8 ms·

Curious to see comments quipping that some of the math problems geared towards young kids are too hard. I'd recommend taking a look at Singapore Math[0] to get

by lhorie 5y ago

Curious to see comments quipping that some of the math problems geared towards young kids are too hard. I'd recommend taking a look at Singapore Math[0] to get an idea of what kids in those age ranges are actually capable of doing, provided that adults shed preconceptions that children ought to be "sheltered from hard scary stuff", and instead encourage them. There are also great math-oriented games these days (I had some good success w/ prodigygame.com[1]). My youngest daughter is 6 and can solve simple multiplication and division problems. Sometimes she even surprises me. Some time ago, we were introducing ourselves to a new neighbor and the convo went somewhat along these lines: - my son: how old is your dog? - neighbor: she's 8 - son: she's so small, is she a puppy? - neighbor: oh no, she's grown up. 1 dog year is about 7 human years, so- - daughter [interrupting]: oh wow, so then she is 56! The other day, she came to me beaming to explain how she had just solved 38/2 (by doing 40/2, 2/2 and subtracting the results). Gotta say it's a joy to see a kid that enjoys math. [0] https://www.singaporemath.com/ https://www.singaporemath.com/ [1] https://www.prodigygame.com/main-en/ https://www.prodigygame.com/main-en/

