4 ms·

Worth noting that since Common Core came out in 2010, this is how students in most US states are taught multiplication, only instead of partitioning by powers o

Worth noting that since Common Core came out in 2010, this is how students in most US states are taught multiplication, only instead of partitioning by powers of two they partition by decimal digits (e.g. 4 * 56 --> 4 * 50 + 4 * 6). Conceptualizing multiplication this way equips you well for handling large numbers in your head. A high school student today might be shocked to see the sort of complexity third- and fourth-graders in prior generations used to contend with for basic operations: 4 * 56 ---> 4 * 6 -> carry the 2, keep the 4 -> 4 * 5 -> (previous step's result) + (carried 2) -> (previous steps' result) * 10 + (kept 4) This algorithm had to be expanded for each additional nonzero digit in each operand. Most of us who did well before Common Core passively learned the Common Core method independently, out of necessity. Lattice method is badass though.

seri4l 4y ago
For some reason we had something like common core math in my elementary school in the early 2000s and I just had a traumatic flashback. Teacher forced us do EVERY sum like this: 17890 + 456 = 1 x 10000 + 7 x 1000 + 8 x 100 + 7 x 10 + 0 x 1 + 4 x 100 + 5 x 10 + 6 x 1 = 1 x 10000 + 7 x 1000 + (8 + 4) x 100 + (9 + 5) x 10 + (0 + 6) x 1 = 1 x 10000 + 7 x 1000 + 12 x 100 + 14 x 10 + 0 x 1 = 10000 + 7000 + 1200 + 140 + 6 = 10000 + 7000 + 1 x 1000 + 2 x 100 + 1 x 100 + 4 x 10 + 6 = 10000 + 7000 + 1000 + 200 + 100 + 40 + 6 = 10000 + 8000 + 300 + 40 + 6 = 18346 We had to write down everything and weren't allowed to skip ANY step, let alone write down the answer directly. Being taught sums and multiplications graphically is cool, I guess, but this was outright psychological torture.
- replygirl 4y ago
  My English teacher in the seventh grade had us write a short story without a single pronoun and without repeating any adjective, verb, or noun. It was basically a hazing, and probably the biggest factor in my being an ok writer
  - quacked 4y ago
    Wait, did it reduce the quality of your writing or increase it?
    - replygirl 4y ago
      It was a helpful exercise for stretching one's ability to express meaning. The constraints were there to force you to write more thoughtfully; the stories were probably trash even for that writing level, but that pacing and practice were what mattered
- kevin_thibedeau 4y ago
  This has some value in reinforcing that decimal number representation is just a shorthand for polynomials but definitely misguided as a "normal" method of addition.
unnouinceput 4y ago
Now do the necessary steps to see how many it takes to multiply large numbers, let's say 1'785'375 * 7'367'594, in one method vs. the other and then comeback and tell me again if you'll ever use anything else than lattice one.
- replygirl 4y ago
  I hate when I'm trying to figure out how many guests my friend's wedding venue will fit with 1,785,375 to a table and 7,367,594 tables available, Common Core fails me and I've forgotten how to lattice ;)
- bee_rider 4y ago
  If I needed to multiply a pair of seven digit numbers, I would probably approximate them by dropping all but, say, the two most significant digits of each. If that amount of wrongness is a big problem, then I probably should have used a calculator in the first place.
mgdlbp 4y ago
For anyone else not making sense of the old method, that's because it should have '(previous step's result) + (carried 2)'
- replygirl 4y ago
  woops thank you
cyberax 4y ago
> A high school student today might be shocked to see the sort of complexity third- and fourth-graders in prior generations used to contend with for basic operations Really? The classic multiplication algorithm is completely mechanistic. You just need to learn the multiplication table and then even a trained monkey can do it. Then once a student learns and practices the mechanistic way, you can easily explain the math that lays beyond it. The inverse way doesn't really work. I'm working with high-school students, and I'm already seeing the effects of people who can explain me how the algorithm works, but then struggle to actually multiply even 3-digit numbers. Oh, and the lattice multiplication is the worst. It completely obscures the math behind it.
- kevingadd 4y ago
  Some people can't memorize times tables, so the common core algorithm might be more generally applicable for those people even if it's less efficient than using a table. There's some value in finding an approach that works for everyone as an educator instead of one that works for Most if you can do that, I think. In CPU terms, maybe you don't always have the die space for all the tables you need to make a blazing fast implementation of mul or sin or cos, but you can afford to fit a slow iterative solution instead.
  - cyberax 4y ago
    > Some people can't memorize times tables Well, perhaps then schools need to be fixed? Memorization is a skill like anything else, and it can be trained via a variety of ways (memory palaces, mnemonics, writing stuff down by hand). If a student can't remember ~20 non-trivial entries in the multiplication table, then they likely will struggle with anything else non-trivial. > There's some value in finding an approach that works for everyone as an educator instead of one that works for Most if you can do that, I think. Also known as "dumbing down the education". There are trade-offs everywhere. The lattice method simplifies bookkeeping on paper, but try to visualize it for mental math and you'll likely fail. While the classic textbook algorithm is fairly easy to do. So the lattice method is optimized for a use-case that never really matters in practice: being able to multiply numbers on a piece of paper, while not having access to a calculator. While it's pessimized for a use-case that actually matters once in a while: pure mental math.
User23 4y ago
> only instead of partitioning by powers of two they partition by decimal digits (e.g. 4 * 56 --> 4 * 50 + 4 * 6). When I was in secondary school we called this “factoring.” Distributivity is great.
User23 4y ago
> A high school student today might be shocked to see the sort of complexity third- and fourth-graders in prior generations used to contend with for basic operations Evidently a college graduate today would be shocked to see the sort of complexity a high school student was expected to master, if the paper of record is to be trusted[1]. [1] http://graphics8.nytimes.com/packages/pdf/education/harvardexam.pdf http://graphics8.nytimes.com/packages/pdf/education/harvarde...
- mistrial9 4y ago
  humorous, but notice how few subjects there are in that exam. Students in that era were not subjects of relentless streams of ad images, entertainment or other media. There is no conclusion to the experiment of media that has emerged in the last decades, with regard to the attention span, development years for education, or emotional coping.
MichaelRo 4y ago
I dunno. I never heard of the "common core" multiplication algorithm and my 3rd grader kid only knows "regular" multiplication. He grasped it from the first few examples and had no problems with it. "Common core" seems more unnecessary complication than the regular algo which works on arbitrary numbers: 7593 x 267: everything done in one go compared to tons of workarounds and additions. Again, my kiddo does these without blinking and I see no reason to teach him differently.
KingOfCoders 4y ago
Being in elementary in the 70s I do two things: - On paper I do 46 etc. - In my head I always did 450 + 4*6

