As a private tutor, I am incessantly met with complaints about the current method of educating students in mathematics. In many cases, when I meet with a student and parent for the first time, the topic of the dreaded Common Core methods come up. Time after time I hear the same frustrations.
“Why do they make it so much more difficult than when I was in school?”
“What’s wrong with the old way they taught it?”
“If I can’t understand it, then how can my kid?”
“Why do all these steps when you could just do it like this?”
These concerns are very real, and it is never a bad idea to be involved in your child’s education. Taking an interest in how your son or daughter learn lets them know that you care, that you’re there to help them should they get discouraged, and helps them realize the importance of practicing their academic skills. However, I take the unpopular position that the Common Core methods are not inherently bad.
What many people do not realize is that math builds on itself. It is very difficult to comprehend a topic without the foundation beneath it and fully grasping the necessary prerequisite skills. What many Common Core strategies address is not only how to arrive at a correct solution, but also how best to build up the techniques that will be used later on in math. Let’s look at an example.
Say we want to multiply 364 by 12. One of the Common Core methods for this is to use something called partial products. Instead of brute forcing it with the algorithm that many of us know, we do it in pieces. One way would be as follows:
364 x 10 = 3640
364 x 2 = ?
Here again we break into pieces:
300 x 2 = 600
60 x 2 = 120
4 x 2 = 8
All together we have:
600 + 120 + 8 = 728
So our final answer would be 3640 + 728 = 4368.
I know what you’re thinking (because I’ve had it yelled at me before), “That’s so many steps! Why bother?” Well, what do you really do when you line up the numbers and follow the algorithm?
You would multiply 2 by each part on the top, and get 728, then you would go down, put your zero because it’s in the tens place, and then come up with 3640. Hmmm. Hopefully it seems a lot more similar now. It’s the same concept, just the way it has been written is different.
Unfortunately, people are creatures of habit. I will be the first to tell you that if you know how to do something in math, good for you. By all means stick with it, and keep practiced! Where we run into a problem, however, is when a student does not understand how to do the algorithm the way you do. What then? Should I simply keep telling them to do it until he or she might finally accept the process. How many of you knew why to put the zero in the second line when you first learned multi-digit multiplication? How many of you just thought about it now?
Is it important to be able to simply arrive at a correct answer? Of course it is! Wouldn’t it be far more useful later on to have the knowledge of why a process is happening? You be the judge.
The reason I tutor is so that I don’t have to stick to one method only. (More on that in a little bit.) I get the opportunity to find out which method makes more sense to a child rather than only staying stuck, nailed, and riveted to the same techniques regardless of what helps a child learn. Because of this, I have taught both ways to multiply on numerous occasions. Here is what I’ve noticed. When I teach the algorithm to someone who is struggling and it takes hold, they can usually get it and very soon are having no problem. Then I ask them to multiply by a three-digit number and….they get stuck. No idea what to do on the third row with very few exceptions.
The kids who happen to like the partial products method more, however, rarely get tripped up when moving into three digits. Why is this? It’s simple really. The students who do the longer steps don’t need to learn a new rule. Instead they are prepared to extend their knowledge and tackle a larger problem. With the algorithm, it must be taught to put two zeroes on the third line as you are now in the hundreds place. Usually at this point, the child sees a pattern and can move into 4 and 5 digit numbers with little trouble.
Does this mean that one way is superior to the other? Nope. Whichever way makes more sense is the way to teach it. The ability is more important than the method for sure. Once understanding has taken place, then other methods can be taught to help improve speed and efficiency.
But that brings us back to our initial complaint. Why does the school force everyone to do the first way then? Now we are asking the correct questions. There is nothing inherently wrong with the Common Core methods. In fact, they are better for preparing students for more advanced topics later on, if any comparison needs to be made. Where we run into trouble is that the school system has made the mistake of assuming that every person needs to perform calculations in the same manner.
Every person learns differently, and the key to education is figuring out the best way to convey a topic to a student. When the schools only teach one way in order to attempt to reach the majority, there will always be those who are left out. The problem with the new Common Core system is not necessarily the methods being used to teach, but rather the ideology behind when and how to use those techniques. So the next time you have trouble with a topic, or you see your child working through a method that you question the usefulness of, try another approach instead of complaining. I think you’ll be surprised how it takes away the frustration and helps kids grow in leaps and bounds.