Koshkin 5y ago
> 1 dog year is about 7 human years This is the average; the correspondence is not linear...
- inamiyar 5y ago
  Probably true, but the point was that the daughter was capable of quick multiplication, the age of the dog was..decidedly a minor detail.
- whimsicalism 5y ago
  Classic HN
  - MontyCarloHall 5y ago
    Parent comment belongs in the hall of fame right next to the classic "Dropbox is trivial—it’s just an FTP server under version control": https://news.ycombinator.com/item?id=8863 https://news.ycombinator.com/item?id=8863
  - ThePadawan 5y ago
    I see your "classic HN" and counter with a "I'm one of today's lucky 10000!". I was taught the 7 years rule as a kid and only learned as an adult that it's an average, not true for all dog breeds.
    - msrenee 5y ago
      It's also not really true for young dogs. A 1-year-old dog of most breeds is reproductively mature, whereas a 7-year-old human is not.
loonster 5y ago
Which singaporemath? There are several.
- gnicholas 5y ago
  Yeah, would be interested to see an example other than the link provided, which seems to be to purchase workbooks. Are there any good free resources (or free to try/evaluate) online? I heard about Singaporean math a while ago and looked up some youtube videos. It seemed like they showed clever ways to solve highly stylized problems, but nothing that would actually ever come up in the real world. To be fair, I only watched 3 videos, but they were all from different channels, so I assumed they were a decent sample of what Singaporean math is about.
- lhorie 5y ago
  We bought the Intensive Practice series[0], and paced study time at a couple of pages a day (which takes about 20-30 mins), semi-supervised (i.e. kids mostly work on their own, but if they don't understand something, we help clarify). It does take some hand holding at the beginning though. [0] https://shop.singaporemath.com/index.php/product-category/supplementary-and-other-math/math-supplementary/singapore-math-intensive-practice/ https://shop.singaporemath.com/index.php/product-category/su...
  - loonster 5y ago
    Interesting. So was this a supplement to math learned at school or was it the primary math? I was expecting you to name dimensions or one if the other programs they offer.
    - lhorie 5y ago
      It isn't related to school curriculum (our kids go to US public school). It's supplemental in the sense that they get to practice more math exercises than a kid that only relies on school/common core curriculum.
    - koolba 5y ago
      Most school math is pathetically slow. IIRC, they don’t learn algebra till 8th or 9th grade and even then spend an entire year on it.
halgir 5y ago
> I'd recommend taking a look at Singapore Math[0] to get an idea of what kids in those age ranges are actually capable of doing, provided that adults shed preconceptions that children ought to be "sheltered from hard scary stuff", and instead encourage them. So much this. I've managed to make learning fun for my three year old son. All too often we turn some daily scenario into a fun exercise and a well-meaning family member will exclaim "he can't possibly know that!". I assume they intend to shield him from the inevitable failure they believe I'm setting him up for by asking these questions, but he usually figures it out. And when he doesn't, he still gets a kick out of understanding it when we go through it together. I repeatedly ask them to not make these comments. The more often he hears them say these things, the more liable he is to start believing them himself and say "I can't figure this out because I'm only x years old". I believe that if kids were allowed to be challenged and excel at the things they show an interest in and predisposition to, the scholastic standard would be much higher. Instead of adults deciding what children of certain ages are "supposed to" be able to do and not to do. My biggest fear at the moment is for his excitement at learning being crushed when he starts school.
- TheHonk 5y ago
  > My biggest fear at the moment is for his excitement at learning being crushed when he starts school. That happened to my little brother. He was reading a lot of books before he started school, but somehow un-learned it while being there. "I can't read that because we haven't learned about the letter K, yet" was something you could hear him say.
  - jozvolskyef 5y ago
    Maybe try explaining to him that school and other institutions tend to optimize for the average person, so unless his goal is being average, he'll need to take responsibility.
thebiss 5y ago
My personal experience is very very different, and is why I "quip these are too hard." I explain below, but since Singapore was mentioned, I need to ask a cultural question first: What do parents and teachers from outside the US do when a child DOESN'T understand math? How is math taught so that kids don't end up crying, getting sick, or hating themselves when faced with math problems? Or is there selection bias: it does happen, but "those kids" are left behind, and never seen by the rest of the world? My personal experience with kids and math: I'm in the US, and have one child who repeatedly could not complete math work during school, and would bawl and protest how stupid they were when given math homework at home. Completing it would take hours. Far behind, they could not multiply at age 8 or do fractions at 11. Tutors couldn't cover in an hour what other students finish in 10 minutes. Yet doctors indicated there's no learning disability. So this leads to my perspective: a prodigious child may certainly be capable of these and enjoy the challenge. But for some others, this may succeed in making them feel worse about themselves, because it's yet another example math they don't understand.
- halgir 5y ago
