6 ms·

Six-year-olds know multiplication?

by warent 3y ago

jasonjayr 3y ago
Some do, yes. If they have an aptitude for basic sums then pointing out that 3 x 3 is the same as 3 + 3 + 3 sets them down the right path ...
- hammyhavoc 3y ago
  I had it explained at a very early age as "three lots of three", and to imagine it like three boxes of three ice-creams. Treating the multiplication symbol as one would to indicate quantity in a list, thus calculating how many ice-creams there are.
  - aaronharnly 3y ago
    Found the Brit! As an American I’d never heard the “lots of __” phrasing until I watched Numberblocks (a British show) with my kid…
    - deleted 3y ago
      [deleted]
    - scotteric 3y ago
      Pharmaceuticals and other manufactured goods are sometimes referred to in 'lots' meaning a batch.
    - logifail 3y ago
      > Numberblocks We don't live in the UK but our kids watch Numberblocks. Our youngest started rattling off all kinds of number stuff which I know for sure she hasn't yet encountered in school. Me: Wow ... how do you know that? Her: Numberblocks! Me: Umm ... OK!
    - technothrasher 3y ago
      I've never watched Numberblocks, but I do like to watch a good game of Numberwang!
      - hammyhavoc 3y ago
        That's Numberwang! > Numberwang theme tune
- adastra22 3y ago
  I think you need to spend more time around six year olds ;)
  - Eisenstein 3y ago
    My 6 year old nephew can do primes and I taught him to count and add in binary.
    - ineedasername 3y ago
      I'm not sure that HN readers-- a community that will disproportionately skew towards folks educated &/or employed in STEM fields-- are indicative of other people's contact with 6-year old kids.
- 13of40 3y ago
  The technique used by the Oregon public school system in the 80s went something like "Hand the child a 10x10 grid of numbers, then tell them, absent of any other context, that they must be memorized." I like your way better.
  - retrac 3y ago
    Ontario's 1990s curriculum was pretty awesome. The idea of dimension and sets were both introduced simultaneously and joined, using multiplication. Started in the 2nd grade and they just kept elaborating. Number lines and groups of items. (Tied it into geometry, too. Square numbers came up by at least 4th grade.) What is 3 x 3 but moving 3 units, 3 times in one dimension? Now, memorize these tables up to 12 x 12, you won't always have a calculator at hand.
    - mulmen 3y ago
      > you won't always have a calculator at hand. I do though. I still blow minds when I put my iPhone calculator in scientific mode. Math education is important for many reasons. But teaching it as a practical survival skill using no tools does a disservice to the student. Either it is useful as a problem solving exercise or it is a practical skill that should take advantage of tools. "Just memorize this stuff" isn't useful because it backfires into hating learning. Nothing about math makes it ideal for memorization and none of my math teachers spent any time on study skills.
      - wpietri 3y ago
        Nah. As somebody who ends up doing a ton of mental math, I think it's valuable. Yes, they should also learn how to use tools. But developing a feel for numbers is valuable, and I think that is much harder to do if one always relies on a calculator. (And yes, of course, this should be learned in a way that doesn't involve the kids hating it. But that's possible.)
        mulmen 3y ago
        Phrases like "you won't always have a calculator at hand" only serve to erode trust in the educator. It's simply not compelling, and for all practical intents and purposes is untrue. Even on backpacking trips I have a cell phone, even if it is off. If you believe mental math is useful then say that and explain the benefits. Students can smell a lie.
hnlmorg 3y ago
My 6 year old is learning multiplication at the moment.
Bootvis 3y ago
The mathematically curious probably do. I did.
abofh 3y ago
Some even post on HN!
- hammyhavoc 3y ago
  That explains some stuff!
deleted 3y ago
[deleted]
gorkish 3y ago
They dont usually know formal arithmetic multiplication but they well understand the concepts of repeated addition and subtraction. Most places in the world do start teaching multiplication at age 6/7.
gus_massa 3y ago
My six-year-old likes Numberblocks https://en.wikipedia.org/wiki/Numberblocks https://en.wikipedia.org/wiki/Numberblocks https://www.google.com/search?q=Numberblocks https://www.google.com/search?q=Numberblocks . She knows a little more about multiplication than what I expected, probably 2x and 3x when x is small, (but as other sibling comments say not a general theory or how to calculate 287263 * 137167).
- ineedasername 3y ago
  Number blocks is a great show, my 5yo watches and, being entertained by it, absorbs more than I could easily get him to sit still for. Then he asks me questions about what he watched and is more engaged with my answers as a result. Making a subject "fun" is alright, but making it entertaining (IME) makes for more productive engagement.
ddispaltro 3y ago
yeah they do counting by 5's counting by 2s, etc. So how many 5s in 20, they say four, yay!
jlokier 3y ago
Yes. Simple multiplication and even division and fractions are part of the national curriculum at ages 5 to 6 in the UK. Which is about the age when I remember learning them decades ago too. I think we learned how to add and multiply fractions too. By age 6 to 7 they're expected to understand that addition and multiplication are commutative, while subtraction and division are not.
apomekhanes 3y ago
Yes, I learned long division fairly well around that time. I was fortunate (/ disruptive) enough to be sent to a "Montessori school". Long division was definitely pushing it when I was about 5 or 6, but, honestly, given steadier instruction in math starting earlier, I suspect I could have been entirely solid on long division by that time and moving on to algebra. And, I think this is true for a reasonable proportion of children. My experience, ultimately, was much less ... 'high-quality', let's say. When I left the Montessori school (by 3rd grade), I learned practically no math from then until after high school. First, in normal 'elementary' school (US), multiplication was still being covered in 6th grade. Then, suddenly (from my perspective), letters were being brought into the picture in 7th or 8th grade. So, in my arc, math started to not make sense, at all. From my perspective, we had spent multiple years on multiplication and long division, which I already understood very well by the end of 2nd grade ... so, there was the period where I basically didn't learn anything, where it seemed like we'd reached the end of math or something. Or, perhaps, like there were some sort of subtleties remaining in multiplication and division. It just gave me a chance to be bored with all of it, boredom correlates heavily with mistakes with kids with attention issues (IMO), this fed into some sort of doubts about my understanding of everything etc., and then, suddenly, there was new material again starting in 7th grade. Material that was 'mechanical', and that didn't seem to have explanations I could understand. Ultimately, I struggled along with that garbage through high school, then, after, took a course where we actually did PROOFS. Basic number theory stuff - modular arithmetic, etc. Bam, suddenly, the subject started to make sense. Typing this out actually makes me slightly angry. I'm not sure I previously connected it all together - why I had so much trouble with math for some years ... how this 'arc' was pretty much perfectly engineered to make math a problem, for me. In any case, schooling through high school can be a really low quality experience at times - for some students, subjects, etc. The math curricula, methods of teaching, and progression I was exposed to, worked together, in some sense, to make the subject a problem for me. To do almost the opposite of what was intended - to pretty well impede learning. There's no one factor in that story I can point to and say 'here, fix this' ... no one involved in the story was actively attempting to do anything other than what they thought was best or what they were required to do, but, the net result was honestly worse - I now believe (and believed some years ago, even without quite this analysis) - than if I'd just been given some selection of math material to pick from and been allowed some sort of semi-self directed coursework. Even better, though, if I'd simply had that course with proofs / basic number theory in, say, 8th grade ... guh, would have avoided so much pain, I'm pretty sure...

