An Essentially Creative, Even Artistic, Pursuit

Surveys of American students find that the majority of us feel relatively good about ourselves and mathematics through elementary school, an opinion that takes a sharp nose-dive starting in about middle school and continues in a downward trend through high school. This pretty much tracks with my own experience. I was usually pretty good at figuring it out and aside from a couple clinkers, I tended to bring home A's and B's. I even managed a surprisingly high score on my college entrance SAT test, an achievement I ascribe to my strategic ability at test taking more than any mathematical aptitude, which encouraged me to continue pursuing mathematics coursework through my first couple years at university even though I had no future plans that seemed to call for those higher-level math skills.

But even as I was capable of playing the math "learning" game, I didn't like it. I found it tedious and pointless. When I expressed this opinion around adults I was mostly told, in so many words, that I was wrong. When I shared it with my peers, they mostly agreed it was boring, with the exception of the occasional friend who, was, if not joyful, at least able to take a puzzle-worker's pleasure in ciphering. Those were the friends I chose as homework partners, especially if they were pretty girls, which may at least in part explain why I could keep my grades up while despising the work.

Today, as a preschool teacher, I don't attempt to "teach" math, yet all day long I see children engaged happily in both solitary and collaborative mathematical pursuits through their play. It's quite clear to me that humans, young ones at least, take great pleasure in the organizing, sorting, and patterning that lies at the heart of what we call mathematics. They take great joy in counting, in comparing, and in those eureka moments that come with mathematical discovery. It flows through them as naturally as, say, art. 

So what happens? Is our national "hatred" of math a problem with humans or a problem with how we try to teach it?

In his book A Mathematician's Lament, mathematician Paul Lockhart strongly argues that math is an essentially creative, even artistic pursuit, a notion that is rarely reflected in how we attempt to teach the subject in American schools. It is an eye-opening read that really got me thinking.

What if we taught art the way we teach math? We start by showing students all the colors, not to play with, but to memorize. Then, after a few years of that, we give them two or three colors and permit them to only paint straight lines over and over until they've mastered them. Then we work on arcs and then other curved lines for a few years. Finally, after many years of this sort of drilling, we move on to shapes where we drill some more. Then comes more repetitive drilling on colors, color mixing, composition, until finally, after many tedious years, the art student, now at a university, is finally permitted to actually create something of his own. Oh, and never, ever take a peek at someone else's paper. It's a ridiculous, backwards idea, but in a very real sense, this is exactly how we attempt to teach math.

I have a good friend who holds degrees in both physics and math. He once told me in frustration, "The problem with math in high school is that they think it's about numbers and memorizing and right answers. There are no right answers in math! It's messy!" You see, for him, math is a blank canvas upon which he can explore, guided by his questions and creativity. This is how I see math being explored by the children in our preschool classroom.

I'm a product of the sort of math education one finds in our schools today: one of rote learning, where you don't get to ask your own questions or express your own creativity. I'm sharply aware of how ignorant I am, but I do know what math is not: it is not algorithms and ciphering, even as that forms the basis of what we call "math education." I do know that math learning can and should be a joyful, fully human experience, one, like art, that is not discrete from the rest of the world, but woven through everything we do, yet we are producing generation after generation of young adults who "hate" math. 

This is not a problem with people or math, it is clearly a problem with how we expect children to learn it.

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Until He Was Ready To Walk Away

I used to keep a collection of styrofoam around the place, but over the years I've disposed of it and not just because it takes up a lot of storage space. Sure it's fun to stick or hammer things into it, like golf tees, but that idea invariably and ultimately turns into a festival of breaking, then shredding, leaving those static electricity filled tiny toxic balls all over the place, which is a mess worse than glitter and not nearly as festive.

Still, when someone from our community purchases new electronics or something that comes with large pieces of the stuff, they often think of us. I don't even know where our most recent pieces came from, but I'd spotted them stashed where the kids couldn't reach them on the playground so decided to make use of them for a day.

