Wednesday, November 19, 2014

Getting Off Autopilot: Ours is Definitely to Reason Why

(originally published at

A survey of helpful websites tells me that the opening sentence of a paper should be “attention grabbing” to “pique the interest of readers.” It also tells me that it’s my “big chance to be clever.” Sadly, I’m not feeling very clever today, so I’m going to rely on the cleverness of someone who came long before me.

As Socrates said, “The unexamined life is not worth living.”  That may be a little extreme—I’m sure there must be some value in living totally in the moment, unburdened by reflection and self-doubt.  My cat seems to enjoy it. But thinking about our lives does give life some weight, some meaning. We were blessed (or cursed) with the ability to reflect, and as far as we can tell, we’re the only animals possessed of that gift (or burden). So we might as well put it to use.

Unfortunately, Socrates also said, “All I know is that I know nothing.” And I don’t believe he was a young man when he said it. So perhaps a lifetime of self-examination isn’t all it’s cracked up to be.

It’s a funny thing about knowledge. Often, when we learn something new, we crystallize the idea in a memorable and easily-repeatable format so that we can remember it, and so that we can bring out our little gem of wisdom and share it with friends. Unfortunately, nuggets of knowledge leave out a lot of nuance and complexity, and can end up leading to mis-understanding.  We may know the full meaning behind our words, but our listeners may have no idea what we’re trying to teach them. They’ll remember the catch-phrase, but they may not understand it. And after multiple re-tellings, we may even forget the meaning behind the words.

I think we are most guilty of this when we’re explaining rules and procedures to students. We want our charges to be able to remember basic facts and processes quickly and easily, so we give them short phrases—often in rhyme. For example:

“Ours is not to reason why; just invert and multiply!”

That’s how I was taught to divide fractions. That’s how a shockingly large number of Americans have been taught, and are still being taught. And why not? It’s effective; I can still do it, decades after first learning it. I don’t know why I’m supposed to invert and multiply, or why it works, or what it means, but my helpful little rhyme tells me not to worry about asking why. It’s not important for me to understand that a fraction is, itself, a little division problem—that ½ means “one divided by two.” It’s not important for me to remember that the relationship between multiplication and division mirrors the relationship between addition and subtraction. I don’t need to understand how numbers work; I just need to remember the rhyme and do as I’m told.  

I’m sorry to say that after an entire K-12 education in “just doing it,” I am now one of those adults who says he “doesn’t do math.” And this is criminal, because what is math, really? It’s just a language we use to solve problems in the world. God knows, we all have to solve problems, so we should probably all learn to be fluent in that language. I’m trying to get better, now, in my fifth decade of life. I shouldn’t have had to wait so long.

We’re in the middle of a battle, at the moment, between the authors and advocates of new standards that demand rigor and conceptual understanding in math instruction, and a variety of angry adults who want to know why their children are being asked to figure out nine different ways of solving simple math problems. It doesn’t take much investigative reporting into credit card debt, house foreclosures, or picture-based cash registers in fast food restaurants to figure out that adults in this country are, by and large, Bad At Math. But that doesn’t stop us from getting angry at anyone who dares to teach our children differently than we were taught. This is, I suppose, the legacy of learning nursery rhymes that tell us never to ask why.

Here’s another example of autopilot instruction from elementary mathematics…

“If you need to multiply by ten, just add a zero” 

It’s not a rhyme, but it’s memorable. Is it true?  Sure. If you want to multiply 237 by 10, all you have to do is add a zero at the end, giving you 2,370.  That works. Don’t ask why it works. Don’t worry your little heads about what it means. Just do it.

Unfortunately, the approach stops working after a while.  Decimals become a problem, because obviously, 2.37 x 10 is not 2.370.  Of course, you could learn another little rule about where to put your zero when you’re dealing with decimals. But at a certain point, it starts being counterproductive to add codicils and amendments to your nursery rhymes. You could just learn something about how numbers work, and then you wouldn’t have to worry any more.

I’m picking on math instruction, but teachers can go on autopilot in the humanities just as easily. How many times have you heard (or said) the following to explain the difference between a metaphor and a simile:

“A simile uses like or as”

All of my English teachers phrased the distinction that way, and I’m pretty sure I used the phrase myself, back in the day. And it’s accurate, as far as it goes. It’s a true statement. It’s just a useless one. It doesn’t teach you anything.

