Rules and tools

I was helping an 8 year-old with a math problem the other day.  It looked like this:

She pointed to Luke’s pencil and said “Well, it’s not this one because you aren’t supposed to start in the middle of the ruler.” She then proceeded to try to convince herself in various ways that one of the others (besides Luke’s and Nate’s) was right.

It’s possible that no one actually told her “you aren’t supposed to.”  Someone is more likely to have said “don’t,” by which that person meant “it’s easier math-wise to do it this way.”

But we don’t tend to say things that way.  We tend, in the interest of simplicity, we imagine, to say things like “don’t” and “you should” and so kids get into the habit of turning our words into rules.  Rules that in cases like this make tools (like rulers) more difficult to use.  Every time we tell kids how to do something rather than telling them it’s how we do it, we train them to hear things as rules.  It keeps them from investigating, and then they not only get stuff wrong on tests, they don’t learn how the stuff really works.

In the case of the ruler, if kids have the chance to notice that when you don’t start at zero you have to account for the extra space between zero and the beginning of whatever you’re measuring, they get to realize what the ruler’s actually doing. Rather than feeling, as many of them do, as though the ruler is  just another mystery invented by the adults, and their only chance of survival in the world of adult rules is to do as we say and hope they don’t forget one of the rules.  When they’ve had the chance to explore and really come to understand, they’re less likely to panic if one day a test question comes along, asking them to, like this one did, really notice and account for length. Not to mention that often in the course of real life activity (sewing, building, decorating), it’s actually easier to pinch a measuring tape at, say, two and 14 and hold the resulting 12 inches where you want them than it is to try to anchor the awkward zero end of the tape, and stop at the 12.

One way to help kids find their way to the kind of understanding that will allow them to use tools and knowledge effectively and comfortably is to acknowledge that when we show them how to do things, we’re really just showing them how we do things.


Getting tough

I watched a talk this morning by an economist named Tyler Cowen about the impact of stories.  Every time you tell yourself this kind of  story (good guys/bad guys good neighbor/inconsiderate neighbor, good teacher/bad teacher etc.), Cowen says, you’re lowering your own IQ.  He’s taking liberties, of course but his point is well taken nonetheless.  Stories of good/evil right/wrong disregard the vast complexity of, well, everything.  And they leave us with little more than the comfort of believing we’re right or that we’re in the right camp.  Forgoing this kind of dichotomy means digging deep, looking farther into things than we generally go to the trouble to look.

In Cowen’s talk about stories he mentions the common story structure of “getting tough.” When we’re faced with what feels like an untenable problem, we often resort to getting tough. This is a popular one, he says:

“We [tell ourselves we] have to get tough with the banks. We had to get tough with the labor unions.   We need to get tough with: some other country, some foreign dictator, someone we’re negotiating with.  Now again the point is not against getting tough.  Sometimes we should get tough.  That we got tough with the Nazis was a good thing. But again this is a story we fall back upon all too readily all too quickly when we don’t really know why something happened we blame someone and we say ‘We need to get tough with them.’  As if it had never occurred to [a] predecessor, this idea of getting tough.  I view it usually as a kind of mental laziness, a simple story we tell: we needed to get tough, we need to get tough, we will have to get tough.”

He didn’t mention one of the greatest domestic examples of the getting tough story.  In the realm of education, we almost always resort to getting tough, on one thing or one party or another.  We get tough on teachers, we get tough on school systems, we get tough on budgets, we get tough on everything that has anything to do with the education of children. Because, I think, we can’t figure out what else to do.  And getting tough feels noble.  It feels consistent with the work ethic of our culture.  It hollers “Look how committed we are!  We’re so tough on this!  That proves how much we care about it!  We never give up!  We get tougher and tougher!”

And of course what happens is that all that getting tough trickles down to kids, who for the most part are doing what kids do automatically, which is learn, learn, learn, explore, explore, explore (though it sometimes looks like testing or pushing).  And then when it doesn’t work, when kids still don’t learn what we think they should when we think they should, we get tough directly on them. We take things away, we limit, we lay down the law.

What if we dug deeper?  What if we were to take the case that Cowen’s right, that this getting tough is a lazy story – a fall-back response born of paralyzing complexity?  Because it is.  So complex: Every time a new person is born, the adults charged with preparing that person to thrive on its own have an entirely new problem.  We say everyone’s unique, but if everyone is, which we know from genetics that they are, then we have a major challenge on our hands.  What works for one will not necessarily work for another. In fact it probably won’t.  What on earth can we do about that, if we really mean it that we want the best for everyone?  Who can blame us for falling back on an easy story, for saying “OK, well, we better just try harder to get them to memorize their facts and sit still and toe the traditional line.  Even if it seems like it’s wasting their talents, making them fight amongst themselves, making them sick. We don’t have much choice, because we can’t possibly give each of them something different even if that is what they need.”