  I appreciate this point. But I don't think it's about setting extremely high standards across the board and leaving those who can't keep up behind. For me it's about losing the mindset that children of certain ages are incapable of doing certain things and deliberately holding them back (with nothing but the best intentions I'm sure). I have a friend who is a published poet and prosaic genius. But she literally cannot solve 2x=4. I'm not being hyperbolic. Pushing her in math as a child would probably have been catastrophic for her emotional well being. But limiting her in other skill sets (like literature) would be equally catastrophic in terms of wasted potential (and the well being that comes with excelling at something you care about).
  - themodelplumber 5y ago
    I agree. There is a lot of Be Like Me in the thread. The arguments need to be exposed to more diverse psychological scrutiny than is available on HN. We can care for students, emphasize their gifts, provide math education when it is desired, AND achieve good educational outcomes. These aren't mutually exclusive...
ransom1538 5y ago
These seem pretty challenging for a 5 year old. I am pretty sure if I was interviewing senior engineers this would stump them - and I would get walk outs: https://i.imgur.com/lRfEQOs.png https://i.imgur.com/lRfEQOs.png (from his book).
- HarryHirsch 5y ago
  You'd get walkouts? Any person with normal intelligence and average facility with math realizes within 3 minutes that (2*3)-5 = 1. People who have trouble with that problem have no guts.
  - Arnavion 5y ago
    random1538 didn't say what kind of engineers they were hiring, but if it was software engineers I'd be confused by it too. I know the solution to the problem, but only because I've seen it before and thus know the method to solve it. If they were hiring cooks / chemists / anyone that is expected to have experience with measuring liquid volumes, it might make sense to assume they have the experience needed to solve this problem.
    - deleted 5y ago
      [deleted]
  - thereare5lights 5y ago
    This requires realizing that you can stop pouring. It isn't as in your face obvious as you're making it out to be.
    - bigyikes 5y ago
      The solution became immediately obvious to me after reading your comment. This leads me to believe that the question isn’t testing for math ability nor intelligence. It just requires you to realize the trick. Maybe it tests for creativity / lateral thinking ability?
harperlee 5y ago
Sure, but the actual document states that The book is addressed to school and university students, teachers, parents – to everybody who considers the thinking culture an essential part of the personality development. Not sure where the 5yold number came from.
dxbydt 5y ago
Singapore Math & Prodigy are good recommendations. I'd also add IXL, Beast Academy, AOPS & RSM to the mix. Our public school here in Indiana was training middle schoolers for the Math Bowl statewide competition. I spoke to one of the teachers at the school and volunteered to help. She handed me a bunch of math problems. I quickly hacked up a web app to help the students train. Imagine my shock & surprise when a month later, our humble public school team took home the first prize[1], in a tournament that had some 300+ schools, many of which had private coaches. Congressmen from Indianapolis drove down to our little town to hand over the trophy & plaques! Since then, I do a weekly zoom session with those middle schoolers, sort of a Summer Math program. We work through AMC 8/10 problems & finish up with a friendly competition on the web app so I can track their progress. I believe competition math can be a lot of fun if taught well. [1] https://twitter.com/Hoosier47906/status/1400221783173775369 https://twitter.com/Hoosier47906/status/1400221783173775369
SilasX 5y ago
I agree with your general point, but if you want to give math problems that inspire creative, rigorous thought, you need to make them very clear, with as little ambiguity and assumed knowledge as possible. These problems don't do that. Examples: Kopecks being indivisible, there being only one book at a specific price in the first problem, books being on a shelf in a specific order (13). >>A brick weighs one pound and half the brick. How many pounds does the brick weigh? As a native speaker, that doesn't even make sense, and I don't know a natural way to express it that doesn't do most of the work of the problem. (Another comment indicates it means "a brick's weight is equal to half of a brick plus one pound".)
- cema 5y ago
  Well, it sounds awkward in Russian as well as English but it works.
roamingdave 5y ago
I couldn't agree more. It's always interesting seeing people shelter their kids from thinking that might become frustrating. I forgot who said it but there was a quote like: "don't be afraid to push your brain, you won't break it!" Of course someone will reply to this talking about burnout which is real but a common sense approach to introducing cognitively difficult topics to kids is very different from that. A couple of weeks ago one of mine (4yo) asked what the 'D' in 2D and 3D is since I had mentioned it to her while watching a movie. I took out a small ruler and went over to a corner of the TV unit. We then put the ruler along one edge and I explained how that's one measurement or 1D and how we can make a dot with a marker anywhere along that line. We then repeated for the next perpendicular edge and said that it's now two measurements or 2D. You can see where this is going. After 3D we talked about how we can now put a point anywhere in this imaginary cube. She responded by asking how 4 rulers would look! Kids are incredible and we frequently underestimate them. (edited to add the age in there since it's relevant)
- gibba999 5y ago
  I don't think people understand burnout. If your kid is studying 16 hours per day, bored, you're gonna get burnout. Burnout isn't about challenge -- which is good. If you have dinner table conversations about hard topics, that isn't leading to burnout.
deleted 5y ago
[deleted]