My idea was to combine the styrofoam with pipe cleaners. It's not the first time we've done this and while there are usually a few kids who get into the process, it's not generally one of the most popular things we do at the art table. Last week, however, there were even fewer takers than normal. The parent-teacher assigned to the project did her best to role model playing with the things, but the station was evolving into a game in which kids were placing "orders" for things like pipe cleaner "bracelets," "flowers," "glasses," which the adults then manufactured for them. It's a fine activity, I suppose, and I guess the kids had found a way to make it fun so who am I to judge?

That's how things stood when my friend took a seat at one corner of the styrofoam and pulled a container of pipe cleaners toward himself. If he had taken note of what the others were doing, it wasn't apparent. He started by successfully sticking one end of a pipe cleaner into the styrofoam, then another, then another. As he worked, he began to twist the fuzzy wires, bending the pieces together, weaving them together, purposefully tangling them. He didn't say a thing as he worked, concentrating fully on his creation.

I was tempted to sit beside him, either to ask about what he was doing or to, as I often do, begin narrating his process in the hopes of attracting more kids to the project because everyone wants to be part of our classroom's ongoing stories, but I didn't. Instead, I left him to his solitary work, a man with a vision. I stopped by several times over the course of the next half hour as his magnificent tangle became increasingly complex. When he was finally finished a half hour later, he pushed himself away from the table and didn't look back.

I gave some 40 kids the opportunity to play with the styrofoam and pipe cleaners over the course of the day, most of whom declined the invitation and even those who accepted it tended to treat it like a kind of drive-by activity, something not worthy of their full engagement. But one boy did and that's enough for me to call it a success.

We carefully uprooted his sculpture from the styrofoam and put it in his cubby to take home. I'm sure from his mother's end, it just looked like he had simply crushed and twisted a collection of pipe cleaners in his fists, the work of a moment. Most preschool art goes home this way, a product that can't by itself tell the story of how it came to be. I've described the visible part of his process here. I can make guesses about what he learned. I could question him. I could even, I suppose, devise some sort of pre-test and post-test and compare the results to produce "data," but at the end of the day no one but this boy will ever know what questions he asked and answered while creating this purposeful tangle of pipe cleaners stuck into styrofoam. 

It needs to be enough for us to know that it engaged him until he was ready to walk away.

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Questioning Authority

If you would be a real seeker of truth, it is necessary that you at least once in your life doubt, as far as possible, all things. ~Rene Descarte

On the first day of school, the day I meet many of our two-year-olds for the first time, I make sure our box of plastic farm animals is handy. As the kids arrive I greet them, then introduce one of the pigs by holding it up and saying, "The pig says, 'Moooo.'"

Most of them laugh, "No, the cow says 'Moo!'" or "The pig says, 'Oink!'" Some squint at me like I'm crazy, often glancing up at their mothers as if to say, You're leaving me with this guy? In fact, I tend to do a lot of this sort of goofing around. I might, for instance, sing the Alphabet Song with the letters in the wrong order, "D, N, Q, P, T, R, A . . ." Or maybe I'll insist that the carrot sticks are candy, or that the book we are about to read was printed upside down, or that I'm listening with my nose. You see, I want children to really listen to me and if I say something that doesn't match up with what they already know to be true I want them to call me on it.

That's right, it's an overt attempt to cause the children in my care to question my authority. I want them to know that not only is it okay, but that I expect it. You see, I want the children I teach to grow up to be citizens who are not only able to identify BS when they detect it, but to speak up about it. As the kids get older and more experienced in correcting Teacher Tom, I might push back, insisting for instance that I've heard pigs say 'Moo' with my own two ears. Sometimes I'll even say things like, "Listen, I'm the grown-up and you're the kid, of course pigs say 'Moo.'" It's deeply gratifying when they refuse to budge from their insistence that I'm wrong, often laughing at it like a joke, but sometimes angrily, letting me know that they aren't having any of it.

Of course, the whole idea of children questioning a teacher's authority is a challenging one for many people, especially those who only know traditional schools, but in a democratic society, authority is not imposed, but rather granted by the consent of the governed. I, like any authority figure, shouldn't be saying anything I can't defend, and when I do, I deserve to be called on it by a thoughtful, educated citizenry. I'm not the boss of these children, but rather an older (and hopefully wiser) colleague who just happens to be sharing this part of their journey with them. When they one day pass on from my company, I hope they do so knowing that it's not only their right, but their obligation, to question those who would set themselves up as authorities . . . And that also includes their own parents.

