Blog Post: What's Right with Math Today
Joe Koelsch is the Dean of Instruction at KIPP Memphis Academy Middle. Before that, he taught math for 6 years.
You’ve probably seen the video. A split screen with two people solving the same multiplication problem. On the left-hand side of the screen a teacher uses “common core” math to solve the problem. She breaks down numbers, draws boxes and makes what seems like a simple problem infinitely more complex. All told, it takes about 3 minutes. On the opposite screen, a person uses “old school math” to solve the same problem in about 24 seconds, and then goes on to make a cup of coffee. The headline is, “This is what’s wrong with math today.”
The message is simple, and I hear it from both parents and teachers—even some math teachers—every day: why is math so much harder now than it was when I went to school? In the next few paragraphs I hope to answer that question using the example from the video… so if you haven’t watched it yet, take a few minutes now.
Let’s start by talking a little bit about the multiplication algorithm—the process being used on the right side of the split screen and how most of us learned to multiply. What most of us understand about this method can be summed up in the following way:
1. Multiply both numbers in the top number by the first digit in the bottom number.
2. Add a 0.
3. Multiply both numbers in the top number by the second digit in the bottom number.
4. Add the two answers together to find your solution.
These simple steps can be used to answer any 2-digit by 2-digit multiplication problem. It’s easy to teach, to learn and to replicate. Unfortunately, most of these benefits rely on the same faulty foundation: that doing math is about repeating a process to quickly find an answer.
It is this thinking that has created generations of uninspired and bored math students and teachers, and has left the United States ranked 38th out of 71 countries assessed in a recent international math assessment (http://www.pewresearch.org/fact-tank/2017/02/15/u-s-students-internationally-math-science/).
So, what about this “new math” is different?
For one, it is built on the belief that students should have a deep understanding of WHY they are doing what they are doing, before they worry about solving problems. In the example above, most students (and adults) have no idea why they are multiplying both digits in the top number by the first and second number separately—much less why they’re adding a 0. Without this understanding math is simply a game of memorization, which rewards students for quick and accurate repetition, not deep thinking. This has left generations students saying they are not “math people” simply because they don’t work quickly.
Common core math seeks to change this thinking by making the aim of math to understand deeply even at the cost of speed and efficiency. The area model is a perfect example. Rather than rushing through a process, it seeks to build understanding of the process by first breaking both numbers down by their place values. 35 is actually made of up a 30 and a 5, while 12 is made up of a 2 and a 10. So, when you are multiplying a 2-digit number by a 2-digit number, you’re actually doing doing 4 smaller, easier multiplication problems and then adding up all the answers. By making these partial product visible using the area model, students can clearly see how each of the numbers are working together to build their product
Another belief on which common core math is built is that math is all connected. While the standard way of completing a multiplication problem is really only applicable to…well… multiplication problems, the area model links arithmetic to geometry and later on to algebra as students learn about the distributive property and polynomial multiplication. By making these connections explicit, students can begin to see that math is not a complex series of processes to be memories and applied as quickly as possible, but rather a simple system of a few basic truths that can help us to better understand the patterns that exist all throughout our world.