by lhorie 5y ago

Koshkin 5y ago

> 1 dog year is about 7 human years This is the average; the correspondence is not linear...

inamiyar 5y ago
Probably true, but the point was that the daughter was capable of quick multiplication, the age of the dog was..decidedly a minor detail.
whimsicalism 5y ago
Classic HN
- MontyCarloHall 5y ago
  Parent comment belongs in the hall of fame right next to the classic "Dropbox is trivial—it’s just an FTP server under version control": https://news.ycombinator.com/item?id=8863 https://news.ycombinator.com/item?id=8863
- ThePadawan 5y ago
  I see your "classic HN" and counter with a "I'm one of today's lucky 10000!". I was taught the 7 years rule as a kid and only learned as an adult that it's an average, not true for all dog breeds.
  - msrenee 5y ago
    It's also not really true for young dogs. A 1-year-old dog of most breeds is reproductively mature, whereas a 7-year-old human is not.

loonster 5y ago

Which singaporemath? There are several.

gnicholas 5y ago
Yeah, would be interested to see an example other than the link provided, which seems to be to purchase workbooks. Are there any good free resources (or free to try/evaluate) online? I heard about Singaporean math a while ago and looked up some youtube videos. It seemed like they showed clever ways to solve highly stylized problems, but nothing that would actually ever come up in the real world. To be fair, I only watched 3 videos, but they were all from different channels, so I assumed they were a decent sample of what Singaporean math is about.
lhorie 5y ago
We bought the Intensive Practice series[0], and paced study time at a couple of pages a day (which takes about 20-30 mins), semi-supervised (i.e. kids mostly work on their own, but if they don't understand something, we help clarify). It does take some hand holding at the beginning though. [0] https://shop.singaporemath.com/index.php/product-category/supplementary-and-other-math/math-supplementary/singapore-math-intensive-practice/ https://shop.singaporemath.com/index.php/product-category/su...
- loonster 5y ago
  Interesting. So was this a supplement to math learned at school or was it the primary math? I was expecting you to name dimensions or one if the other programs they offer.
  - lhorie 5y ago
    It isn't related to school curriculum (our kids go to US public school). It's supplemental in the sense that they get to practice more math exercises than a kid that only relies on school/common core curriculum.
  - koolba 5y ago
    Most school math is pathetically slow. IIRC, they don’t learn algebra till 8th or 9th grade and even then spend an entire year on it.

halgir 5y ago

> I'd recommend taking a look at Singapore Math[0] to get an idea of what kids in those age ranges are actually capable of doing, provided that adults shed preconceptions that children ought to be "sheltered from hard scary stuff", and instead encourage them. So much this. I've managed to make learning fun for my three year old son. All too often we turn some daily scenario into a fun exercise and a well-meaning family member will exclaim "he can't possibly know that!". I assume they intend to shield him from the inevitable failure they believe I'm setting him up for by asking these questions, but he usually figures it out. And when he doesn't, he still gets a kick out of understanding it when we go through it together. I repeatedly ask them to not make these comments. The more often he hears them say these things, the more liable he is to start believing them himself and say "I can't figure this out because I'm only x years old". I believe that if kids were allowed to be challenged and excel at the things they show an interest in and predisposition to, the scholastic standard would be much higher. Instead of adults deciding what children of certain ages are "supposed to" be able to do and not to do. My biggest fear at the moment is for his excitement at learning being crushed when he starts school.

TheHonk 5y ago
> My biggest fear at the moment is for his excitement at learning being crushed when he starts school. That happened to my little brother. He was reading a lot of books before he started school, but somehow un-learned it while being there. "I can't read that because we haven't learned about the letter K, yet" was something you could hear him say.
- jozvolskyef 5y ago
  Maybe try explaining to him that school and other institutions tend to optimize for the average person, so unless his goal is being average, he'll need to take responsibility.

thebiss 5y ago

My personal experience is very very different, and is why I "quip these are too hard." I explain below, but since Singapore was mentioned, I need to ask a cultural question first: What do parents and teachers from outside the US do when a child DOESN'T understand math? How is math taught so that kids don't end up crying, getting sick, or hating themselves when faced with math problems? Or is there selection bias: it does happen, but "those kids" are left behind, and never seen by the rest of the world? My personal experience with kids and math: I'm in the US, and have one child who repeatedly could not complete math work during school, and would bawl and protest how stupid they were when given math homework at home. Completing it would take hours. Far behind, they could not multiply at age 8 or do fractions at 11. Tutors couldn't cover in an hour what other students finish in 10 minutes. Yet doctors indicated there's no learning disability. So this leads to my perspective: a prodigious child may certainly be capable of these and enjoy the challenge. But for some others, this may succeed in making them feel worse about themselves, because it's yet another example math they don't understand.

halgir 5y ago
I appreciate this point. But I don't think it's about setting extremely high standards across the board and leaving those who can't keep up behind. For me it's about losing the mindset that children of certain ages are incapable of doing certain things and deliberately holding them back (with nothing but the best intentions I'm sure). I have a friend who is a published poet and prosaic genius. But she literally cannot solve 2x=4. I'm not being hyperbolic. Pushing her in math as a child would probably have been catastrophic for her emotional well being. But limiting her in other skill sets (like literature) would be equally catastrophic in terms of wasted potential (and the well being that comes with excelling at something you care about).
- themodelplumber 5y ago
  I agree. There is a lot of Be Like Me in the thread. The arguments need to be exposed to more diverse psychological scrutiny than is available on HN. We can care for students, emphasize their gifts, provide math education when it is desired, AND achieve good educational outcomes. These aren't mutually exclusive...

ransom1538 5y ago

These seem pretty challenging for a 5 year old. I am pretty sure if I was interviewing senior engineers this would stump them - and I would get walk outs: https://i.imgur.com/lRfEQOs.png https://i.imgur.com/lRfEQOs.png (from his book).

