Updated below, Tuesday afternoon, January 24, 2017.
Adapted from the Twitter feed December 10, 2016. Posted January 23, 2017.
Math ain’t natural. But it is beautiful.
Taraji P. Henson as NASA mathematician Katherine Johnson doing some of the math that would send the Mercury astronauts into space and bring them home again in the movie about the team of African American women computers who helped get the United States space program underway, Hidden Figures.
Personal prejudice: Most people can’t do math. What we call math is actually simple arithmetic. Adding, subtracting, multiplying, and dividing. Calculating. What Jethro Bodine in his pride at his sixth grade education called cipherin’. Nobody does math, and can do math, until they understand why multiplying two negative numbers together produces a positive number. I’ve never understood that one. So I can’t do math.
I can cipher like a wiz, though. Like a sixth grader, at any rate.
This Paley Center panel discussion on Hidden Figures was interesting and I can't wait to see the movie but I was a bit disgruntled by the way people on the panel who know better talked about math as if it's all arithmetic and anybody can do it and do it well if they put their mind to it and get over the idea it’s too hard.
The panel included the movie’s director Ted Melfi; author Margot Lee Shetterly, who wrote the book the movie’s based on; Dale Davis Jones, a Distinguished Engineer at IBM; astrophysicist Jedidah Isler; and actor Aldis Hodge, whom I know best as the supernerd and hacker Hardison on Leverage and who was introduced, to my delight, as a “micro-mechanical engineer”---he designs and builds watches. The moderator was Dr. Knatokie Ford, senior policy adviser in the White House Office of Science and Technology Policy, a post you have to wonder’s going to exist in the Trump administration. If it does, it’ll probably be held by a Baptist Minister. The audience seems to have been made up of junior high and high school students. I think the panelists were trying to encourage kids, particularly girls and young women, and even more particularly girls and young women of color, to take up math and stick with it in order to go on to careers as scientists and engineers. This is a good thing.
But I didn’t like it that learning to do math got implicitly compared with learning how to write a sentence that parses.
As the son of a physicist and computer scientist who, hard as he tried, never could get me to follow his math when he helped me with my homework, and as someone who was an A student in math in grade school but was stymied by ninth grade algebra and defeated in eleventh grade by calculus, and as the father of someone who has struggled with a severe math learning disability---dyscalculia they’re calling it these days---and is two daunting math courses shy of completing his degree, I’m here to tell you...
Math ain’t natural.
We don’t think in numbers. We’re not good at holding them in our heads. Most of us count “One, two, three, many” and then, if we’re forced to go higher, “Many more, and a lot!” and that’s as high or as complex as our numbers get.
Some of this is the result of biology, anatomy, and evolution---the evolution of bodies, and then the evolution of culture.
Evidence suggests that humans were talking to each other from the start, putting words to their feelings, coming up with ideas that could only be created with words, naming things. Naming things is what made us human. We evolved to speak and we evolved from speaking. Culture, art, and society are the result of words. We didn’t start counting until later when societies became more complex and more things needed to be sorted out. We can see our ancestors inventing math.
Some of it is a matter of habit and training.
The writing skills required to write a decent cover letter or quarterly report aren't much different than those required to write a novel. But the math the heroines of Hidden Figures do to send astronauts into space and bring them home again is a little different than what you use to balance a checkbook. I can teach students to write a good cover letter using a poem by Adrienne Rich, or a play by William Shakespeare, or a blog post by Ta Nehisi Coates. In fact, I have. But I would be in awe of the professor who can teach her students how to do math using the General Theory of Relativity. And in the course of a day having to know what words mean precisely and how to use them effectively---having to make yourself understood and having to understand what others are trying to mean by using the words they’re using---comes up more often than having to cipher.
Sometimes “You know what I mean” covers it. But, generally, “you” doesn’t. That kind of sloppiness with words leads to fights, lawsuits, and messy divorces. People have to be more precise in their use of words, if only to stay out of trouble. More precise than they usually have to be with numbers. To take care of most of our daily business we can get by with simple arithmetic. Often, we’re not really using numbers at all. We don’t calculate. We don’t cipher. We don’t have to. We remember. If we paid attention and studied and did our homework in grade school, we memorized just about all the calculations we’ll ever need. We don’t have to calculate that 2 + 2 = 4 or 10 x 10 = 100 every time. And handling more complex numbers is a matter of remembering our way through columns of numbers. If we remember to carry and know how to round off, we’re usually fine. Close enough is good enough.
