Quick. No pencil. No paper. No fingers. No Calculator. Not even an abacus.
Solve the following:
Did you? And more importantly, how did you?
You may have seen the chart below, or some of the multitude of similarly presented discouragements to the nation’s public educational professionals. As you probably know, that’s a group of which I am enamored, proud and, when necessary, defensive. This is one of the times when I think a defense is necessary. You’ll note that the creator of this little ditty made the mistake of closing with a question. As I’m fond of telling anyone who’ll listen: “Don’t ask questions you don’t want the answers to.” My answer follows the chart. Enjoy.
I'm so glad you asked.
Actually, the "new way" really is one of “the old ways” that most of us actually do math in our heads. Those who use pencil and paper...well, that's not always handy, is it? And as for the calculator crowd, as with the Google gaggle...well, let's go back to talking about people who are willing to think at all.
For the sake of this example, my processing of the problem works this way:
293 is 7 less than three hundred. So, subtract 300 hundred from 568 and add the 7 to get 275. On paper, that probably looks like a mess. In my head, Apple Hill is 275 feet higher than Banana Hill. (Of course, I would have to confirm that there is an Apple Hill and/or Banana Hill by Googling them. And I would then find links to follow, and I would, that would explain to me the relative merits of growing apples on taller hills than those on which bananas should be produced. But that’s the kind of thing I do when I’m either procrastinating or trying to entirely avoid thinking about something else. So it can wait while I endeavor to make us think about this.)
What I’m seeing in Common Core is about teaching people to think (i.e., to process mentally—without paper, pencil, calculator, computer, smart-phone, a smart-enough-friend, or even enough fingers and toes to avoid searching for an abacus). More importantly, it’s about teaching people to think more quickly, more creatively, and at a younger age. One important side-effect will be a greater appreciation among those students for the varying ways in which different individuals and groups approach and solve problems. This is a good thing, and is likely to decrease bullying behavior by lowering the number of children who imagine that someone who shouts loudly, threatens others, and occasionally backs up their threats through physical violence must be...if not "right" about a particular issue, then at least...placated. So, we may be promoting a culture in which "thinking people" not only don't "engage in bullying behavior" quite so much, but may even speak up in opposition to those who do. And these changes may result because they appreciate that someone may think and act differently from them and still be deserving of air, warmth, water, and food. As I said, this is a good thing...that many oppose by shouting loudly and threatening others, if not resorting to physical violence (that I know of, yet).
Thus, the critics of common core, generally speaking, seem to have some other set of priorities. Foremost among them seems to be that children should not be trained to think better than the vast majority of their elders. At least that's the tone I perceive in the critiques I keep seeing.
So, to close, let’s consider “The Old Way” that all of us, apparently, found so intuitively logical during our own mathematical novitiate.
So, starting from right to left, which is, of course, how we were taught to do everything else in life prior to third grade (NOT):
- Step One: Starting on the right side, because we were told to, three is less than eight, so we can simply subtract and that leaves us five in the ones column, which is, of course, the third column, not the first column (which one might expect since it was called the ones column, but that hardly needs explained to brilliant children like we once were). But remember, we’re starting from right to left, even though that's just like…well, nothing else in our educational career has prepared us to do.
- Step Two: Despite the fact that two is less than five and we should be able to simply subtract, leaving us three in the hundreds column (which is the first column, since there clearly aren’t a hundred columns, and the other two are the tens and the ones—but you already knew that going into second grade math, didn’t you?), we’re working from right to left, so the center column—“the tens column” as anyone should be able to intuitively deduce—is next. But nine is more than six, and while it would seem simpler to subtract six from nine, the nine is under the six, so we’re subtracting that instead. By a later grade we would know that this would leave us negative three, and our subsequent answer would be 3(3)5, since we all knew to put negative numbers in brackets. But let’s imagine that there was a developmental process to our education, and force ourselves—as the teacher would have—to go back and try again.
- Step Three: Since Step Two failed to meet with the teacher’s approval, we’re going to subtract nine from six in the tens column despite the apparent impossibility of doing so. Thankfully, there are hundreds that we can take from the first column (which is the third column we’re dealing with, but you’re already starting to think that either Hebrew or Mandarin will be your next language class, so we’re all good with that, right?). Now, we take one of the hundreds from the five, making sure to cross out the five and write in a four, then adding the one to the six. This does not make seven, however. The one that we added to the six is a one from the hundreds place. And, before you ask, “No, it’s not one-hundred-and-six, either.” (Remember, you’re much smarter than today’s public school teachers. So don’t you dare fall behind at this point!) The one that we took from the five in the hundreds place is added to the six we already have in the tens place, which means we have one hundred and sixty, from which we will subtract—not nine, but ninety—leaving us with seven(ty).
- Step Four: Assuming we remembered to cross out the five in the hundreds place and write-in the four instead, we’re now faced with the simple task of subtracting two from four and getting two. But I will mention here that even though we memorized “two plus two is four,” unless we engage some level of critical thinking, number sense, and logical reasoning, we’ll have to wait until we memorize “four minus two is two.” In either case, though, I think we might be excused for understanding that the meaning of any of the following is not so immediately evident, nor even so intuitively deducible as proponents of “the old ways” have suggested.
So, why isn't this a better answer?
(I have some aspirin for you here in my drawer.)