One of my Facebook acquaintances, I don't remember who, recently put up a link to this video.
I would like to think that all of my readers are men of sense and will see that this bright child is being educationally tormented by being taught a faddish baloney way of doing what should be simple addition. And by the way, it's universally acknowledged that the children are counted wrong if they don't use these new-new-math methods, even if they get the answer right. Sweet. The mother is to be praised for bringing it to the attention of the world at large. It's also good that she taught her daughter the so-called "standard algorithm," aka normal addition, which will actually allow her to extrapolate the concepts of addition to numbers of any size she encounters. Now the mother needs to take the next step and get her child the dickens out of a school system that is trying so hard to mis-educate her.
The video makes an excellent point at the end, to wit, that the curriculum in question deliberately does not teach children to work with numbers larger than the thousands' place because the "array" method is so cumbersome that it cannot be applied to such numbers. Of course it can't. If you're already using a three-dimensional cube drawing to represent the thousands' place, what are you going to make the poor child draw for the ten thousands'? N-dimensional shapes? I shudder to think what they'll try to do to teach decimals... Hence, as the video points out, children taught in this way actually get the misconception (so much for "conceptual understanding") that addition problems using larger numbers are essentially more difficult to solve than those using smaller numbers. Congratulations, "professional educators." You've just ditched one of the the great beauties and virtues of the Arabic numeral system--its ability to be easily extrapolated, both in representation and in manipulation. Maybe you should just go back to using Roman numerals now.
But if you read the comments section under the Youtube video, you will find educators defending this nonsense, sometimes with condescension. Here is a sample:
This is definitely not the fault of Common Core! The child clearly has conceptual understanding and knows how to decompose numbers, AND kudos to the parent(s) for being involved and showing their child the algorithm! As a teacher, I used this strategy as the basis for the concept. As my students progressed, so did the strategy. We moved towards the algorithm or "stacking" as the child called it.
As a math educator and content specialist, this video is totally out of context. These strategies are wonderful for conceptual development and understanding place value. Teachers who use these methods effectively understand that ALL students need to go from the concrete like base 10 blocks then build to the abstract, which would ultimately be the "Stacking method." The traditional algorithm can destroy and hinder students from developing number sense and understanding of place value.
Nothing to see here, folks. These strategies are wonderful, wonderful. And golly, how did any of us ever survive and learn "number sense" and "understanding of place value" without being forced to draw endless boxes, cubes, and dots before we could add three simple numbers?
I am a middle school math teacher with a Masters in Teaching. This girl is explaining and drawing pictures to represent place value. This is an important concept to understand which many students don't learn as thoroughly as she has. Once this conceptual understanding has been developed students can then add the standard way. Math is not just about finding the right answer, but understanding how you get there. From this video I see meaningful learning going on here.
Repeat after me: You think it's bad, but it's all really good, good, good. The fact that the child got the wrong answer using the incredibly cumbersome drawing strategy is unimportant, because math isn't "just" about finding the right answer. (In other words, we don't really care if they can't find the right answer at all!)
And here's my personal favorite (as far as I read):
It always amazes me how non-educators (all of you commenters) can be so "knowledgeable" about teaching. Teaching kids to memorize meaningless (to them) algorithms for the last 150 years has not exactly catapulted our country to the top of the global math class. Perhaps if parents supported the instruction presented at school instead of undermining it at home, this child wouldn't be so confused.
That one's really priceless. The mother is to be blamed for "undermining" the teaching the child got at school by actually teaching the child to add at home! Because after all, the mother is not a Professional. How dare she do something she wasn't told to do, just going ahead and educating her own child in some way different from what the teachers at school were doing? She should shut up and get with the program, and soon America will be competitive in the world again, and we'll owe it all to the Professionals. The plebeian non-professional educators should get their ignorant fingers out of the pie.
I don't even want to ask what this special snowflake Philosopher King wannabe thinks of home schooling. We can take that as read.
There is a common theme here, of course--the allegation that this silly method is teaching true understanding while the rest of us aim merely (God forbid) to teach children how to get the right answer.