That’s in casual conversation. In practical situations, when numbers matter, we still get by without doing math or, much arithmetic. Instead, we guesstimate. We eyeball. We measure by matching the lines on a measuring cup and count out the required amounts according to the instructions. We look for the sign that says “SALE” and---if we can’t remember what we paid for the same item last time, and we probably can’t, because, like I said, we’re not in the habit of keeping numbers in our head---trust that “SALE” equals “cheaper”. To “do” a lot of everyday math, you need to be able to read more than add and subtract, and tell a good story.
If you’re painting your living room, it’s useful to have a rough idea of how many square feet of wall you have to paint so you can estimate how many gallons of paint you have to buy. Saves money and extra trips to the paint store. But an important part of the job is telling the clerk mixing the paint what you hope the room will look like when you’re done and another is describing the result to your friends at work when the photo on your phone doesn’t capture the full effect. And you don’t need to keep whatever measurements and calculations you started with in your head once you’re done. Nobody at the office wants to hear exactly how many square feet of wall you turned from taupe to eggshell white. They might want to know how many gallons of paint you had to buy and what that cost, but they’re more likely to ask you to define taupe and eggshell white and explain why you chose the color change. What they’re really asking for is a story. “Tell us the story of how you painted your living room.”
Learning to write is learning how to tell a good story. Sometimes it’s a better story if there are numbers to illustrate it with. Sometimes the stories are about the numbers. But the ability to tell the story gives the numbers meaning, purpose, and effect.
Even at work, if you’re not a scientist, engineer, or an accountant, and math is called for, you don’t have to do the math yourself. You can use a calculator, ask Alexa, read the fine manual, check the price list, or call Bob over, he’s good with numbers. But then you better be able to explain to Bob what the problem is and what you’re looking for him to help you with. You need to be able to tell him that story.
So...as a self-important writer and as someone who has taught writing, I can’t help thinking that after elementary school, taking courses in composition, rhetoric, and literature is more not only more useful than taking classes in math, I think it’s more important!
The ability to think clearly requires you to have the words for you mean and be able to put them in the best possible order. But communicating effectively, telling good stories, requires a breadth of knowledge about how the world works and what makes people tick and that imagination that requires a liberal education and the development of a sympathetic imagination. After a certain point, teaching reading and writing becomes teaching history, philosophy, psychology, ethics, and morality, and even science. Teaching math is always a matter of teaching harder and harder math.
Math is about itself. Reading and writing are about everything else.
So, as someone who’s earned his bread teaching in the humanities, I’m jealous of the attention and the money directed at the math and science and engineering departments. I resent that the humanities have to justify their continued existence with crass economic arguments.
“Hey! Our students can get good jobs too! Well, at least they learn some stuff that can help them once they get good jobs, like how to write a memo or make an effective sales pitch!”
I hate the word neoliberal. But I only know it as an online epithet. Certain cadres of internet "Progressives" like to use it as an all-purpose insult for liberals and Democrats who don’t adhere to any point of their programmatic political doctrine, and as such it has whatever meaning the user gives it because it suits his purposes or feelings at the moment. Which is to say it has no real meaning. But if it does have any meaning in the analog world, it’s when it describes the self-interested principle that social good is best achieved by letting capitalism take its natural course. If it saves money or makes money and some of that money is used to promote the general welfare, then hooray! And if that’s what it means, then our colleges and universities have become hotbeds of neoliberalism.
STEM is a neoliberal dream.
Promote STEM and the government will throw money at your school. Promise the kids good jobs and they’ll flock to your school and more government money will follow. Target minorities and girls in particular and even more money sluices in. And look at the good you’re doing while you build the endowment and hire more administrators. Those kids get a first class education (Never mind that most of their classes are taught by grad students and adjuncts.) and will likely get good jobs when they graduate. They’ll become productive members of the wealth producing elite and isn’t that the whole purpose of education and of life, in general?
I don’t like any suggestion that the reason for going to college is job training. Students shouldn’t learn the principles of science, technology, engineering, and math just because that’s where the money is.
In no way am I saying students don’t need to learn to do math. It’s critical to critical thinking. It teaches them to recognize patterns, make associations, see things individually and grouped rather than lumped together.
The country would be better off if everybody knew how to use words precisely and how to think with numbers.
Like I said, we often get by with “You know what I mean.” Donald Trump ran his whole campaign depending on it. Of course what he really depended on was people not knowing what he meant and, it turns out, they didn’t.
Trump may not have won even the first Republican debate if more people knew how to use their words and knew when others didn’t or were using them to mean what they don’t mean, they being the words and politicians on the make using words to dissemble, distract, and deceive.