Maybe it's a radical idea, but without it, I can hardly hope for our democracy.

Several years ago, I had put chunks of ice in our sensory table. As the four and five year olds arrived, children who had been with me since they were two, I said, "Hey! I put ice in the sensory table, but now there's water in there! Who put the water in there!" I did my best to sound frustrated, angry even.

"Teacher Tom, no body put water in there. The ice is melting."

"Melting?"

Taking turns contributing what they already know about the world, we then went into a group discussion about the properties of ice as we played with it. As we talked, I pulled out some rock salt, which we sprinkled on the ice, accelerating the melting process. When talk turned to how we could get the ice to melt even faster, we had the idea of heating it up in a pan over a burner. We encircled the pan to watch the ice quickly turn to water, then to steam. What else could we melt? We tried a crayon. We learned that crayons melt, but the paper wrapper doesn't. We tried a candle. We learned that the wax melts, but the wick does not. One of the children wondered about wood. Would it melt? Many of the children thought it might, but others were sure it would burn, so we put one of our blocks in the pan and, sure enough, after a few minutes it began to smoke. We learned that wood does not melt; it burns. Then one of the boys suggested metal.

Now, I knew they had me on that one. I know that metal can be melted, but our little hot plate couldn't generate nearly enough heat. We tossed a paper clip in the pan. It got hot, but didn't melt. That's when I said, "Listen, metal does melt. The problem is that this burner doesn't get hot enough. If we could make it hotter we could turn it into liquid."

There was a moment of silence as the kids processed what I'd said, then as a unified front they pushed back:

"No, Teacher Tom!"

"You're wrong!"

"You're joking!"

All of them doubted me. They weren't prepared to take my word for it. I tried to persuade them, but at the end of the day the kids went home firm in their belief that metal could not be melted. And I went home feeing frustrated. How would I prove it to them? The next day I phoned a steel mill locate in the south end of the city, thinking that a smelter might be just the kind of dramatic evidence the kids needed. Naturally, they laughed at me saying, "We're not letting preschoolers into a smelter." Then I thought maybe I could just find a video of a smelter, but rejected it under the reasoning that I don't want the kids to believe everything they see on the internet either.

And so it remained this way for several weeks until I one day recalled that my wife had grown up in Vienna where they have a New Years tradition that involves melting small lead figurines in spoons over candles. The liquified metal is then tossed into a bowl of water and the new shape of the lead tells your fortune for the coming year. I got in touch with one of my wife's friends who sent me a package of the figurines.

When they arrived, I told the kids, "Today, I'm going to prove to you that metal can be melted." We went outdoors because I was somewhat concerned about the fumes (I've since learned that a candle can't generate enough heat to cause the lead to release toxic fumes). I lit the candle and the children stood in a semi-circle around me as I held a spoon over the flame, staring at that figurine until, finally, it melted into a pool of liquid metal.

It was only then that the kids believed me. These are the kinds of people I want as my partners in the great project of self-governance. 

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Evidence Of A Day Well Played

Some of you may be aware that the West Coast has been slammed with heavier than normal rains, causing all manner of problems for our fellow left coasters to the south, but in these parts farther north we're set up for wading though these atmospheric rivers. 

It's part of our lifestyle and, indeed, once you've accepted the fact that you will be slightly damp from October through May, a process that takes several decades if you weren't born here, you can even sometimes be grateful for it.

We've certainly been grateful for the wet these past couple weeks. Not long ago, the adults turned up for a weekend work party at which one of our main missions was to relocate the sand that has eroded down to the lower level of our huge sandpit back to the upper level. 

The first thing the kids noticed when they returned to school the following Monday was the massive pile of sand at the top of the hill, but now that they've knocked that down a bit, the part of our shovel-and-wheelbarrow engineering project is the giant hole we left at the bottom.