Let's back up. What's the cause of the never-ending nonsense and faddishness in the discipline of education? No, believe it or not, I'm not going to say a Communist plot to take over the country and brainwash our kids. (I'm a big devotee, when it comes to teaching children to read, of the self-described European liberal Rudolph Flesch, an ardent advocate of systematic phonics. Flesch was definitely a man of the left and was incredulous when he realized in the 80's that phonics education had been turned in the U.S. into a left-right issue.) No, the real cause of the morass of education as a discipline is Science Envy. To some extent, all "soft" fields in the Academy are afflicted by Science Envy, but the largely faux discipline of Education has one of the worst cases. Eager to prove that it has a raison d'etre (which to a large extent it doesn't), Education has to make itself appear to itself to be scientific. What does science do? It makes discoveries. It makes progress. It finds new particles, new cures. It continually adds to the stock of human knowledge. If educators merely used tried and true methods to teach children the basic skills they need to become scientists (and many other things) it wouldn't look like a branch of science itself, qua discipline. So educators, viewing themselves as professionals constantly assisting human progress, must continually come up with something new. What lies behind the worst academic fads is the love of innovation for its own sake. I'm not speaking here of political correctness or of "educational" activities that really are direct forms of indoctrination in themselves. Nor am I speaking of issues like the selection of literature books or of which figures in history to focus on. I'm speaking rather of new math and new-new math and whole language and inventive spelling--of what we see in the video.
Don't get me wrong: Certainly political progressives can make good use of all this hatred of tradition, the confusion, the continual innovation, and especially the tripping up of good students. The more you stir the pot and make everybody look equally dumb, the more opportunity for propaganda and controlling the masses. I acknowledge that. But most of the foolish new methods in and of themselves, I believe, are in the first instance invented because of the drive in education as a field to appear to be generating and teaching new discoveries.
Sometimes educators can sell the public on this idea of progress in education directly. "We've been doing x for 150 years, and our educational ranking is terrible. We need something new." You see that in one of the above comments. Or, "We used to think y, but now we know better. I used to hate such-and-such a new method, but now I've seen how happy it makes children, how full of self-esteem, and I'm convinced."
But often as not, they feel that something more is required. That's where the great fake conflict between competence and understanding, make that Understanding with a capital U, comes into play. Here's how the script goes:
1) Say (preferably convince yourself first) that competence in the actual skill or possession of the actual knowledge which most people think of as the goal of some area of education is in Great Tension with deep and profound Understanding of that field of knowledge.
2) Tell the parents and everybody you're trying to convince that teaching kids that field isn't just about that competence or knowledge. You see this in the above comment where we're condescendingly told that learning math isn't just about finding the right answer.
3) Use a new method or approach that is absolutely terrible at giving children the competence or knowledge that parents and other laymen actually want them to receive from that part of their education.
4) Respond to complaints that the kids are getting the math answers wrong, don't know basic facts, or can't read or spell by saying, over and over again, that teaching that field isn't just about getting the answers right, learning facts, being able to read well or spell right. Do this while pointedly ignoring the core of the complaint--namely, that the students aren't learning those things at all or that they are learning them only very poorly. Also respond by insisting that the students are gaining true Understanding, and insinuate that this is much better than the bourgeois ability to add, subtract, multiply, divide, read, and spell. It helps if you really believe these talking points.
The thing is, we've heard this whole script before. Back in the day (by which I mean twenty years ago or so) the big fad was Outcome-Based Education. (Does anyone else even remember that phrase?) Everybody was all about helping kids really to understand history, not just memorize facts. Which was an unsubtle way of saying that they weren't going to teach kids many facts in history anymore. Six years ago (or so), I was pointing out on a thread on the old Right Reason that apparently children in public school are not being taught their multiplication tables and are being taught to use calculators instead. Sure enough, as predictable as the rising sun, on came a defender of the don't-memorize-facts school of thought to tell us that the multiplication table is "memorized trivia" and doesn't contribute to true mathematical Understanding. And here in the defense of this bizarre and cumbersome method of addition we find the same pattern played out yet again.
What people who aren't caught in the grip of reflexive educational defensiveness ought to realize is that, of course, understanding, real understanding, is not at odds with memorization, that the two actually assist one another. The conflict is entirely invented as a way of attacking knowledge, competence, and the use of memory as an aid to doing basic functions swiftly and easily. If you memorize true facts, these will act as anchors to prevent your attempts to delve deeply and creatively from getting off the rails. If you have something true memorized you may have a chance to come to understand it more and more deeply as time goes on. If you have to construct everything from the ground up by a cumbersome method every single time, there's a non-negligible chance that you'll just get it wrong.
Moreover, convoluted attempts to force what is alleged to be a deep understanding by new methods can readily result in just the opposite. The law of unintended consequences strikes again. We see in the above video how what is alleged to be a way of helping children gain Understanding actually results in misunderstanding--that large numbers are harder to add than small numbers.
The saddest part of all of this is that millions of people all over this country are literally trapped in an educational system that is using their children as guinea pigs for every bad method that comes along.
Only slightly less sad is the case of people who could do better for their children but voluntarily don't, for a variety of reasons. One of those reasons is the misconception that their kids are better off being taught by pros. Just the opposite is true. As with the "socialization" canard, so here. What is widely bruited as a reason against home schooling is actually a reason for it. The children in public schools (and most private schools) are indeed taught, God help them, by professional educators.