Six-year-olds know multiplication?

by warent 3y ago

Six-year-olds know multiplication?

Some do, yes. If they have an aptitude for basic sums then pointing out that 3 x 3 is the same as 3 + 3 + 3 sets them down the right path ...

hammyhavoc 3y ago
I had it explained at a very early age as "three lots of three", and to imagine it like three boxes of three ice-creams. Treating the multiplication symbol as one would to indicate quantity in a list, thus calculating how many ice-creams there are.
- aaronharnly 3y ago
  Found the Brit! As an American I’d never heard the “lots of __” phrasing until I watched Numberblocks (a British show) with my kid…
  - deleted 3y ago
    [deleted]
  - scotteric 3y ago
    Pharmaceuticals and other manufactured goods are sometimes referred to in 'lots' meaning a batch.
  - logifail 3y ago
    > Numberblocks We don't live in the UK but our kids watch Numberblocks. Our youngest started rattling off all kinds of number stuff which I know for sure she hasn't yet encountered in school. Me: Wow ... how do you know that? Her: Numberblocks! Me: Umm ... OK!
  - technothrasher 3y ago
    I've never watched Numberblocks, but I do like to watch a good game of Numberwang!
    - hammyhavoc 3y ago
      That's Numberwang! > Numberwang theme tune
adastra22 3y ago
I think you need to spend more time around six year olds ;)
- Eisenstein 3y ago
  My 6 year old nephew can do primes and I taught him to count and add in binary.
  - ineedasername 3y ago
    I'm not sure that HN readers-- a community that will disproportionately skew towards folks educated &/or employed in STEM fields-- are indicative of other people's contact with 6-year old kids.
13of40 3y ago
The technique used by the Oregon public school system in the 80s went something like "Hand the child a 10x10 grid of numbers, then tell them, absent of any other context, that they must be memorized." I like your way better.
- retrac 3y ago
  Ontario's 1990s curriculum was pretty awesome. The idea of dimension and sets were both introduced simultaneously and joined, using multiplication. Started in the 2nd grade and they just kept elaborating. Number lines and groups of items. (Tied it into geometry, too. Square numbers came up by at least 4th grade.) What is 3 x 3 but moving 3 units, 3 times in one dimension? Now, memorize these tables up to 12 x 12, you won't always have a calculator at hand.
  - mulmen 3y ago
    > you won't always have a calculator at hand. I do though. I still blow minds when I put my iPhone calculator in scientific mode. Math education is important for many reasons. But teaching it as a practical survival skill using no tools does a disservice to the student. Either it is useful as a problem solving exercise or it is a practical skill that should take advantage of tools. "Just memorize this stuff" isn't useful because it backfires into hating learning. Nothing about math makes it ideal for memorization and none of my math teachers spent any time on study skills.
    - wpietri 3y ago
      Nah. As somebody who ends up doing a ton of mental math, I think it's valuable. Yes, they should also learn how to use tools. But developing a feel for numbers is valuable, and I think that is much harder to do if one always relies on a calculator. (And yes, of course, this should be learned in a way that doesn't involve the kids hating it. But that's possible.)
      - mulmen 3y ago
        Phrases like "you won't always have a calculator at hand" only serve to erode trust in the educator. It's simply not compelling, and for all practical intents and purposes is untrue. Even on backpacking trips I have a cell phone, even if it is off. If you believe mental math is useful then say that and explain the benefits. Students can smell a lie.

