Where am I going with this? Common Core. Have you heard about it? It's the federal government's attempt to take over education from the states and the local authorities. It's a setting of national standards and methods and an arm-twisting approach to compliance that uses our tax dollars to force every state to be on board.
There are a host of things which are disturbing to me about Common Core. The changing of standards in reading and literature bother me like nobody's business, the data mining of students for federal databases scares the poop out of me, but what makes me sad is what they've done to math.
Common Core takes this already difficult subject and makes it nearly impossible to comprehend. Here's an example from a textbook that aligns with CC standards (a friend of mine read this to me over the phone from her daughter's math text. If you want the name and publisher, I can get that info for you. I just don't have it handy.)
We're going to be dividing 128 by 4. That is:
If you just jumped right in there and answered 32, you're a smarty pants and you're wrong. Because Common Core isn't about getting the right answer. It's about the process. You did it the old fashioned way of thinking. There's no more "there are 3 4's in 12 and 2 4's in 8 so the answer is 32" business. Slow it down, speedy.
Here's one of the Common Core methods using the distributive property:
First break the 128 down into hundreds, tens, and ones so that you have:
Then simplify it further (and I'm not sure why we're calling this simplified) to:
So for our next step, we simplify it further by dividing the numbers in the parentheses and get:
Then you add all those numbers together and arrive at:
Yes, I know that that's the answer you had almost immediately using the old-fashioned kind of math you learned in school, but that 32 was wrong because you didn't think it out the right way. You see, under CC standards you could have answered 30 and gotten the problem right if you had thought it through correctly. CC math isn't about teaching math, it's about teaching you how to think.
Now, I'll just stop there and be honest with you. A part of all mathematics education is centered around teaching the students to think logically. Logical thinking has always been a part of math curricula. What is wrong with the new way of doing it is that there is no logic to this way of doing math. It's a short cut.
Here's another nerd confession from me, there was a time that I was a mathlete. That's right. I did competitive mathematics and it was fun, by golly. That's why I can tell you that the CC problem I wrote about above has a place. It's fast mental math. It's a trick. It's a way of doing math as quickly as possible in your head. That's where the CC people found it. If you read the reasoning behind teaching math in this manner, they will cite the fact that mathletes do it this way because it's faster. And it is. In your head.
The problem that I see is that in order to be able to do it the mathlete party-trick way, you have to understand the mathematical concepts. We're back to "math is a language."
Let me put it this way.... A few years ago, there was a commercial on the radio for a Spanish language learning program that promised to teach you Spanish in just minutes a day and faster than you'd ever learned it before. In fact, they promised, you could learn a Spanish phrase by the send of the commercial if you could just spell the words socks. (That's what they said. I can't make this stuff up.) So the woman on the commercial would spell "S. O. C. K. S." and the announcer man would say "You just spoke Spanish." and he would go on to tell the listeners that they had just said "that is what it is" in Spanish. Technically, he was right, I suppose. The phrase in Spanish - Eso si que es - does mean "that is what it is." She "spoke Spanish," I guess, but it didn't teach her how to speak Spanish. It's a trick.
No one who heard that commercial really believed that the woman was speaking Spanish. She had leaned a handy phrase to repeat back, but if you had asked her what the word "que" meant, she could not have told you. In order to learn Spanish, you have to learn the words. You have to learn about how those words work together. You have to learn it step by step before you can speak it well enough to use it out in the real world.
Math is the same way. Your brain learns it as a language you speak. You have to learn it step by step and get a good grasp of the numbers, the rules, and how they all work together or you're not fluent in it. The problem with this new way of teaching math is the students have only been taught tricks and phrases to memorize, but not how they actually work together. Which means they can't speak it. And if they can't "speak" the simple sentences, then they're going to be lost when they get to anything that requires them to use logic and deductive reasoning to figure it out. Which is what is happening to our students when they run smack up against the wall of higher mathematics. Algebra and calculus? No way. There are a few smarties who will have learned to speak math in spite of the way they were taught, the same way that some people will figure out Spanish from learning how to do silly things like spell socks. Those people are the exception.
CC math is just the "new math" of the 60s and 70s rebranded and repackaged, but now with the weight of the federal government to push it forward. New math was an abysmal failure that dropped math literacy rates everywhere it was tried. Calling it Common Core and training the teachers in this "new method" is not going to change the fact that it doesn't teach math. It teaches an irrational approach which is confusing to people who don't already understand the concepts you're trying to "shortcut" around. Which makes me start to wonder who benefits from a generation that can't do higher levels of math and struggles with basic concepts, and why is the government willing to use it's power and our tax dollars to push that agenda?
Want to see common core in action? Here's a video of a teacher trying to explain long division using Common Core's other approved method - partial quotients. Please keep in mind that this is supposed to be making it "easier."