I never liked the “new math.” That is, math that was taught differently from the way I had learned it so many years ago. I had been a good math student and learned the “old-fashioned” way -- so that must be the right way. Right? Then, as a parent, every few years I discovered that there was yet a new way, supposedly a better way, of learning math. But why learn a new way—that parents have to figure out and learn all over again if they want to help their kids—when the old way was good enough! I trust you can pick up on my parental exasperation.
Now that my kids are grown, I thought I was done thinking about math curricula. Then, wouldn’t you know, NPR comes out with another story about math. Why we mostly teach it as we do and how it can and has been taught otherwise. Different people with different needs in different times and circumstances have required different ways of thinking about math—and numbers. The story got me ruminating about the nuances of math as a reflection on our human capacity for symbolic thought in our many varied circumstances of life. Math is actually a useful discipline to teach us something about perspective.
Take the number nine, for example. What are the different ways in which that number (or any other number) might be expressed? As the square root of 81? Or 3 squared? As 4 apples plus 5 oranges? And when and how does it matter that different fruits are in the equation? Or consider just what else the number nine might represent. The amount of money left on my Starbucks card? The distance to the nearest hospital? Or the time that it takes to get there? And are you measuring in minutes or hours? On city highways or country backroads?
As humans, we know a lot of things. Our capacity for representing, learning and explaining information is quite phenomenal. However, what we know—or think we know—is expressed through symbolic means and often dependent upon our subjective perspective—our own personal vantage points or experience. That’s why we have to be so careful with what we think we know about the world. And sometimes we have to let go of our certainty.
A few years ago I was introduced to the following poem by Yehuda Amichai. At first I didn’t get it. The place where we are right? What is he talking about? I believe in right and wrong. Sure, sometimes there’s ambiguity, indifference or some middle ground, but some things are just -- right. It’s a real destination and you know it when you get there, right? Read. Think of the places where you are right. Read again. Think again.
The Place Where We Are Right
From the place where we are right
flowers will never grow
in the Spring.
The place where we are right
is hard and trampled
like a yard.
But doubts and loves
dig up the world
like a mole, a plough.
And a whisper will be heard in the place
where the ruined
house once stood.
Don’t get me wrong: there are verifiable, reliable facts to be known. Two plus two is still four, but so is three plus one and the square root of sixteen. There’s more to life than twos and fours—in any real or symbolic sense. Our acquired knowledge and explanations are useful—until they aren’t any more. For instance, classical physics has been essential for explaining much in our world but we have been able to understand and accomplish so much more with the development of quantum mechanics.
We are in dire need of such advancements in our understanding of social relationships to create civil societies and peace across the planet. Being “right” about anything is not the end game. It’s the process and the variables that are equally important. For instance, any “traditional” equation for law enforcement with pre-determined set variables isn’t necessarily the right way or the only way to get to a civil society. Greater knowledge of additional variables such as unintentional bias, systemic racism and the human brain from the amygdala to neurochemistry are essential inputs into the civil society equation.
Those of us who live in and are beneficiaries of the dominant culture are often quick to settle on the right answer about race relations and so much more that currently constitutes our social structures, i.e. our social equations. But despite our impulse to resist new ways of thinking, we can’t stop learning. There’s more than one way to do the math. We must go beyond the places where we are right.