Abetted by the rain, the children have been working our new cast iron pump (that's right, we finally purchased a new one after more than two decades) and shovels to create rivers that have fed a great lake, beginning the erosion cycle anew. 

If anyone knows how to play in a huge mud pit, it's kids from around here. They have the rain gear, although their boots are hardly high enough to avoid being overtopped and it would take more than a mere raincoat to keep it all out, but remember, these kids really don't know what it's like to not be slightly damp for eight months of the year.

I reckon a lot of schools, even ones around here, forbid the kids from splashing in the mud. 

In fact, I know from experience that a puddle like this one would be cause for caution tape barricades in most places and what a terrible waste of a genuine opportunity to meaningfully engage with the real world and the people we find there.

Some days, we're so covered in wet sand that adults stand by the door with brooms to sweep the children before they come inside. 

We sweep the floors and vacuum the rugs at least twice a day, often more, and still large quantities of our play ground go home each day with the children in their treads and cuffs and ears and hair, winding up in the carpeting of their cars and on their entry way floors. Indeed, the kids probably don't stop shedding sand until they finally taken their bath. The ring they leave in the tub is evidence of a day well played.

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The Rigor Of Play

The opposite of play is not work, it's rote. ~Dr. Edward Hallowell

Our outdoor classroom is one big slope and within that slope there are many ups and downs, reflecting our city which is built on hills. We're forever experimenting with gravity out there, rolling and flowing things downhill or dragging and pushing things up. There are parts of the space that are so steep one needs a running start to get to the top and there is very little flat upon which to rest one's legs.

We have a pair of wagons, which are regularly used on the hills. Once, we made an airplane. 

From my photos, it's easy to see the physics and engineering learning, but those were minor aspects, side-effects, of the bigger, more important project, which was figuring out how to get along with the other people.

There are those who question the "rigor" of a play-based curriculum when, in fact, we're engaged in the most rigorous curriculum known to mankind. There is simply no greater or more important challenge than the one of balancing our own individual desires and needs with those of the other humans with whom we find ourselves. 

A play-based curriculum is rigorous because of it's subject matter, which is the all-important one of getting along with the one another, something children are passionate about. Traditional schools, on the other hand, are rigorous simply because they attempt to teach less interesting things by rote, lecture, and text book, the most difficult way to learn new things because most children find them tedious and frustrating. It's an artificial rigor designed, I guess, to make the adults feel important.

Many people confuse hating school with rigor, saying things like, "It prepares them for life," but those of us who work in a play-based environment spend our days amongst children who love school, who arrive each day eager to tackle the challenges of community, and I would assert that there is no better preparation for life. Make no mistake, it's not pure joy, it's not all laughter. There are tears. There is conflict. There is negotiating and compromise. Children might complain, but they return each day eager to engage, to figure out the things they are most driven to figure out: the most important things of all.

There was so much to learn about flying our airplane together. Would it be safe? Where would everyone sit? How many of us can go at a time? Who gets to steer? Who rides and who "launches?" How do we get it back to the top of the hill? How do we make sure everyone gets a turn?

For the most part, we adults stood back, taking a few pictures, letting the kids work it out. Sure, the first few times they launched themselves down the hill, I jogged just ahead of them, prepared to intervene in the name of safety, but as it turned out on this day, I was unnecessary, even when the airplane crashed and burned.

I'll take the real rigor of play over the artificial rigor of rote any day. And so would the kids.

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Not Yet Discouraged Of Man

Every child comes with the message that God is not yet discouraged of man.  ~Rabindranath Tagore

I've written before about our 4-5's class and their superhero games. There is a core group of kids who arrive each day ready for that and nothing else. They've begun making plans even before they arrive, often choosing a particular costume or t-shirt or jacket, sometimes even having come up with a story line. We begin our days outdoors and the first of the superheroes to arrive generally mill about as they await their fellow superheroes. Sometimes they can't wait for their friends and start with me, detailing who they are, what powers they have, and what bad guys they will defeat. As friends arrive however I'm forgotten in the urgency of organizing their game:

     "I'm Batman!"

     "I'm Lego Batman!"