seri4l 4y ago

For some reason we had something like common core math in my elementary school in the early 2000s and I just had a traumatic flashback. Teacher forced us do EVERY sum like this: 17890 + 456 = 1 x 10000 + 7 x 1000 + 8 x 100 + 7 x 10 + 0 x 1 + 4 x 100 + 5 x 10 + 6 x 1 = 1 x 10000 + 7 x 1000 + (8 + 4) x 100 + (9 + 5) x 10 + (0 + 6) x 1 = 1 x 10000 + 7 x 1000 + 12 x 100 + 14 x 10 + 0 x 1 = 10000 + 7000 + 1200 + 140 + 6 = 10000 + 7000 + 1 x 1000 + 2 x 100 + 1 x 100 + 4 x 10 + 6 = 10000 + 7000 + 1000 + 200 + 100 + 40 + 6 = 10000 + 8000 + 300 + 40 + 6 = 18346 We had to write down everything and weren't allowed to skip ANY step, let alone write down the answer directly. Being taught sums and multiplications graphically is cool, I guess, but this was outright psychological torture.

replygirl 4y ago
My English teacher in the seventh grade had us write a short story without a single pronoun and without repeating any adjective, verb, or noun. It was basically a hazing, and probably the biggest factor in my being an ok writer
- quacked 4y ago
  Wait, did it reduce the quality of your writing or increase it?
  - replygirl 4y ago
    It was a helpful exercise for stretching one's ability to express meaning. The constraints were there to force you to write more thoughtfully; the stories were probably trash even for that writing level, but that pacing and practice were what mattered
kevin_thibedeau 4y ago
This has some value in reinforcing that decimal number representation is just a shorthand for polynomials but definitely misguided as a "normal" method of addition.

