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Comment by philh | Hacker News Reader

I find the comments that people can't understand this method to be kinda bizarre.

I haven't heard of common core, but after a few moments of looking at this, the algorithm becomes clear: 432 is between 80 and 800, so repeatedly subtract 80 until you get below 80. Then repeatedly subtract 8. Keep track of the subtractions you're making, and add them up.

Slower and more verbose than the method I learned, and I'm not defending (or condemming) it, but I kind of wonder if some people have a reaction like "this is not what I would have expected to see, and I can't immediately understand it, so it sucks".

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I think the problem is that the parents were taught how to do things, not how to think about things.

Nowadays, you don't learn long division so you can divide two numbers given a large amount of time and a big sheet of paper. Your computer will do that for you. You learn it as a precursor to algebra and number theory and as a way to apply an algorithm practically. That's what the Facebook comments don't understand.

(I don't really see the benefit in this case, but I'm tired of the knee-jerk reactions about everything new.)

Ironically, the previous generation was also supposed to be taught how to think rather than just how to do math:

https://en.wikipedia.org/wiki/New_Math

Good point. We should have also taught them to remember to think before posting to Facebook.

I think it's a clever way to introduce the properties of numbers without forcing memorization of a multiplication table. It's a very brute force technique. Of course memorization is useful, but so will understanding these properties as the kids enter algebra.

It's basically just subtracting whatever you can think of until you finish, it isn't really teaching division at all. The main idea is just to prevent having to teach kids the times tables so they can be promoted out of the system easier.

Multiplication is a way to do adding faster, and division is a way to do subtraction faster. Pretty cool if kids are being encouraged to realise that relationship.

It was only when I watched videos of those mechanical "fire control" computers on YouTube that I understood that integration is just a way of adding. Multiplication is adding the same number again and again, which is why integrating a constant (that number) is the same as multiplication. Cute.

Repeated addition is just one multiplication algorithm. I think a much better way to think of multiplication is as an operation on numbers that is related to addition by the distributive law. That law gives the "multiplication is repeated addition" algorithm, as well as the "shift and add" algorithm that most people learn in grade school. Of course, there are more efficient multiplication algorithms than either of those, which is why it is better to think of multiplication independently from addition.

I would also point out that the repeated addition algorithm makes a lot of sense in base 1, but that shift and add makes far more sense in base 2 or higher.

As for integration, I would say it is better to think of it as a limit involving both addition and multiplication.

> Multiplication is a way to do adding faster, and division is a way to do subtraction faster.

Can you elaborate? If you need to do 13 + 13 + 13 + 13, you can do that as 13 x 4, which I guess is what you mean by the first part; but what analagous subtraction could you replace with a division?

Not OP, but I'm guessing he means this:

52/13:

52 - 13 = 39

39 - 13 = 26

26 - 13 = 13

13 - 13 = 0

count the subtractions and you get 4.

As long as we're sticking to integer division, this works out fairly well. Here, a calculation with a remainder:

54/13:

54 - 13 = 41

41 - 13 = 28

28 - 13 = 15

15 - 13 = 2 (smaller than 13, so this is our remainder)

54/13 = 4 with 2 reaminder

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