     "I'm Violet"

     "Who are you?"

     "I'm on your team today."

     "I can fly and turn invisible."

     "I have laser eyes."

They do this every day, even if it looks and sounds no different than the day before. It usually takes at least five minutes, sometimes longer, however, as they figure out the ground rules for the day. There are disagreements, especially when their plans clash:

     "I'm the Flash!"

     "No, I'm the Flash!"

And agreements:

     "We can both be the Flash. I'll be Flash one and you be

     Flash two."

This type of negotiation goes on throughout their play. In fact, it stands at the center of the game, but it's most intense as they convene.

Meanwhile, other kids arrive having anticipated other games, like playing with the cast iron pump or swinging or hunting for jewels. And yet others arrive seemingly with no plan at all, spending the first several minutes of their day observing until they find a place for themselves. Many of these kids are occasional superheroes, some days donning the cape, sometimes not. Once the core group has more or less organized themselves, they then begin recruiting from among these kids, "Are you a superhero?" If the answer is "no," they move on to the next, but when the answer is "yes" a whole new round of negotiation begins. 

A big part of the game is hanging out in their "hideout" or "space ship" or whatever, telling others "Superheroes only." It looks like exclusion, and on one level it is, but all one need do to be included is say, "I'm a superhero" and the gates are opened. Indeed, rather than exclusion it can be seen as an invitation to play, a kind of inducement to increase the population of superheroes. You can come up here if you join us in our game. Many kids have this figured out and play along, breezily saying, "I'm Wonder Woman" whether they mean it or not, speaking it like a password. (A few, of course, don't see it this way and instead feel intimidated which is what lead to our big discussion a few weeks ago, but most accept and understand the deal.)

There have been a few experiments with real exclusion, of course, the kind where others are told some version of "You can't play," but those have been short lived because the superhero game is less fun with fewer people. No, the goal is a big, rowdy game and the kids have figured out that that can't happen if they aren't essentially accommodating and inclusive. In fact, I think this is why the game is so compelling for the kids. Sure, they love experimenting with power through their role playing, but what keeps bringing them back is that it's really a new game every day, one that is shaped anew by all the agreements they have to make with one another to keep the game going, to maintain it day-after-day, hour-by-hour and even minute-to-minute.

In his book Free to Learn, Peter Gray discusses the importance of the freedom to quit in children's play. He argues that the drive to keep the game going causes children to really listen to and accommodate one another, because if they don't kids will start quitting and if too many vote with their feet the game disappears along with them. This is why in a game of street baseball, the 10-year-old doesn't need anyone to tell her to go easy on the five-year-old: if you want the game to keep going it has to be fun for everyone so we toss the ball gently rather than doing our best to strike him out.

Yes, the whole superhero business can be messy and fraught with conflict. There are times when it isn't pretty, when people cry, but for the most part when I step back and watch it, I'm moved almost to tears by what I see: children coming together of their own accord, working to reach meaningful agreements, making space for one another, persuading and being persuadable, setting aside objections in deference to a friend, and ultimately discovering that sometimes it's a bridge too far and the only option is to exercise your freedom to quit. 

We adults have a lot to learn from how children play with one another when left to their own devices, without constant grown-up intervention. In fact, they inspire me in the way heroes always do: it's why I'm not yet discouraged of man.

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Today I'm 55

Ninety percent of life is showing up. ~Woody Allen

Boldness has genius, power and magic in it. ~Goethe

Experience is the name we give our mistakes. ~Oscar Wilde

I went back last night to take a look at what I wrote here on my birthday five years ago. I'm happy to report that I still stand by every word, so I'm sharing it again today with a few edits to account for the passage of time.

Now I'm 55. It's not exactly a milestone birthday, but I nevertheless think that permits me the indulgence to offer a piece of unsolicited advice.

That's a long time to have lived, don't you think? Fifty-five years? I've seen over half a century. I've lived in historic times. I should by now know most of what I'm ever going to know about life. I've still got my health, accented by a few well-earned aches and pains. I love my work. This should be my time, baby!

