- #1
newjerseyrunner
- 1,533
- 637
I've seen a lot of complaining on the internet by parents about the new way addition and multiplication is taught in American schools. I looked at it, and have to admit, at first, I thought it was insanely overcomplicated and worse than the way I was taught where you did one digit at a time and worked right to left.
Then I started to realize that the way they were doing it was actually what I do in my head all day every day and I think anyone in a mathematical job would agree.
If you haven't heard of it yet, addition is done like this: 37542 + 34726 used to be done by adding the 6 and the 2, then moving to the left and repeating with the carry if there is one. In algorithm terms: recursion. The new way is to do it via recursion too, but starting on the other side and using rounded values instead. 37K + 34K, then 500+700, then 42+26. (In school they'd actually teach 30K+30K then 7K + 4K, but we're not children so we can handle two digits at once.) The obvious advantage is that you have a reasonably precise estimate after only the first step.
Multiplication looks really weird. 432 * 286. They're taught to built a table with the modulus' of the placeholder's position in the table across one axis, then the same across the other.
Then they fill in all of the boxes and add them up. I have to admit, it looked really weird to me, but then I just decided to do the big calculation in my head and see how I got there. I realized that I do the same splitting up into boxes in my head, but I do it to scale, where I envision my 400 much larger than the 30. So I quickly understood that this is using geometry to solve the equation by breaking the multiplication of arbitrary numbers into adding areas of nice round numbers.Do you think there is a specific advantage to teaching children to think this way? I developed my way of doing arithmetic this way over years of working with hexidecimal numbers. Do you think this will be a passing fad or a paradigm shift for how children are taught math.
Then I started to realize that the way they were doing it was actually what I do in my head all day every day and I think anyone in a mathematical job would agree.
If you haven't heard of it yet, addition is done like this: 37542 + 34726 used to be done by adding the 6 and the 2, then moving to the left and repeating with the carry if there is one. In algorithm terms: recursion. The new way is to do it via recursion too, but starting on the other side and using rounded values instead. 37K + 34K, then 500+700, then 42+26. (In school they'd actually teach 30K+30K then 7K + 4K, but we're not children so we can handle two digits at once.) The obvious advantage is that you have a reasonably precise estimate after only the first step.
Multiplication looks really weird. 432 * 286. They're taught to built a table with the modulus' of the placeholder's position in the table across one axis, then the same across the other.
Code:
____|_400_|_30_|_2_
200_|_____|____|___
_80_|_____|____|___
__6_|_____|____|___