unnouinceput 4y ago

Now do the necessary steps to see how many it takes to multiply large numbers, let's say 1'785'375 * 7'367'594, in one method vs. the other and then comeback and tell me again if you'll ever use anything else than lattice one.

replygirl 4y ago
I hate when I'm trying to figure out how many guests my friend's wedding venue will fit with 1,785,375 to a table and 7,367,594 tables available, Common Core fails me and I've forgotten how to lattice ;)
bee_rider 4y ago
If I needed to multiply a pair of seven digit numbers, I would probably approximate them by dropping all but, say, the two most significant digits of each. If that amount of wrongness is a big problem, then I probably should have used a calculator in the first place.

mgdlbp 4y ago

For anyone else not making sense of the old method, that's because it should have '(previous step's result) + (carried 2)'

replygirl 4y ago
woops thank you

cyberax 4y ago

> A high school student today might be shocked to see the sort of complexity third- and fourth-graders in prior generations used to contend with for basic operations Really? The classic multiplication algorithm is completely mechanistic. You just need to learn the multiplication table and then even a trained monkey can do it. Then once a student learns and practices the mechanistic way, you can easily explain the math that lays beyond it. The inverse way doesn't really work. I'm working with high-school students, and I'm already seeing the effects of people who can explain me how the algorithm works, but then struggle to actually multiply even 3-digit numbers. Oh, and the lattice multiplication is the worst. It completely obscures the math behind it.

kevingadd 4y ago
Some people can't memorize times tables, so the common core algorithm might be more generally applicable for those people even if it's less efficient than using a table. There's some value in finding an approach that works for everyone as an educator instead of one that works for Most if you can do that, I think. In CPU terms, maybe you don't always have the die space for all the tables you need to make a blazing fast implementation of mul or sin or cos, but you can afford to fit a slow iterative solution instead.
- cyberax 4y ago
  > Some people can't memorize times tables Well, perhaps then schools need to be fixed? Memorization is a skill like anything else, and it can be trained via a variety of ways (memory palaces, mnemonics, writing stuff down by hand). If a student can't remember ~20 non-trivial entries in the multiplication table, then they likely will struggle with anything else non-trivial. > There's some value in finding an approach that works for everyone as an educator instead of one that works for Most if you can do that, I think. Also known as "dumbing down the education". There are trade-offs everywhere. The lattice method simplifies bookkeeping on paper, but try to visualize it for mental math and you'll likely fail. While the classic textbook algorithm is fairly easy to do. So the lattice method is optimized for a use-case that never really matters in practice: being able to multiply numbers on a piece of paper, while not having access to a calculator. While it's pessimized for a use-case that actually matters once in a while: pure mental math.

User23 4y ago

> only instead of partitioning by powers of two they partition by decimal digits (e.g. 4 * 56 --> 4 * 50 + 4 * 6). When I was in secondary school we called this “factoring.” Distributivity is great.

User23 4y ago

> A high school student today might be shocked to see the sort of complexity third- and fourth-graders in prior generations used to contend with for basic operations Evidently a college graduate today would be shocked to see the sort of complexity a high school student was expected to master, if the paper of record is to be trusted[1]. [1] http://graphics8.nytimes.com/packages/pdf/education/harvardexam.pdf http://graphics8.nytimes.com/packages/pdf/education/harvarde...

mistrial9 4y ago
humorous, but notice how few subjects there are in that exam. Students in that era were not subjects of relentless streams of ad images, entertainment or other media. There is no conclusion to the experiment of media that has emerged in the last decades, with regard to the attention span, development years for education, or emotional coping.

MichaelRo 4y ago

I dunno. I never heard of the "common core" multiplication algorithm and my 3rd grader kid only knows "regular" multiplication. He grasped it from the first few examples and had no problems with it. "Common core" seems more unnecessary complication than the regular algo which works on arbitrary numbers: 7593 x 267: everything done in one go compared to tons of workarounds and additions. Again, my kiddo does these without blinking and I see no reason to teach him differently.

KingOfCoders 4y ago

Being in elementary in the 70s I do two things: - On paper I do 46 etc. - In my head I always did 450 + 4*6