There is a lot of hoopla out there about common core and for the most part, I ignore what people have to say. I doubt that most people who write something on Facebook for or against common core have actually analyzed the standards or the reasoning behind any of them. Now, I am no expert, but I have been to hours of training, I've studied the standards for math, and I am on the pilot team for common core math at work. I thought I might write a little bit about common core so that those of you who care can get some inside information.
First of all, I am not a piano player. Anyone who actually plays piano would testify to this. I know how to play piano just like I play every other instrument I play - just enough to know how little I actually know. I love the piano and I wanted to learn how to play. I had two goals: I wanted to play the first movement of Beethoven's "Moonlight Sonata" and I wanted to be able play jazz style piano. I already knew how to read music and which notes corresponded to which keys on the piano. I practiced the first movement of moonlight sonata like crazy. I played it every day. I had a piano teacher critique it and help me through the parts I didn't understand. I listened to it over an over again. Now, I can play the first movement. I can play it well enough to convince someone that I might actually be able to play a little.
So the first task was complete, on to Jazz. I had a lesson with a really great jazz piano player I know. I sat down with him and he had me play a C chord, which I did...and that was the first and last part of the lesson I actually understood. He went on to talk about circles of fifths and how one scale can be changed to another and transposing and all sorts of things that were so natural to him and he assumed would be natural to me. So I postponed my jazz instruction because I now know what it takes to play jazz. I know that if I want to riff and run as if I'm playing from my heart, I have to have the strongest of foundations in music theory and piano practice.
I can't yet play jazz, but I can play math. Math is not some mystery to me, it is not magic. It is an interaction of numbers that have distinct relationships with each other. The relationships between numbers are well known to me. I know them like I know the relationships between characters on "Gilmore Girls". For example, if you asked me, "What is 30 - 12?" I might simplify it in many different ways. I could write the numbers on top of each other and subtract by borrowing. I might also see the 2 becomes 10 by adding 8 and 8 and 12 make 20 and 20 and 10 make 30 so 8 and 10 are 18. I might also picture a number line and break that number line up into jumps of 5's and see that 12 needs 3 to be 15 and 15 needs 15 more to be 30 so 3 and 15 are 18. You may think that these other methods are time consuming and tedious, but they actually make it tons easier for me to do subtraction in my head. While others need to write down 30-12 and then cross out the 3, make it a 2 and add a 1 next to the 0 and then start subtracting, I would much rather add my way to 30. I find that I actually add to solve most of my subtraction problems.
Here's the deal. It doesn't matter which way you get the answer as long as it's right, but because I know the ins and outs of number relationships, I am able to choose the path that works the best for me. I get the numbers. I know what I'm doing no matter what method I'm using. I play math like a jazz musician, letting my heart express itself freely because I have the foundations of understanding how the mathematical musical structure works.
We are a society that loves shortcuts. We want the fastest solutions, the shortest way. We want to know the answer. We are an answer driven educational society as opposed to a process driven society. We learn algorithms (a set of steps that lead to a solution) without knowing anything about why we are doing it. Some of you may remember how to change a mixed number into an improper fraction. Some of you may just barely remember what those words mean. Most of you have no idea why you multiply the denominator with the whole number, add that product with the numerator and then write a new fraction with that sum over the same denominator. And because most of you don't know why you do that, most people forget some or all of the steps or mix them up or have a vague sense of familiarity with that process and think, "Can't I just make them all decimals and let my calculator do it?" My answer is, "No." Asking a math teacher that question is like saying to a literature professor, "Can't I just watch the movie instead of reading the book?" Memorizing algorithms is actually really hard. Memorizing algorithms when you don't even know why you are doing it is like trying to memorize the words to poem you don't understand in a language you don't speak. It's incredibly difficult to do.
We have taught our students the shortcuts but not the math. They have little to no number sense. About half of my students last year, when given the problem of 15.25 - 1 actually would consistently get 15.24 and not 14.25 because they followed the subtraction algorithm: write the numbers on top of each other and subtract. There wasn't a picture in their heads about how much 15.25 is and how much 1 is. There was no connection to money or measurements or any other practical application. There was an incorrect application of the algorithm. Because the algorithm meant nothing to them, they had no concept of whether their answers were right or wrong.
Common Core math is an effort to force our students to take the long way. To force them to see and explain why they are doing something. This means that students will often be expected to write out a long procedure that we, as well trained adults, know a super quick shortcut for. That shortcut will eventually be taught and the students will add that to a set of tools they have a firmer understanding of, but in the meantime, they need to learn the why's and how's. It is painful to teach a child that in order to add 5 and 6 they need to draw a number line and draw 5 jumps of 1 and then 6 jumps of 1 and then count the jumps and find that it is 11. But the reward is that when I ask the same child to add 5 and -6, he or she can draw 5 jumps of 1 in the positive direction, jump 6 jumps backwards and land at -1 and really trust that that is the answer without trying to remember which rule it is. Trust me. I have taught the lowest performing students in my school using a similar method for the past 5 or so years and it is amazing what they can do. They know what 3/4 looks like and can compare it to other numbers. They can add numbers with decimals and not mix up place value. It is the long way, but it is the way that will keep math understanding in our students' minds.
Common Core math is not perfect, neither are the books that present it, nor the teachers that teach it. It takes a lot to train yourself as a teacher to let your students struggle. It is new to us too and we will fail frequently as we attempt new methods of teaching, assessing, grading, and learning. If you have a child in the public school system, you will probably be frustrated frequently with many aspects of the new standards being taught. But here's the thing: If I don't take the time to learn the why, I'll never be able to play jazz and in the long run this is the path that will get us there.
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