Algorithm-o-rama
So, my son is in second grade but has math with the third graders. Right now their area of focus is “Regroup Ones and Tens.” This is a picture of what he is doing:
His complaint is that he doesn’t like the way they are doing it. In his mind #2 looks like this: 200 + 300 = 500, 80 + 60 = 140, and 4 + 7 = 11. So the answer is 651. He is disturbed by the idea that he has to work right to left. To him it is counter-intuitive (for obvious reasons, I think).
“Not liking something is not a reason for not doing it” would be my normal reply but in this case I’m not so sure. What is gnawing at me is something he said about #13. He sees the 6 + 5 as 11 (and has obviously been instructed to write that down in an attempt to explain why we leave the 1 in the “ones place” and move the ten to the “tens place”). I’m a little puzzled why they stop there and don’t write down 130 somewhere to be consistent, but anyway when he got to the end he added the 9 and the 1 and said it was 10. That bothers me. He doesn’t see it as 1000. I’m not sure if he sees it as 900 + 100 and hasn’t made the connection that 10 100′s is one thousand, or if he doesn’t even see it as that.
I’m pretty sure if he were doing it the way he wanted to do it (left to right), he would have no problem getting 900 + 120 + 11 = 1031. And he would understand the magnitude of the number. I’m afraid he is starting to just do stuff because the teacher says to. This is where kids start to dislike math. “I can do this stuff in a way that makes sense to me (and is mathematically sound) so why do I have to jump through hoops? That’s stupid.” I would agree.
So now I’m running through how I might broach this issue with his teacher. I want to do it in a way that doesn’t smack of “I know better than you.” Then, anticipating her response to “he needs to use the standard algorithm in order to do subtraction with ‘regrouping’” I’m again wondering why? He can come up with a method of working left to right with subtraction as well. One that reinforces place-value like what he does with addition.
Before I take this on, I need to know where I’m wrong. I’m thinking that I personally do not use any standard algorithms for addition or subtraction. Or multiplication or division for that matter. (In fact I’m convinced that partial products when multiplying both makes more sense and makes things easier in high school when we need to start multiplying polynomials.) I mean, does anyone other than third graders use standard addition and subtraction algorithms? Can we do without them?
