The Myth of the Mathematical Mind
It was 1966 and I sat at my desk listening to my ancient, (even for those days) red GE radio with white dials. The AM station (FM radios were way too expensive for my dad’s wallet) KYSN (1460) was playing a version of the rock and roll classic song Gloria. I was making much better progress figuring out the lyrics to the song than trying to decipher the Algebra 2 problems in the book in front of me. I liked my Algebra teacher. And when he explained a problem on the board, I understood it. And I knew that when I asked him about the problem I was stuck on, he would explain it and it would seem perfectly clear. But now it made no sense to me. I looked at the answer in the back of the book, but it was useless. I could not make a connection. I didn’t even know how to start. The radio went to commercial, so I fiddled with the dial and was rewarded by picking up KOMA out of Oklahoma City. And so it went night after night. To no one’s surprise, I failed Algebra 2. Twice. No irony there. And all of the tutors I worked with didn’t understand why I didn’t understand. Everything they said made sense until I tried to do it myself.
My parents and teachers accepted my failure. “Some people have a mathematical mind and some do not,” they said. It was interesting to me that this logic didn’t apply to other subjects. Especially PE where I was supposed to use my toothpick arms to climb a rope my hands couldn’t fit around all the way up to a ceiling that was 10 meters off of the ground. The only failure that was acceptable was in math. And so it went until I got old enough to get tired of it. While stationed at Ft. Riley in 1972, I enrolled for one math class at KSU. I was determined to break my math phobia. With the help of a first year teacher from India, I succeeded. I finally understood why I didn’t get it.
What was different about her class was that she taught math as a language that we had to learn how to read and write. All of my other teachers had assumed I understood the difference between reading a math problem and reading an essay. They assumed I could follow the shortcuts they took in their heads. People who are really good at math, who have a mathematical mind, do not understand how to help those who don’t. Because of this fresh perspective, that math is a language rather than a set of facts an processes to memorize, a new world opened up for me. I’m not saying I became a math whiz. After all, just because most people know how to write does not mean they become successful writers. What I did learn was why I struggled and how to help others who struggle as well. That knowledge served me well in my public school teaching career. After I retired, I helped a lot of adults get their GED, and for most, it was math that presented the greatest hurdle. The biggest obstacle to their success was changing the beliefs about their mathematical abilities.
Society and culture constantly reinforce the idea that only certain people have the ability to do math. Exhibit A is a recent article on math education by Susan Engle of Bloomberg News. She suggests dropping anything beyond basic math as a requirement for students past 3rd grade. She even suggests that children only require twenty minutes of instruction per day to achieve these basic math skills. It reminds me of the citizen who suggested at a school board meeting that the district could save money by not hiring certified teachers for kindergarten classes. “Anybody with a high school diploma can teach kindergarten,” he said. I had never seen the two sweet ladies who taught the five-year-olds angry before. I remembered that moment when I saw Kindergarten Cop for the first time and wondered if it changed his mind.
This is not my first essay on education. I will spare you a tirade about about non-educators making sweeping pronouncements about education reform. But the elitist attitude about math is not only wrong but dangerous. Because of electronic devices, people need to understand algebra and geometry a lot more than they need basic math. Your phone will do basic math. Figuring out how long you can talk before the phone needs a recharge is algebra. People do algebra problems in their heads all the time. Figuring out distance between gas stops, how much you can spend in the grocery store or restaurant, and how much time until lunch are all basic algebra problems. One reason we have so many financial problems, both individually and as a society, is our poor math skills. Those poor skills have a variety of causes. Experts such as book publishers, school district officials, and college professors have made plenty of mistakes in trying to address the problem. But acceptance of failure, as well as resistance to change, is high on my list of things that are both fixable and extremely necessary.
We have national and international experts on math and teaching math. We need to listen to them and adopt their curriculum and frameworks. We need to train teachers, especially elementary teachers in how to teach math differently than they have been (see my essay on common core math). We need to force textbook publishers to adhere to these new standards. And then, most importantly, we need to work with parents to change their attitudes about mathematical instruction. The so-called “New Math” disaster of the Sixties and Seventies provides a blueprint of what happens when we do too much too fast without getting parents on board. The pushback on “Common Core” is another. When parents don’t understand how to help their kids do homework, or when the homework looks too different from their personal experience, there will be problems (pun intended).
Educators also need to grow a professional backbone. We need to hold ourselves, our colleagues, and parents accountable. When books start using a (*) or a (●) instead of an (X) to show multiplication and parents complain, we need to hold our ground. When parents want to argue that “that’s not the way I was taught” because we ask kids to write remainders as fraction in division problems, we need to hold firm. There are important developmental reasons for these changes. We need to learn them and become experts that parents can trust. A lot of parents don’t trust teachers now, and why should they? When most teachers are asked why they do something, they answer, “Because that’s the way the book does it.” Teachers who thoroughly understand their subjects do not use that line because they are thinking beyond the text.
Today, most teachers who teach a math class fall into one of two categories. Those who are so good at math that they don’t understand the struggles of students and those who only know just enough math to teach the lessons in the books. We need all teachers of math to know it well enough that they themselves think mathematically. We all need to change our attitude about math. We need the mindset of Gene Kranz towards teaching children when he said during the Apollo 13 crisis, “Failure is not an option.” As I struggled to climb that rope every day in PE class, I kept trying because I had to succeed to pass the class. Every day that I got a little higher was a victory. I didn’t ever have hope of becoming an athlete any more than most kids will become mathematical experts. For the record, it took me 12 weeks, but I finally made it to the top of that rope.