And he might not have won if more people could handle numbers on the fly.. If they could evaluate the numbers politicians throw around instead of react to them. “Gee, that sounds like a lot!” But is really it a lot? Is it too much? Or too little? Better if they understood the system and how things work and have worked or ought to work, realistically as opposed to how they wish it did. More of those more people should include journalists.
“Drain the Swamp means what? The alligators get to come live in my swimming pool?”
“You’re not going to cut Social Security or Medicare but you’re going to sign Paul Ryan’s budget? But destroying Social Security and Medicare is built into Paul Ryan’s budget. Paul Ryan’s budget doesn’t balance unless there’s an economic miracle but it’s that balancing of the budget that brings about the miracle. Which is circular non-reasoning, but on top of that, in order to even come close to the point where the economic miracle will take care of things, Ryan has to get rid of Social Security and Medicare.”
Now, of course, the world needs scientists, engineers, and mathematicians. More of them and better ones. The world needs poets and painters and musicians and actors and dancers and historians and philosophers too. More of them and better ones too. The world must be peopled and the people must be educated, liberally, so that they know to treat each other as people and how to do that. Which sounds very egalitarian of me but my idealism has an hard, pragmatic, elitist, and, well, neoliberal core.
One of the goals of good teaching is identifying, nurturing, and helping to hone talent. And while talent has a way of discovering itself sometimes, often it needs someone to come looking for it. A kid might not know she has the talent. He might not know he’d enjoy using that talent. They might not know opportunities are there for them to live lives built around and out of using their talents. And then they take a class, the get a teacher, they meet a friend and...their world opens up! They’re not just on their way up and out by way of a good job. They’re on their way to careers that will make them happy and productive, productive in the sense of making the world a better place to live in and not just a place with more money circulating. Their happiness and the hopefulness that follows from it spreads and the moral and spiritual wealth of the People increases. That’s true for children with any sort of talent, not just a talent for doing math.
That’s the ideal reward of good teaching. The practical side of the job includes teaching skills that allow less talented and untalented students how to do competently what their talented classmates do with mastery. This helps them to be better in the fields where they are the talented ones and, where it doesn’t help with that, a sense of competency---real competency, being able to do something well if not expertly---it still helps them on to happier, more hopeful, more productive lives.
There’s more. In learning the skills that allow the less talented and untalented to do competently what their more talented classmates do with mastery they learn what it takes to be a master of a talent or a skill. They learn how things work, and they learn what it takes to make things work. They don’t learn to be experts themselves, necessarily, but they learn what expertise is and where it comes from.
You can’t confidently hire an expert and put their expertise to work for you if you don’t understand what beyond their degrees and credentials make them expert. You either take them at their word that they know what they’re doing or...you don’t. You resent and reject them on principle, and get Brexit and Trump as the reward for your skepticism.
At any rate…
Jedidah Isler was the first African American woman to earn a Ph.D. in astrophysics from Yale. Dale Davis Jones is the first African American woman to be named an IBM Distinguished Engineer, which is a job as well as an honor. Mentoring younger engineers is one of a Distinguished Engineer’s responsibilities. I would guess this is the basis of Jones’ and Isler’s stake in STEM education and in education in general. They want kids to have the same opportunities they’ve had.
And it appears that that’s one of the lessons of the movie Hidden Figures. More than being able to do math that sends the Mercury astronauts into space, it’s about being able to put your talents, skills, brains, ambitions, and dreams to work for your own happiness and for the betterment of the world, and that requires getting an education and making the most of your advantages and finding the courage and strength---in yourself and from the company of others of like minds and like dreams.
So, despite my disgruntlement, I’m as whole-hearted a champion of kids taking math as I am of their taking every other subject.
But there is one more thing, another reason for taking math classes all the way through grade school and up into college.
I can’t do math. But I’ve seen it done often enough to know something about it.
Math isn’t natural. But it is beautiful!
And I think everyone can and should learn to appreciate its beauty
I wouldn't compare learning to do math to learning how to write. I'd compare it to learning how to compose music.
Maybe this is why so many mathematicians and scientists are also good musicians.
I don’t know about engineers, but I have this about mining engineers.
Updated to reflect my final grade: I liked this post when I was finally done with it, but Sherri's comment had me feeling like I didn't read the question correctly and blew the assignment, and now that PZ Myers has taken his red pen to it, I feel like I flunked the final. To tell you the truth, though, I haven't had this much fun being wrong in a long time. Here's Professor Myers' corrections: Being Human Ain't Natural.
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