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*
5 comments:
So what does it say when I add to subtract?
If I were a finger counter, I would have said, "Eight," then as I said nine, I would have held up one finger, and so on. By eleven I would have had three fingers.
If there's one thing my dyslexic son has taught me is that there are a thousand ways to reach the same answer--and that's a damn lot of fingers!
I admire your love for you job. Your students are very lucky to have you!
catwoods said exactly what I was going to say. I always counted up. And would say three...always. O_o What is that?
Cat and T, "counting up" is an awesome method, and I'd love it if some of my kiddos could grasp it ... because they can count forwards a lot more easily than backwards. ;)
And that method still works on the "how far between" perspective, as opposed to the "take away."
Curious ... if you saw 11-3, would you still count up, or would you take-away in that situation?
I still add. Three plus eight equals eleven. My brain automatically transfers the equation to read something like, "I was given eight." Not, "Someone took three from me."
Funny, I've never thought of it in these terms. I suppose the only time I consider the negative impact of numbers is when I balance my check book!
Do you realise how many centuries the human race fought over the concept of negative numbers and you want a bunch of snot-noses to get it in one scholactic quarter? Well yes they are damned lucky!
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