What if we wrote a new story?  What if we wrote a story like “We have to get creative.”  Or “We have to start from scratch.” Or “Maybe we should listen to what kids are trying to tell us.”  What if we noticed that getting tough isn’t working, hasn’t worked for years, decades probably, and it’s not about to start working just because we say it louder or convince more people that we have no choice?

Both, and; Milo

Two either-or traditions in education – that one must identify with one discipline over another, and must choose between learning for practical reasons and learning for its “own sake” – can really undermine progress toward the secure livelihood and fulfilled life most people want for their children.  

In Adam Gopnik’s recent New Yorker piece about the 50th anniversary of The Phantom Tollbooth, Gopnik writes that author Norton Juster’s story of young Milo’s journey was an argument “for the love of knowledge, against narrow specialization… for learning, against usefulness.” Continue reading

Scare tactics and school zones

Fifteen miles per hour is very, very slow, for a car.  It occurred to me that in as hurried a world as this one, it’s quite amazing that (most) drivers are willing to slow down their vehicles that much in order to avoid endangering children outside of a school.

Then yesterday I heard a story about something that happened inside a school – a teacher using the threat of humiliation to motivate a group of fourth grade students to memorize answers to the single-digit multiplication problems. Continue reading

Lessons that aren’t

Sometimes lessons (piano, art, etc.) are great.  You find a great teacher, and the results are just what you were hoping for.  Your child learns a lot and loves the learning.

Often, though, lessons are not great.  Often they’re so bad that they turn an interest – something a child was excited to learn, wanted to know more about and have the chance to master – into a chore.

Sometimes this is because the teacher is not a good fit (for the child or the material or both).  But sometimes the teacher’s fine, and kids lose interest anyway.  The problem may be that lessons are not what kids are craving. Lessons are a logical response to interest – we see that a child is seeking further exploration or investigation in some area, or some kind of support we know we can’t provide.  It’s clear that they’re ready to go further, so we look to teachers and lessons.  But kids are not always ready or looking for instruction.

What if instead we were to connect the child with someone who could be a mentor in the area of interest?  Someone who would work alongside, model technique, be available for questions, make suggestions when suggestions are welcome?

This kind of an approach would make it possible for the child to continue exploring and experimenting and figure out whether she is truly suited to the pursuit.  It would also make it more likely that she’d eventually (or soon) ask for instruction and training.

There are of course children who take quickly and well to early lessons.  But many others don’t, so it’s worth considering the preliminary step of mentorship.  The bonus of adding that step is that it also makes room for those (of any age) who love their craft, whatever it may be, to share it with young people without having to turn it into lessons.

Beyond suffering

A few weeks ago I wrote about how kids are oriented toward fun, and how adults tend to be wary of this orientation.  It’s one thing to enjoy one’s self, we think, but too much attention on fun seems like it might suggest that a child isn’t motivated to do the hard stuff in life that prepares a person for adulthood.  It seems like a commitment to fun might eventually lead to, say, a 29 year-old child living in the guest room.

It helps to trade out the word fun for a word that’s a little less culturally charged.  Fun seems too much like the antithesis of work and productivity.  And we’re clear that the American Dream, whether we think of it as yachts and country club memberships, home ownership and health insurance, or a diet of organic food and a solar-powered car, is accessible via hard work.  Suffering, actually.  Kids can recite some variation of this ethic in their sleep: “You have to learn that sometimes you have to do things you don’t want to do.”  This is what we say when we’re worried that they’re getting too focused on fun – when they’d rather be running around outside with their friends than bent over a math book, when they’d rather build and rebuild a pirate ship out of Legos than read, when they decide to study art instead of economics. Fun freaks us out.

