what’s wrong with kids today?
Math Rant: Subtraction
This will not be a rant about how even some kids in advanced math classes have to count on their fingers to subtract (or add). I’ll save that one for another time. (For the record, with deaf kids “counting on fingers” is fairly equivalent to tapping on the desk and counting in your head.)
No, this rant is about the failure of someone (or several someones) earlier along the line failing to address both types of subtraction.
Two types of subtraction? Whatever are you talking about, Miss Lewis?
Yes, two types.
If you think of beginner’s subtraction, what do you think of? Probably the idea of “take away.” Johnny has 10 apples, and Jimmy takes 4 of them away. How many does Johnny have left?
Nothing wrong with that. Totally valid interpretation of subtraction. But it’s not the only one, dagnabbit!
There is also the HOW FAR perspective. And I don’t have the stats to prove it, but my gut says this is the more frequently useful angle in real life.
Take the problem 11 minus 8. Here’s what I see over and over in my classroom:
*holds 11 on one hand, then starts counting off on the other*
10, 9, 8, 7, 6, 5, 4, 3. I counted 8 places before 11, and the answer is 3.
Why? WHY? Even if you must count, here’s all it takes:
*hold 11 on one hand, start counting off on the other*
10, 9, 8. I’ve arrived at 8 and it took 3 steps to do it, so the answer is 3.
To me, this says these kids were taught a procedure for subtracting and memorized it without really going deeper. So I need to dig in and do some remodeling in their heads.
Even better is when they see 11 – 8 on the paper and borrow. So the tens place becomes zero and the ones place becomes … 11. Fortunately, that’s a little more rare.
*sigh*