A simile uses like or as…but why? To do what?  That’s the part we seem to leave out. And it’s not an inconsequential part of the equation. A metaphor is a complete and unlimited comparison between two things. It says Thing 1 is Thing 2. A = B. Love is a rose. That guy eating pizza over there is a pig. Because the phrase puts no limit on the comparison, it implies that the comparison is total: love resembles a rose in all of its aspects and attributes. That guy eating pizza has every possible characteristic of a pig. A simile, on the other hand, precisely because it uses like or as, puts a limit on the comparison. If love is as fragile as a rose, then the resemblance is limited to that fragility. Love is neither red nor flowery nor thorny nor green-stemmed. And if it is thorny, well, then, “Love is as thorny and fragile as a rose.” How’s that?  And the guy eating pizza? Maybe he only eats like a pig.

Every time I explain this to someone who claims to have “never gotten poetry,” they thwack their forehead and say, “D’oh!” Which, incidentally, is exactly what I do when someone finally explains a math rule to me in language that makes sense.

Our autopilot parroting of rules isn’t limited to esoteric topics. Poetry is difficult. Outside of school, not everybody reads it or writes it. But how about simple paragraphs? Everyone has to write a paragraph, now and again. And what’s the rule that so many English teachers give their students to remember? 

“A paragraph has five sentences”

First of all, no it doesn’t. Not always. And second of all, if you think it has to, then why? Why five, exactly? What kind of sentences are they? Just five random sentences in any order, as long as there are five? We don’t define sentences by how many words they contain; why would we define paragraphs that way?  There are children in classrooms all over the country who are getting papers marked as incorrect, just because some novice teachers or aides are implementing a rule that they, themselves, don’t understand. A paragraph isn’t a numerical equation. It’s an elaborated or explained idea. A sentence states an idea, but a paragraph explains and illustrates and perhaps defends that idea. Once it has done its job sufficiently, the paragraph is done.

The Five Word Rule

Here’s one more rule I love:  If you encounter five unknown words on a page of a book you’re reading (again with the fives), you should stop reading the book, because it’s too difficult for you and it will only frustrate you.  We can call it the Five Word Rule. Yay! Simple to name, simple to remember, simple to apply. Unfortunately, it’s nonsense. I encounter words I don’t know all the time. That doesn’t stop me. The key to comprehension is ideas, not words. If I can get the gist of a sentence without knowing one particular, strange word, then I’m fine. If I can get close to the meaning of a word using context clues, so much the better. What I need is the idea contained in the sentence. If I get that, I’m understanding what I’m reading.  So if on a single page I encounter five sentences that I can’t make sense of, then I might be inclined to set the book aside. Because the sentence is what contains the idea that I need to understand. And if I’m missing five ideas on a single page, I’m not getting much out of the book. What the Five Word Rule teaches children is that they shouldn’t have to work to understand something. Why bother figuring out context clues? Why think through the meaning? Just count up to five and chuck the whole book. Go back to Dr. Seuss or something—something you already know how to read.  Treading water is fun.

I’m being a little harsh here, I know. There are teachers all over the country who are using the Five Word rule thoughtfully and carefully, and are teaching their students to work and grow and learn. In fact, there is probably nothing wrong with any of the rules I’ve picked on here, if they are used thoughtfully and purposefully. But that’s the whole problem. They’re not, far too often. When we fall back on easy rhymes and catch-phrases and use them in place of actual explanation and illustration—actual teaching—we’re in trouble. We’ve switched over to autopilot. And we need to catch ourselves, when we do that. We need to wake up, switch back to manual control, and drive our instruction.

Philosophy can be lovely and eloquent until you have to live by it. Saying that the unexamined life is not worth living puts quite a demand on us—any of us, regardless of our profession. It asks us to stop going through the motions and really listen to the things that come out of our mouths. It asks us to watch ourselves as if from across the room, and say, “Does that make sense, what I’m doing? Is that a good thing to do?”  It’s not a comfortable or a pleasant activity, but it’s a discipline we should all develop, even if it’s only once a year. It seems to me that as educators, we should be role models of examining actions and re-thinking positions. Just because we’ve said always something in a certain way or always taught some things in a certain order doesn’t make it right. Every once in a while, we need to stop, and think, and decide.

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