So instead of fun, let’s call it vitality.  Let’s imagine that when they make or attempt to make these choices (outside, Legos, art), they’re actually demonstrating a commitment to vitality.  They’ve noticed that when they’re doing these things, they feel alive.  They have energy, they feel light, they’re participating.  If you look at a child, or any person for that matter, and you see them going after something that brings them to life this way, it’s hard not to imagine that they’re on the right track.  And the really good news is that it doesn’t mean that they won’t ever choose to do something they don’t necessarily “want” to do.  If kids know and are allowed to pursue the experience of feeling alive and being committed to keeping that experience at the forefront of their lives, they’ll have reason – motivation – to endure what they have to do in service of that experience.  Even if it’s not always fun.  If you’re studying art, for example, because you find it invigorating in some way, you’re more likely to be patient with the parts of your studies that may in their own right be less than invigorating – practicing a particular technique over and over and over, or reading up on the financial ins and outs of selling your work, or even working extra hours at your day job because it means you can keep up your studies in the evening.  If someone tried to get you to do any one of those things and it wasn’t connected to something that gave you an experience of vitality, they’d just feel like Things You Have To Do.  If you feel alive and energized by building things out of Legos and you need a new $60 bulk set in order to build what you’ve got in your imagination, the extra chores you have to do for your neighbors in order to earn the money aren’t necessarily things you Want to Do, but you’ll do them without having to be told that it’s important to do things you don’t want to do.

We can teach kids to search for the realms in which they can experience profound commitment, or we can try, in a vacuum, to get them to do stuff we think they should do.  When they’re actually committed, they’ll still be able to use our guidance, but we won’t have to force them to do things just to teach them the lesson of doing things you don’t want to do.  In fact, the whole notion of Don’t Want to Do tends to fade and even disappear in the face of actual self-driven commitment.  Don’t Want To is a relic of a worldview we could let go of if we weren’t such creatures of habit.  We say we want kids to have better lives than we had, but we cling to our beliefs about how hard life has to be.  Every day kids are trying to show us how to be committed to vitality, to be guided and informed by it, and every day, we try to steer them toward suffering.

Tools for a fraction renaissance

Many a parent has told me that if only they’d had a set of fraction tiles when they were young, math would have gone very differently for them. That may even be understating things.  It’s hard to imagine a handful of plastic pieces could significantly change the course of a life, but then again, things are in a bit of a state, math-wise.

If math can go differently from how it often goes (ie Not Well), the course of a person’s whole life, not just math success, can be altered substantially.  This is not to say that you can’t have a perfectly good life if math doesn’t go well for you (nor that fraction tiles are necessary).  It’s just that math is held as such a staunch indicator of intelligence and promise that if you get the impression that you’re not one of the ones who’s good at it, it’s likely to get in your way to some degree. And that degree is not usually small.

All of this is to say that in my opinion there’s no purchase (including fancy curriculum, fancy enrollment, fancy tutoring) that is likely to make quite the difference that a set of fraction tiles can make.  Fractions are often the turning point for young learners of math; all the adding and subtracting of whole numbers made sense, came easily, and then suddenly those whole numbers were stacked on top of each other, separated by little platforms, and they got new names.  Maybe, kids think, I’m not so good at math after all.  The fraction tiles can help.

And you don’t even really need to do much with them.  The tiles pictured above are available with magnets (or can be easily equipped with magnets), so they can be… stored… on the refrigerator, just like those trusty Fisher-Price alphabets of yore.  Anyone who goes near the refrigerator sees them, sees that the fourths are twice as big as the eighths, that four twelfths fit in a third, sees how they all relate to the whole.  And then they’re there for reference too.  If you’re baking and you want to halve a recipe you can ask someone to check the fridge to see how much half a fourth is, or just go over and do it yourself (out loud: “Let’s see.  A fourth is when it’s broken into four pieces.  If the fourth got broken in half again, it’d be the same as… (sift around until you find the right-sized piece)  the eighth.  So I need an eighth of a cup.”

There are languages, apparently, in which fractions have names that make sense and reflect their conceptual basis (I’m told that in Chinese, 3/5 is “out of five parts, three”).  In English, not so much.  Without the linguistic support in place, the least we can do is let kids learn the concept first, let them see the fracturing and make sense of the notation with their eyes and hands before we expect them to make sense of it abstractly.

If you can get your hands on a set of tiles and get them up on the fridge when your children are still toddlers, great.  They’ll get familiar with them the way kids get familiar with anything they see a lot from the time they’re very young – without even trying.  But no matter how old your kids are, no matter how old you are, it’s not too late to let the tiles make a difference!  And you may even find that your teenager, or your neighbor, or your high-achieving college graduate daughter will walk by one day, wonder why you now have fractions on the fridge, and then suddenly exclaim “Oh!  NOW I get it!”

Because most of us, still, don’t. It’s not just you.