HarryHirsch 5y ago
You'd get walkouts? Any person with normal intelligence and average facility with math realizes within 3 minutes that (2*3)-5 = 1. People who have trouble with that problem have no guts.
- Arnavion 5y ago
  random1538 didn't say what kind of engineers they were hiring, but if it was software engineers I'd be confused by it too. I know the solution to the problem, but only because I've seen it before and thus know the method to solve it. If they were hiring cooks / chemists / anyone that is expected to have experience with measuring liquid volumes, it might make sense to assume they have the experience needed to solve this problem.
  - deleted 5y ago
    [deleted]
- thereare5lights 5y ago
  This requires realizing that you can stop pouring. It isn't as in your face obvious as you're making it out to be.
  - bigyikes 5y ago
    The solution became immediately obvious to me after reading your comment. This leads me to believe that the question isn’t testing for math ability nor intelligence. It just requires you to realize the trick. Maybe it tests for creativity / lateral thinking ability?

harperlee 5y ago

Sure, but the actual document states that The book is addressed to school and university students, teachers, parents – to everybody who considers the thinking culture an essential part of the personality development. Not sure where the 5yold number came from.

dxbydt 5y ago

Singapore Math & Prodigy are good recommendations. I'd also add IXL, Beast Academy, AOPS & RSM to the mix. Our public school here in Indiana was training middle schoolers for the Math Bowl statewide competition. I spoke to one of the teachers at the school and volunteered to help. She handed me a bunch of math problems. I quickly hacked up a web app to help the students train. Imagine my shock & surprise when a month later, our humble public school team took home the first prize[1], in a tournament that had some 300+ schools, many of which had private coaches. Congressmen from Indianapolis drove down to our little town to hand over the trophy & plaques! Since then, I do a weekly zoom session with those middle schoolers, sort of a Summer Math program. We work through AMC 8/10 problems & finish up with a friendly competition on the web app so I can track their progress. I believe competition math can be a lot of fun if taught well. [1] https://twitter.com/Hoosier47906/status/1400221783173775369 https://twitter.com/Hoosier47906/status/1400221783173775369

SilasX 5y ago

I agree with your general point, but if you want to give math problems that inspire creative, rigorous thought, you need to make them very clear, with as little ambiguity and assumed knowledge as possible. These problems don't do that. Examples: Kopecks being indivisible, there being only one book at a specific price in the first problem, books being on a shelf in a specific order (13). >>A brick weighs one pound and half the brick. How many pounds does the brick weigh? As a native speaker, that doesn't even make sense, and I don't know a natural way to express it that doesn't do most of the work of the problem. (Another comment indicates it means "a brick's weight is equal to half of a brick plus one pound".)

cema 5y ago
Well, it sounds awkward in Russian as well as English but it works.

roamingdave 5y ago

I couldn't agree more. It's always interesting seeing people shelter their kids from thinking that might become frustrating. I forgot who said it but there was a quote like: "don't be afraid to push your brain, you won't break it!" Of course someone will reply to this talking about burnout which is real but a common sense approach to introducing cognitively difficult topics to kids is very different from that. A couple of weeks ago one of mine (4yo) asked what the 'D' in 2D and 3D is since I had mentioned it to her while watching a movie. I took out a small ruler and went over to a corner of the TV unit. We then put the ruler along one edge and I explained how that's one measurement or 1D and how we can make a dot with a marker anywhere along that line. We then repeated for the next perpendicular edge and said that it's now two measurements or 2D. You can see where this is going. After 3D we talked about how we can now put a point anywhere in this imaginary cube. She responded by asking how 4 rulers would look! Kids are incredible and we frequently underestimate them. (edited to add the age in there since it's relevant)

gibba999 5y ago
I don't think people understand burnout. If your kid is studying 16 hours per day, bored, you're gonna get burnout. Burnout isn't about challenge -- which is good. If you have dinner table conversations about hard topics, that isn't leading to burnout.

deleted 5y ago

[deleted]