - The scores don't effectively measure learning. - The need to prepare students for tests undermines the ability to try different teaching approaches. - Scores don't change overall but the distribution of scores change. - The distribution of scores don't change but the demographics of the students in a given part of the distribution change. - There are confounding factors such as budget or classroom size.
    - WalterBright 6y ago
      I don't understand how someone can learn math, yet be unable to solve math problems on a test. In my 16 years of education, I saw a consistent 1:1 correlation with learning the material and doing correspondingly well on the tests. That consistency included myself - when I learned the material, I'd ace the test. When I didn't learn it, I failed the test. There wasn't any magical "learned but didn't test well" going on.

hansbo 6y ago

Tom Lehrer did a funny song about New Math: https://www.youtube.com/watch?v=UIKGV2cTgqA https://www.youtube.com/watch?v=UIKGV2cTgqA

rjsw 6y ago

I was taught this when I started school in the UK. It seemed fine to me but I wasn't really thinking about alternative teaching methods at age 4.

rlvesco7 6y ago

Within home schooling communities, Singaporean style math has quite a following. Singapore also tends to score quite high on international exams. Basically, they focus on fewer topic more deeply. They also teach from concrete to abstract. I wish American schools would adopt this. https://en.wikipedia.org/wiki/Singapore_math https://en.wikipedia.org/wiki/Singapore_math

red_admiral 6y ago
That was how I was taught, in Europe, decades ago. We didn't call it Singapore Math, we just called it Maths. And we used Cuisenaire Rods instead of bar charts.
- deleted 6y ago
  [deleted]
mkoubaa 6y ago
“I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times.” -Bruce Lee
ivan_ah 6y ago
There is another project called JUMP math which has shown some great results, and is now getting adopted widely in Canada. Essentially the approach is to present concepts as bite-sized chunks (more scaffolded) and make students gradually work their way up to tougher problems. If you think about it, it makes sense: if the problem in math is people get stuck at some foundational step where they are required to "get" something, and start to think they "suck at math" because they are missing this piece, then making the steps VERY small will make sure everyone can make those steps, thus making everyone "good at math." Similar to Singapore math, it's not based on a "textbook" that you read but an "exercise book" that you write and solve exercises in. I don't have personal experience with teaching using this approach, but I have heard many good things. books: https://www.amazon.com/s?k=jump+math https://www.amazon.com/s?k=jump+math (non free) samples: https://jumpmath.org/jump/en/learn https://jumpmath.org/jump/en/learn podcast: https://www.cbc.ca/listen/live-radio/1-63-the-current/clip/15756534-john-mighton-on-math https://www.cbc.ca/listen/live-radio/1-63-the-current/clip/1...

thrower123 6y ago

The biggest problem seems to be that they spend a helluva lot of time on math instruction, but not very much time actually doing the math. For anything through AP calculus, you'd be better served going down the volume and spaced repetition route that math programs like Saxon use. Do things over, and over, and over, and over again until they are second nature. There's no magic bullet to get around that work that you have to do to master something.

mathgenius 6y ago

My grade two teacher demonstrated "venn diagrams" one day, it absolutely blew my mind. She had a bunch of coloured shapes scattered on the floor, then put one hoop over the triangles, another hoop over the red shapes, and then, what to do with the red triangles? My six-year-old brain loved it when she put one hoop overlapping the other one. And yet to this day I refuse to memorize the multiplication table. Rote learning is easier for the teacher: easier to teach, easier to mark. It's not just mathematics, it's all the subjects in school. Many of the "geniuses" merely survive school, nothing more.

soVeryTired 6y ago
I found myself thinking about multiplication tables in the shower today. I think you can get away with knowing the tables for 2, 3, and 7 really well. The rest is just tricks: 4: 2x twice 5: add a zero and divide by 2 6: a 3x followed by a 2x 8: 2x three times 9: 3x twice Beyond that, it’s repetition of those tricks, plus the distributive property of multiplication over addition.
- TeMPOraL 6y ago
  Nice, though I still prefer the trick for 9 that I was taught: 9: 10x, then subtract once.
  - jjk166 6y ago
    Another: for X from 1 to 10, the digits of 9x will add to 9, and the leading digit will be x-1. You can do this visually by putting up all your fingers and putting down the Xth one - this splits your fingers into two groups, the first is the tens place digit while the second is the ones place digit.
    - jmlundberg 6y ago
      They keep adding to nine. 137×9 = 1233 . 34457×9=310113. When it breaks down: 99x9=891 sums to 18, sums to 9.

hprotagonist 6y ago

it’s so simple/so very simple/that only a child can do it! (and remember kids, base 8 is just like base 10, really — if you’re missing two fingers) https://www.youtube.com/watch?v=UIKGV2cTgqA https://www.youtube.com/watch?v=UIKGV2cTgqA

monoideism 6y ago

I still believe New Maths is a great idea. The main problem was that most teachers didn't get it, and so couldn't teach it. And parents were angry their kids were learning math that they couldn't understand. So it was an implementation issue. The concept was sound.