Here's one thing I know: Goethe was right, there is magic in boldness. If 90 percent of life is just showing up, then I'd say another 9 percent is boldness.

Of course, boldness must be formed from something; otherwise it's just brashness or, worse, its embarrassing cousin, braggadocio. I've found one does need at least a little genuine, deep-down confidence to pull off boldness, and that can only come from experience or out-of-this-world innate talent. Since I never discovered my world class innate talent, I'm left to rely on experience. 

I'd say that 90 percent of boldness comes from that confidence. And 90 percent of that confidence comes from experience.

And experience is the name we give our mistakes.

So, you know, the secret to life is to show up and make some mistakes before it's too late.

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"I'll Help You"

Like every preschool with which I'm familiar we celebrated Valentines Day this week by exchanging messages of love and friendship with one another. I know, I know, it's a "Hallmark holiday," but so what? I like that we set aside at least one day every year to celebrate love in all its forms. Our tradition is that each kid makes his or her own construction paper pocket, decorated with hearts, lace, and other bits and bobbles, which serves as a "mailbox" into which classmates deliver their Valentines. In the morning, I set up long tables in the large room across the hall from the class room, lay out the pockets, then as the kids arrive, they start their day by distributing their cards. At the end of the day, they take them home then spend the afternoon enjoying them. It's straight-forward and simple.

The kids in our 4-5's class have come to understand that they are indeed in charge of the curriculum, and one boy in particular almost daily requests some special activity or another. Often they are things that require some prep time so we often have to agree to the following day, but not always. On Wednesday, he asked for "mat slamming." The tables were still set up in middle of the the big room, so I answered, "How about tomorrow? Those tables are in the way."

He answered, "We could move them. I'll help you."

These are fairly heavy folding tables with plenty of pinch points for good measure and they are stored in a closet where they lean against a wall standing on end. I wasn't really sure how he was going to help me, but I wasn't going to do anything to extinguish the sentiment, so said, "Alright, come on."

As he propped the doors open with doorstops of his own accord, a handful of other kids asked what we were doing. They wanted to help too. I said, "The first thing is to fold up these tables and move them into that closet over there. First, we'll have to tip the table on it's side so we can fold the legs." We worked together to tip the table, then I showed them how the legs worked, making a point of pointing out those pinch points. Without discussing it, two of them held the table still while the other three wrangled the legs into place.

They seemed to have it, so I walked over to the closet to wait for them saying, "It goes in here."

At first they struggled. They were able to get the table moving by sliding it along the floor, but they couldn't get it heading in the right direction. "Teacher Tom, we can't steer it."

I said, "The person in front is the steerer. The rest of you are the motors." That was what they needed. I thought I ought to handle the job of stashing it into the closet if only because it was too small of a space for five kids. I took the table from them and before I'd finished leaning it again the wall, they already had the next table on its side. This one had a slightly different mechanism for folding the legs, but they figured it out before I did and were soon maneuvering this one toward the closet as well.

The first two tables had been rectangular, but the third and final one was round. This one they were able to roll to the closet as everyone agreed that round tables are easier to move.

Now it was on to the gym mats which were stacked in a corner. They were no longer helping me; it was their project and I was only there in a supervisory capacity. I said, "Next we need to set up the mats." They wrestled and wrangled them. They played and ran and fell onto them. They argued and complimented and suggested and agreed. It was an inefficient project, one that got sidetracked by tumbling, chase, and general horseplay, but at any given moment at least one of them was working to set up the long runway we needed to play the game of mat slam.

I noted that I was calm, feeling no need to coach or cajole, which of course was a result of it not being my project, but theirs. I knew this because when it's my project I coach and cajole because I have internalized the dictatorship of getting from point A to point B in a straight line, whereas the kids intuitively embraced the democracy of getting there together no matter the zigs and zags, listening to their hive mind intuition rather than mere logic.

Finally, after a good half hour, they got everything set up to their satisfaction. According to the clock, getting ready for play had eaten up all the time we had allotted for play. If I'd been sticking to the schedule, we would have now had to tidy up, so of course we ignored the schedule: we'd done the important part of working together, I could hardly rob them of their reward.

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