You don’t even have to be part of the education world to know what people think about common core math. It’s like suddenly everyone is an expert on educational psychology and math curriculum. And I do mean everyone – politicians, stay at home moms, the cashier at the gas station on the corner. The verdict is in: “Common core math is the actual devil.” But what if it isn’t?
What if I told you that the reason you hate common core math is because you don’t actually know how to do math? Ouch. But it’s not your fault! You don’t understand math because you weren’t taught common core math!
Let me back up and begin by filling you in on my personal history as a math student. I always hated math. If you told me twenty years ago that I would end up a math teacher I would have laughed and then possibly cried. Don’t get me wrong, I was “good” at math by the standards of the day. I climbed my way up the public school math ladder, acing every test and seemingly mastering every skill. I made my way to the tippy top – AP BC Calculus – the highest level of math offered. I topped off my career as a math scholar by achieving a final grade of 100% in that class and a 4 on the AP exam. I’m not telling you this to brag, I have a point, I promise.
Despite all of what looked like impressive achievement, I was not a good math student. What’s worse, I didn’t even realize I couldn’t actually do math until I got to college and began an education course about how to teach math. The professor of that course was Icelandic and I could barely understand a word she said. Have you ever heard an Icelandic accent? I wasn’t entirely sure she was even speaking English at times but what I did glean from her lectures was nothing short of life changing. She stripped it all back to the basics and started talking about something called a “base ten number system.” I had never heard of it. Come to find out it is literally the foundation upon which all of math rests. So how had I made it through AP BC Calculus with a 100% and yet I didn’t know about base ten? Why was I now completely unable to perform the calculus I had seemingly mastered only a couple of years prior? Why was I twenty years old and still counting on my fingers for basic arithmetic? Because, my friends, I was never good at math. I had never even learned math. I was exceedingly good at memorization. That’s all I had ever done.
You see, the “old way” of doing math that everyone is suddenly so fond of involves very little of what math actually is. It’s based on rote memorization. Here, memorize this formula so you can plug the numbers in and get the right answer every time. “Old” math is like memorizing which keys to play on a piano and in what order. You can memorize and replicate Greensleeves but you don’t actually know how to play the piano. If someone said, “now play Clair De Lune” you would be completely out of luck. Take long division for example. You may still remember the old mnemonic “Does McDonalds Sell Cheeseburgers?” for memorizing the steps to long division: divide, multiply, subtract, check, and bring down. Are you a good math student if you can plug numbers into an algorithm, complete a memorized set of instructions, and come out with the correct answer? Or are you a good memorizer? You know who else can do that? A calculator.
Math instruction has changed because technology has evolved. We have machines that can compute complex equations in a fraction of a second while you’re over there “carrying the one,” and “bringing down the five.” We don’t need people who can do math. We need people who can think math. We need more people like Henry Briggs – the mathematician credited with inventing the long division algorithm in 1597. We need another Pythagoras, another Einstein. unless we stop plugging numbers into other people’s formulas, doing work that the calculator in my pocket can do much more efficiently, then we will never progress.
Don’t get me wrong, these algorithms are handy shortcuts and I don’t for one second think we should stop teaching them (we still do teach them, by the way!). But let’s not delude ourselves into thinking that memorization and replication are the same as understanding. If that’s the way you were taught, then when presented with a new problem, one you’ve never seen solved, you won’t stand a chance. You’re doomed to repeat math already mastered hundreds of years ago.
So what exactly is common core math? Allow me to demonstrate the difference with a personal anecdote. In my math class we do something called “number talks.” Basically, I write an equation on the board and give students a few minutes to solve it in their heads. They share their answers and explain how they solved it. One day, I wrote the equation “100 – 92” on the board. Students got to thinking and I could practically see the cogs moving in their heads, fingers scratching out invisible numbers on the carpet where they sat. After what felt like an eternity, they signaled to me that they had come up with an answer – 8 – and we began to share our strategies. I called on a particularly enthusiastic student and he began to explain his thinking:
“Well first I crossed off both the zeros in the number 100. Then I turned the 1 into a zero and the first zero into a 10 and then a 9 and the second zero into a 10 -”
“Wait, you did all this in your head?!” I interject.
“Yeah,” he says proudly.
“Impressive. Go on.”
“Well then I did 10 minus 2 which is 8 so I put that down. Then I did 9 minus 9 which is zero so I put that down. finally I did zero minus zero and that’s zero so I put that down. So the answer is 8.”
Next I called on a student who was raising her hand to let me know she had a different strategy to share.
“I just counted up from 92,” she said, “If you’re at 92, you need 8 more to get to 100.”
“Oh,” I replied, “and how did you know that?”
“Because I know 10 minus 8 is 2.”
Boom. Base ten. No fingers needed. No crossing off the zero and making it a 9. None of that nonsense. It took her three seconds to solve the equation while he was over there trying to keep track of eleven different numbers in his head. They were both correct, but one is excellent at memorizing and one is excellent at math.
Common core is about conceptual understanding. It’s about understanding how our number system works. It’s being able to build a clock from gears and bits of wire, not just being able to tell time. It’s the process, not the final product. The way common core math is taught feels confusing and unnecessary to those who don’t understand it, those who were only taught the shortcuts, in the same way that building a clock is impossible for someone whose knowledge of a clock stops at telling time.
If you look at where our country has stood mathematically among the other developed countries of the world there isn’t much to be proud of. Music – we rock. Sports – we dominate. Cinema – we’re untouchable. Math – cue comedic wah-wah-wah sound effect. This source shows 35 countries consistently outranking the US in math. According to Professor F. H. Buckley at George Mason University, “We throw more money at our schools than just about any other country, and what do we get? For our K-12 school system, an honorary membership in the Third World.” It’s not that we aren’t as intelligent as those 35 other countries. We are arguably some of the best at rote memorization. It’s that for decades we’ve been teaching math all wrong. Common core seeks to rectify that by building conceptual understanding. Give it a chance and I’m sure you’ll see American students rise up through the ranks as capable mathematicians. The next time you count on your fingers to make change or carry the one while leaving a tip on your restaurant check, I hope you’ll remember these words and think, “she may be onto something!”