BearOso 6y ago
The problem with abstract thinking is that there’s often more than one way to represent an answer, so that means the teacher has to actually understand the problems, not just match to an answer sheet. I’m reminded of a widely circulated common core math problem to draw a series of dots showing 4 x 8 or something. The kid drew 4 rows of 8 dots, and the teacher marked it “NO!” and drew 8 rows of 4.
- the_only_law 6y ago
  Maybe a dumb question, but if a non-insignificant number of teachers are simply matching answer sheets why do you need a degree and certification to do it. Doesn’t that indicate that a number are incompetent at at least one very large aspect of the job. Or perhaps, that’s as intended?

cafard 6y ago

I think that I had New Math in sixth grade, and I remember nothing in particular of it but learning about number bases (as Feynman remarked, kind of pointless), and learning the terms commutative and associative--though it was a long time before I grasped the latter.

mcphage 6y ago
> learning the terms commutative and associative--though it was a long time before I grasped the latter I think it's kinda interesting—commutativity is so much a more clearer and approachable property than associativity, and it sounds more useful, but the later is far more important.

motohagiography 6y ago

That we get any STEM talent at all is a quirk of selection and survivor bias, which very likely happens in spite of public education methods, not because of it. I have had some truly incredible teachers, but their ability was pareto distributed. Great teachers have nothing in common with the long tail of inadequate ones. The problem they are trying to solve is how to produce citizens with math skills while preserving the system of one generic teacher talking at 30+ kids with increasingly heterogeneous experiences confined in a room and sitting at desks. It's a stupid problem. The concrete math and geometry you learn from things like music, cooking, carpentry, navigation, engine repair, gambling, and building a basic physical experimental apparatus could take a child "up" to differential calculus in less than a couple of years. We have to look at who becomes a teacher and whether they are transmitting their tangible skills to students, or if they are themselves physically helpless talking heads for a received curriculum. Today, I meet ostensibly educated people and their defining characteristic is they have been institutionalized. Whether it was in grad school or prison is just a matter of taste.

jl2718 6y ago
I’d being institutionalized bad? PhD is nearly a requirement now to progress beyond mid-level in all top STEM fields, sometimes an entry requirement. I think this is because institutionalized people all think the same way, never too much creativity or questioning what is going on. I would say that this is useful for large organizations only, but the startup community is just as enamored with it, most especially venture capitalists as a group. People that don’t submit fully to some system end up not fitting into any system after enough years.

rfsliva 6y ago

I remember learning about sets in elementary school in the 60's - subsets, unions, intersections (joins) - year after year, and thinking that I would never need this. Now I've been doing data engineering since 1989 (when it was called systems integration) and all I do is work with sets. So glad I had that schooling.

godelzilla 6y ago

Why would we expect teachers to understand math when they're generally not mathematicians? Why would we expect teachers to change the system that created them? Why would we expect a system that was created for sorting people to educate people? Students are trained to serve, not to think. https://poibella.org/papers/indefenseofmath.pdf https://poibella.org/papers/indefenseofmath.pdf

unethical_ban 6y ago

Anecdote: I was an ADD kid in the 90s Undiagnosed, but intelligent and bored and distracted easily. So much so, that during math, one other kid and I were sat outside the classroom in the hallway, and with very little assistance from the teachers, given worksheets on base-5 math. I essentially taught myself what different bases are, what digits represent, and so on. I thought of this the other day as I listened to Radiolab do a thoroughly piss poor job of explaining binary, as part of a larger discussion about computer memory and the relevance of 4096 to a computer error. I mean, they spent a lot of time talking about light bulbs going on and off, and then how, if you represent 2, you flick one bulb off and another on, but if you represent 3, you leave the first bulb on, etc. They did finally mention powers, but not in a generic sense. They didn't ever mention that binary is "just" base 2 math like normal math is base 10. It seemed so contrived. I know they were trying to explain it to the layman, but it seems they actually made it more conceptually difficult. I haven't been able to rant about this and here seems like the best spot.

TT3351 6y ago

Standout passage for me: "The villain, if there is one, might be the country’s penchant for the “quick fix.” Had Sputnik not flown, UICSM, SMSG, the Madison Project, and the other experimental programs might have evolved slowly and carefully into a national curriculum; as it was, they were shoved to center stage, lavishly financed, and told to perform a miracle overnight. They couldn’t, so the country passed on to the next educational fad (“back to basics”), labeled the previous one a failure, and blamed it for low test scores and a decline in skills."

hhas01 6y ago

What happened? Well, it was taught to the kids by all those Old Math teachers, using all of their perfectly-honed and time-proven Old Math techniques, of course. Naturally this was a disaster for both sides, so as soon the correct scapegoats were identified and dispatched, they could safely return to their Old, safe, familiar system which is a disaster for only one. https://fs.blog/2016/07/richard-feynman-teaching-math-kids/ https://fs.blog/2016/07/richard-feynman-teaching-math-kids/ Adding together all the temperatures of red, yellow, green, and blue suns? Kill me now.