Advocates jump to defend attacks on a subtraction technique with self-defeating arguments.
Tonight I hope to start The Dawn Patrol , a 303 page crime novel by Don Winslow. I’ll read to page 67 at the end of chapter 23, calculate how many pages I have left and call it a night. So, how many pages do I have left in the book?
I assume you got 236 for your answer. You might have used a calculator, scribbled it out on a piece of paper, or done it in your head. If you did it in your head, I bet you used some kind of counting up method, thinking, like I did, “It’s 3 pages to 70, 30 more to 100, 200 more to 300, and 3 more to 303, that’s 236.”
If you counted up, you’d be hailed by many Common Core advocates. They’d applaud you for not using an algorithm, especially not the old tired one where you line up the numbers by place value and do all that borrowing. They’d say that you understand the fabric of numbers as opposed to just using rote memorization to get the right answer. Some may add that you exemplify the needed new perspective on teaching math that seeks to align math teaching with our true nature as creative beings.
It’d be annoying and self-defeating for multiple reasons.
First of all, counting up is, in fact, an algorithm that also requires rote memorization and mechanical execution of the steps to get the right answer. Second, I’d bet that counting up is older than the written, number-borrowing method. Third, whereas counting up might be a more mindful method, it’s because you have to keep a bunch of numbers in your head, not because of your number sense. Fourth, I’d speculate that the number-borrowing method was invented precisely because of the errors made by carrying running totals in your head. And fifth, who can defend the notion that it takes less number sense to understand why you can borrow from the place value to the left than to understand that you can count by numbers other than one?
Understanding how each method works helps you self-correct. It certainly makes math more interesting. But sooner or later you still have to mechanically do the subtraction or the counting.
So, on the one hand, I completely agree with Common Core Advocates who say we should teach lots of methods to solve problems in math and that we should include the underlying logic behind the methods in our instruction. And I completely get why advocates jump to defend the counting up method because so many parodies of it bounce around social media.
But, on the other hand, I think that if they’re going to include subtitles like, “[W]hy you hate common core and why we need a new perspective in addition” they should at least follow up with an argument that holds water.