There’s been much talk about the Common Core, a relatively new approach to public education, and much of it has been bad. Very bad. In fact, the stuff that’s being taught under the rubric of “Common Core” has been so widely perceived as being flawed and, frankly, downright dangerous to the education of our youth that many states and localities are even attempting to re-brand their educational approach to avoid using the term. What bothers me is the notion of a common core of educational curriculum isn’t necessarily bad, but the implementation of it, derived from a federal, top-down mandate, has been stupifyingly bad. Let’s take an example that I found via Facebook on Allen West’s web site. In order to preserve the image of this example, I’m providing it here on-site.
This is an example of a simple subtraction problem that requires a completely different perspective on mathematics. In the example, the student is asked to review an attempt at the subtraction problem and tell the fictional “Jack” where he went wrong. The parent of the student who was given the assignment took the opportunity to make their frustration with this needless meddling in the teaching of basic math skills known. I sympathize completely. I have a degree in Computer Information Systems and have a better-than-average skill in math, even this many years out of school. In looking this problem over, I could not fathom at all just what the hell they were doing. Their process seemed complete nonsense and I wrote a comment on the Facebook page of the person sharing this link saying so. I even shared it out on my own wall.
Being the kind of person I am and engaged in the profession I have, however, I continued to attempt to analyze this problem and their approach in an effort to puzzle it out. I finally managed to but only because I stopped thinking of this as a math problem and more of a communications/marketing problem. Let me take you on a tour of the matter. Note that the crux of the “math” problem is this number line up at the top with the bouncy little curves that, I suppose, are indicating the math process “Jack” followed. It’s clear that he’s subtracting the number a piece at a time, starting with the higher-order numbers first. (Which is a reverse of the method most of us have learned where we start with the lower-order numbers.) Once done with the highest-order, he would – presumably – continue with each successive lower order until he’s handled them all. He arrives at the wrong answer. The parent who wrote on this then attempts to decipher Jack’s process and can’t do it, either. Nor could I. As I was continuing to ponder this, I looked at the little curves up there at the top and, applying my network diagramming approach, thought that Jack had made this more difficult to follow because, while his big, “minus 100” swooshes were large and thick, the other curves for both of the lower orders were all the same. If I were diagramming a network and the bandwidth of the links were important to know, I’d use lines of different weights or colors to indicate the differences between them. Which is where the eureka moment happened.
The reason he didn’t have 3 different size of swooshes is because he simply missed one. If you assume that the sizes of the swooshes were intentional, then he clearly subtracted the 100’s and the 1’s, but he missed the 10’s. Note that his answer is off by 10, which is the “1” in the subtracted number of “316.” For you and I to make the same mistake using the traditional subtraction approach, we’d have to look at the problem of taking 427 and subtracting 316 by subtracting the 3 from the 4 on the left, the 6 from the 7 on the right, and then just ignoring the “1” in the middle, carrying the 2 straight down.
Ludicrous. And instantly detectable, under our method. With this realization came a sudden dawning of awareness: the method being described is merely a visual, linear representation of a person counting on their fingers and toes. In short, precisely the kind of behavior I worked very hard to get my daughter out of the habit of because that process is incredibly slow. This method is equally slow – and gets worse as the number of digits increases – and adds in the another flaw: it’s prone to error.
As a network engineer, the concept of common protocols is very important and absolutely critical to communication. There’s nothing wrong with setting up a common protocol or a commonly-applied set of measurements for success. I applaud the effort. But just as, in my industry, the common protocol is implemented by different companies in different ways – all good so long as the result is within the requirements of the protocol – it is not necessary to mandate the teaching of a new paradigm of a hard science to achieve a common level of capability between states. Who was it that came up with this method? Why is this method supposedly superior to the methods used for generations? I don’t recall voting on this and I don’t recall the teaching profession reaching out to the community to determine whether this was what we all wanted. I know for a fact that had someone suggested this kind of approach that I’m seeing in math, I would have demanded to know what real benefit accrued from teaching this way and whether that benefit justified the disruption this is causing.