The New Math

image from Reddit.com

For years (yes, even before Common Core) I've been hearing about this "new way" of doing math. Parents complain about it endlessly, they feel like they can't even help their elementary students do math. Finally, one summer afternoon I asked my neighbor to explain it to me. So she told me how they taught her son to subtract large numbers by the nearest ten. My smile must have exploded, "That's how I do math in my head!"

"Really? My son hated it. He's so smart," (now a High Schooler) "but he struggled so much in elementary math. I finally told his elementary teacher one day that I was going to teach him the old way and he caught on right away. He never struggled again. He was so happy when I showed him how to write it all out and follow the basic carry over steps we were taught as kids."

Ugh ... I hated carry over. I still do. The other day, just for fun, I tried to sit down and divide 5 by 52 using the old algorithms I was taught as a kid. My answer, 14. Which I knew was wrong. I knew, in my head that the answer was 10.4 How?  Well, 5 goes into 50 ten times. Two-fifths is more than one-third but less than one-half. So that means the decimal has to be point-four. That is how I do math! That is how I have always wanted to do math. But I was taught algorithms. Yuck, I hated algorithms. Algorithms didn't let me divide to the nearest ten (or double or third) and then fraction out the remainder. Algorithms made me carry over, and subtract, and follow some stupid formula that I had to use to show all my work or I'd loose points. Ugh, algorithms.


One summer (or spring break) when I was home for a week during my college years I pulled out my old school box. Each of the kids in my family had a school box. It was a sturdy paper box that we filled with school work and class reports. Some of the items were purposefully kept by our parents, others were things we choose to put in there. If it ever got too full, we'd have to go through it and throw away things that we no longer cared about. Eventually, I threw it all away. But I'll never forget the discovery I made that sunny day in my parents basement. During my elementary years I was fabulous at math and almost horrible at Language Arts.

The standardized test scores that sat in front of me proved this. I was rarely proficient in Language Arts, and almost always advanced in science and math. My 21-year-old self was in shock. I hated math! I loved reading! Then there were the class reports. Hand written messages from some of my favorite teachers. They all had a common theme. "Alizabeth needs to read lots of books this summer to work on her reading skills. Keep up the great work in math." WHAT???

Apparently my parents followed that advice well, because I remember having such a strong love for reading. Did I, in my earliest elementary years, love math? Maybe I had, maybe I learned to hate it during my older years -- as it began to challenge me more.

Maybe, I hated it because of the way it was taught. Just like my young neighbor hated the way he was taught.

Now, whenever I hear someone complain about the new way of doing math I try my hardest to explain I hated the old way. I yearn for anyone with common sense to know that each child learns in a different way. A teachers job is to teach enough variations of "right" that the student can figure out what works best for them.

Had I been taught number sense and frame tens my whole life path could have been very different from the one I chose. Who knows, engineer, accountant, statistician -- but probably still English teacher. Nothing excites me more than a good book and the challenge of creating critical thinkers.

Ah, critical thinkers. In the past I've always thought History, English, and Science were the only subjects that really taught critical thinking skills. Math had an absolute -- one way and only one way to figure things out -- an algorithm.

Looking over the Common Core State Standards for Elementary Math, I realize Math can teach children to be critical thinkers.

When you see 6x7 does your mind jump to 42 because you have it memorized? Or does your mind jump to 42 because you know 21+21 is 42? Either way, you are right. Math isn't absolute. Anyone who gets into the complexities of Algebra knows that there is more than one way to look at numbers. Heck, by the time you make it to Algebra you start using letters to understand numbers. Whoa!


I remember my High School Algebra classes well. I was one of only three ninth graders in my Algebra II class. Some of the smartest Sophomores in our school were in that class. And I figured my teacher, one of the nicest men I've ever known, was just over complimenting me when he said I understood math better than most the kids in the class. How could that be, I felt so lost every time he taught the lesson. I was dazed and confused, constantly worrying about what I'd say and how I'd act once we were free to work on our problems. I knew two of the tallest, cutest boys in the Sophomore class would turn their desks to face mine, and they'd make me laugh while simultaneously solving problems without effort. I'd pretend to be completing my assignment, knowing full well I'd go home and do it all on my own. In my own brain, in my own way. I'd review the textbook's explanations and then I'd figure out how to do it easier for me. I was always shocked when whatever I was doing matched the answers in the back of the book. Then I'd continue doing it my way.

In my college Algebra class I was once again sitting behind an attractive boy one year my senior. Once the teacher (one of the best I ever had) finished the lesson she'd tell us to pair up and occasionally ask me to tutor him. Looking back I realize that was no coincidence. He understood math the way I did. After each lesson it seemed as if she came to my desk to watch me do the problems my way, just so she could catch any mistakes I might be making, my way, and then she'd let us loose. Or if my way wasn't working quiet right, she'd help me sort it out or stick with me until I understood her way, the textbook's way, the old way.

Sometimes, for fun I tell Ben how I do long addition or multiplication in my head. I don't carry over. I hate carrying over. If I have to carry over I need a paper and a pen -- no a pencil, I'm bound to erase something. I can't just carry over in my head. But I can keep track of rounding up and down from tens in my head. The problem is, I always doubt myself. I always assume I'm going to get the wrong answer, because I was told time and time again that I had to use the algorithm. I had to do math the old way or I'd mess it all up.

I'm not here to argue that the old way was bad form and teachers should only use the new way. I'm not even 100% sure I know what the difference is. I know that during the elementary years they refer to one way as "number sense" and another as "math counts" and one as "algorithms." I also know that Common Core does not dictate which version a teacher uses. It simply outlines the set of skills a child should master by the time one level is finished. The core is the floor, not the ceiling. The skill set listed there is the minimum, not the max.

I hope my children have elementary teachers who are skilled enough to teach them all possible approaches to math and numbers. I hope my children are smart enough and confident enough to think critically about which approach works best for them on each equation.

I hope they don't grow up thinking they hate math.