What if I were to tell you that we have a new way of training auto mechanics. It seems that it takes an awful lot of time to train auto mechanics about all those parts of an engine, and how they all work and there are so many kinds of engines. You see, there are lots of parts on a car, but only a few of them break often. And, some cars are much more common than others. So, the plan is we will streamline the training. We will teach mechanics to do just the most common repairs, how to get in, get out, no need to know how the thing works.
So, how effective would this teaching technique be? Well, I suspect, for the most part it would be very effective. These new mechanics would be able to do the large majority of repairs on most cars. Some of the mechanics would even pick up some knowledge of how the engine worked, just through this process of knowing how to do a few common repairs.
But, what if you have a problem with your car that wasn’t covered in this expedited training course? What if you had a car that didn’t fit the mold? What if you had a problem that was hard to locate? Would your mechanic be able to find it? Maybe, but then again, maybe not. If you had a really sharp mechanic he may be able to figure it out. He may have come up with strategies to solve the unexpected problem. But with no training on how it all works, you have no guarantee.
Well, that is how we have been training our children in math for a lot of years. How were most of us taught to do math? Algorithms. How do you subtract 38 from 52? Well you probably line up the digits, subtract the ones place first, borrowing from the 10’s place because you can’t take away 8 from 2, then subtract the 10’s place. That process you go through is not really subtraction, it is an easy way to figure it out. For most of us, we understand what is really happening here. We get a picture in our head of 52 items and removing 38. The algorithm is a shortcut, a way to figure it out quickly.
But here is the thing, we educators have been moving at such break-neck speed to teach the standards, that we have run out of time to teach kids what is really happening. The last few years of crazy standards, standardized testing and moving at an astronomical pace to keep up with who knows who (specifically in the state of California), has left no time to teach what it really means. It is like the mechanic who can only perform one action. Most kids can do the algorithm, but they may have no idea what it means, how it works, or how it fits all together.
Enter Common Core math. You’ve seen the examples of what seems to be long, crazy, drawn out ways to compute something. Testimonials from parents, professionals, smart people saying, I don’t do math like this, why should my kid?
Well, I will tell you why your kid should learn with Common Core math: your kid should learn Common Core math for the same reason your mechanic should learn everything about an engine instead of just how to do a few repairs. Your kid should learn Common Core math because it teaches kids how math works, not just how to solve algorithms.
I remember learning math as a kid. The plan was to teach us how it works, but here was the process. Teach a skill, show exactly how to do it, give an example, have the kids practice, then they practice alone. Classic teaching, I do, we do, you do. So, as a kid, I would take my example, my few I practiced in class, and my book home and do my homework. Everything worked fine, as long as the problems looked exactly like the example. When it started to diverge, I started to get lost. And then, here is the part where the plan was for kids to figure out how it worked, we would get an extension problem. Take what you have learned, apply it to something completely different, and figure it out. I would look at those, look at my example and have no idea. No one taught me how to do that, how are we supposed to do it?
Well, I am no one’s dummy, as a matter of fact I was very good at math, and it eventually became my favorite subject. But, I wasn’t taught, encouraged, or really even given permission to think on my own (except perhaps in those extension activities I was supposed to do at home). I had the process, the directions the way to do it. As long as I followed the directions, I could do it. Any variation, anything that looked different, and I was stuck. I had no idea where to start or how to solve it.
Move ahead about 40 years, and now instead of learning math, I am teaching math, as well as a few other subjects. Guess what, up until Common Core, not a lot had changed. It was still I do, we do, you do. And, kids still do not understand those extension activities. Here is what did change between then and now: someone decided that kids should learn more math faster. Never mind developmental levels, never mind the time in a school day, never mind that kids can only learn so fast, they should learn more, faster.
Did it work? Did kids learn more math faster? Well, if you look at the scores they did go up, but only on the specific tests that teachers were teaching to. Kids did not really understand math, but many were able to perform a lot of algorithms, as long as it didn’t look different than the example. Yes, just like the mechanics in my original example, for most students it worked fine. They were able to perform prescribed operations as taught.
But here are the unintended consequences: kids can solve math problems, the math problems that were specifically taught, but how often will they see those exact problems in real life? Using this method many students, I may even venture to say most, really don’t know math. Most of us would recognize ¾ as their pieces of a whole cut into 4, or three out of 4 wholes. I have worked with all sorts of students who may be able to perform some operations on fractions, but ask them to draw a model, and many just can’t do it. Ask them to take away half of 8 and tell you the answer, and they may say 7 and a half. They have memorized the rules (if they have a good memory), but they don’t understand the process. And, the kids who don’t have good procedural memory are really lost.
So what does this have to do with the crazy Common Core examples? It is teaching kids how it works, how it looks, what it really means. Does this mean we don’t use algorithms anymore? Absolutely not. They go hand in hand. The algorithms are short cuts, quicker ways to do things. They should learn both, what it really means, and the quicker way to solve it.
This is not to say that Common Core math is the perfect solution, or the only way to teach math, but from where I sit it is the best alternative I have seen to what we have been doing for a lot of years that does not work all that well.
Want to know more? Stay tuned for my view on why parents are frustrated and why teachers are unhappy. Or, check out this link from another point of view.