hnlmorg 3y ago

My 6 year old is learning multiplication at the moment.

Bootvis 3y ago

The mathematically curious probably do. I did.

abofh 3y ago

Some even post on HN!

hammyhavoc 3y ago
That explains some stuff!

deleted 3y ago

[deleted]

gorkish 3y ago

They dont usually know formal arithmetic multiplication but they well understand the concepts of repeated addition and subtraction. Most places in the world do start teaching multiplication at age 6/7.

gus_massa 3y ago

My six-year-old likes Numberblocks https://en.wikipedia.org/wiki/Numberblocks https://en.wikipedia.org/wiki/Numberblocks https://www.google.com/search?q=Numberblocks https://www.google.com/search?q=Numberblocks . She knows a little more about multiplication than what I expected, probably 2x and 3x when x is small, (but as other sibling comments say not a general theory or how to calculate 287263 * 137167).

ineedasername 3y ago
Number blocks is a great show, my 5yo watches and, being entertained by it, absorbs more than I could easily get him to sit still for. Then he asks me questions about what he watched and is more engaged with my answers as a result. Making a subject "fun" is alright, but making it entertaining (IME) makes for more productive engagement.

ddispaltro 3y ago

yeah they do counting by 5's counting by 2s, etc. So how many 5s in 20, they say four, yay!

jlokier 3y ago

Yes. Simple multiplication and even division and fractions are part of the national curriculum at ages 5 to 6 in the UK. Which is about the age when I remember learning them decades ago too. I think we learned how to add and multiply fractions too. By age 6 to 7 they're expected to understand that addition and multiplication are commutative, while subtraction and division are not.

apomekhanes 3y ago

Yes, I learned long division fairly well around that time. I was fortunate (/ disruptive) enough to be sent to a "Montessori school". Long division was definitely pushing it when I was about 5 or 6, but, honestly, given steadier instruction in math starting earlier, I suspect I could have been entirely solid on long division by that time and moving on to algebra. And, I think this is true for a reasonable proportion of children. My experience, ultimately, was much less ... 'high-quality', let's say. When I left the Montessori school (by 3rd grade), I learned practically no math from then until after high school. First, in normal 'elementary' school (US), multiplication was still being covered in 6th grade. Then, suddenly (from my perspective), letters were being brought into the picture in 7th or 8th grade. So, in my arc, math started to not make sense, at all. From my perspective, we had spent multiple years on multiplication and long division, which I already understood very well by the end of 2nd grade ... so, there was the period where I basically didn't learn anything, where it seemed like we'd reached the end of math or something. Or, perhaps, like there were some sort of subtleties remaining in multiplication and division. It just gave me a chance to be bored with all of it, boredom correlates heavily with mistakes with kids with attention issues (IMO), this fed into some sort of doubts about my understanding of everything etc., and then, suddenly, there was new material again starting in 7th grade. Material that was 'mechanical', and that didn't seem to have explanations I could understand. Ultimately, I struggled along with that garbage through high school, then, after, took a course where we actually did PROOFS. Basic number theory stuff - modular arithmetic, etc. Bam, suddenly, the subject started to make sense. Typing this out actually makes me slightly angry. I'm not sure I previously connected it all together - why I had so much trouble with math for some years ... how this 'arc' was pretty much perfectly engineered to make math a problem, for me. In any case, schooling through high school can be a really low quality experience at times - for some students, subjects, etc. The math curricula, methods of teaching, and progression I was exposed to, worked together, in some sense, to make the subject a problem for me. To do almost the opposite of what was intended - to pretty well impede learning. There's no one factor in that story I can point to and say 'here, fix this' ... no one involved in the story was actively attempting to do anything other than what they thought was best or what they were required to do, but, the net result was honestly worse - I now believe (and believed some years ago, even without quite this analysis) - than if I'd just been given some selection of math material to pick from and been allowed some sort of semi-self directed coursework. Even better, though, if I'd simply had that course with proofs / basic number theory in, say, 8th grade ... guh, would have avoided so much pain, I'm pretty sure...