Laugh

“A broad, soundless laugh now appeared on his face and no longer left it.”

-- from “In the Penal Colony” in The Metamorphosis and Other Stories by Franz Kafka

While I am generally happy and satisfied with my life, I admit that I am prone to occasional attacks of listlessness. Now and again, I have a bad day or endure a series of small frustrations, and I just can’t shake the blues. I end up sitting in my apartment, staring at a wall, wondering why my life isn’t what I thought it would be by now.

Last Thursday was one of those days. I was sad and lonely for no particular reason, and as I sat on my couch waiting for an appropriate time to go to bed, all I could think was that I wanted, very badly, to laugh.

I’ve always believed that laughter is one of the world’s greatest healers. A good bout of laughing really makes the rest of the world go away. The physical exertion of laughing hard forces the restless feelings out of me. The emotional release of laughing shifts my focus away from the negativity. Laughter is a never-fail, lasting cure for the blues, and the harder and longer I laugh, the better I feel.

So, on Thursday, I was really wishing for a laughing fit. My mind drifted to episodes in my past that left me unable to stop laughing. I hoped that the memory of one of these occasions would trigger me to laugh myself out of my funk.

I thought of the rehearsal for the play during my senior year in high school when we first started using props. One of the characters carried around a doll, believe it to be her dead son. The first time I saw the doll was during a run of the scene when my character was introduced to the doll as if it were a 5-year-old boy. My castmate walked on stage, said, “Mrs. Savage, this is my son,” and held out a doll of Steve from Blues Clues. The giant head, ugly shirt, and buckle shoes were too much for me, and I broke out laughing. The other cast member started to laugh too, and soon enough we were so far gone that the director sent us home. It was not my proudest moment, yet I remember feeling that comforting sense of exhaustion and release that a good laugh brings. (It’s very unlikely that she will ever read this, but I would bet that Disa still remembers this, too.)

I thought of the Easter weekend of my senior year in college, when a friend and I were making a whole chicken for dinner. We were rinsing the chicken in the sink to help thaw it out when, quite suddenly, the giblets came flying out and slid up the side of the sink fast enough to rise to eye level before landing back in the sink with a loud, metallic thump. My friend and I had a complete laughing meltdown that lasted for hours. (You remember, don’t you, Candace?)

I thought of the hayride I went on as an undergrad that unfortunately, occurred on a rainy, windy, cold evening. My friends and I sat hunched under our hoods, feeling the rain soak us through to our skins, hating life, and muttering complaints under our breath. Finally, one unforgettable person, determined to lighten the mood, yelled, “We are having a good time! Everybody just shut up!” The entire wagon dissolved into laughter even as we choked on the rain being blown into our faces. We continued laughing about that moment for years. (I miss you so much, Stephen.)

I thought of the time, shortly after moving to Chicago, that I came home from a bachelorette party feeling more than a little tipsy. One of my roommates was with me and stayed out in the front yard talking on the phone as I walked into the apartment. My other roommate had apparently been doing yoga while we were gone, as there was a large yoga ball sitting in our living room. In my state of inebriation, I apparently could not quite work out what the yoga ball was or why it was there, so I carried it out to the porch and rolled it down the stairs to my roommate, saying, “Look!” We both laughed until tears were rolling down our cheeks.

It was easy to remember plenty of fits of laughter, but the memories didn’t have the effect I was hoping for. I remembered the feelings of euphoria and release, but all I could do was smile or sometimes let out a small chuckle. The real laugh felt somehow trapped inside me, unable to really get out.

It’s been about four days now, and I still haven’t really laughed the way I want to. I’ve tried calling up more memories; that hasn’t done it. I’ve tried forcing myself to laugh harder at things that are only moderately funny; that hasn’t worked either. Perhaps true, gut-wrenching, blues-healing laughter can’t be manufactured. I’m just going to have to wait.

There are other ways to shake off my blues. I can work on the various projects that are laying around my apartment. I can play with my cat. I can get out into the fleeting sunshine, when the sun makes an appearance. I can hold onto that silent laugh trapped inside me and hope that when I do dissolve into laughter again, the experience will leave me contented and worry-less for a while.

I bet it will. And I bet I won’t see it coming. (Look at me! I’m being optimistic!) In the meantime, thanks to all of you who have laughed with me over the years. I remember those moments with a clarity and sentiment I can hardly explain, and I wish you all plenty more moments of suffocating laughter.

Million Billion Trillion

“Instead of thinking about the monkeys I think about all the kids in the world, how they’re not TV they’re real, they eat and sleep and pee and poo like me. If I had something sharp and pricked them they’d bleed, if I tickled them they’d laugh. I’d like to see them but it makes me dizzy that there’s so many and I’m only one.”

--from Room by Emma Donoghue

In my five years of working in the education field, I have learned that most mathematical concepts can be placed on a continuum from easy to teach and learn, to tremendously difficult to teach and learn. The basics of three-dimensional objects, for example, are pretty easy since there are so many good models of three-dimensional solids in the real world. A shoebox is a model of a rectangular prism, a soup can is a model of a cylinder, and so on.

Two-dimensional geometry moves a little way down the continuum toward hard. There are many real-world models of two-dimensional figures, but they all have small problems with them. A piece of notebook paper is a pretty good model of rectangular region, but the paper does have some thickness, whereas a true rectangular region does not. The rails of train tracks are a decent model of parallel lines, but they are never perfectly straight and don’t continue forever. Plus, train tracks appear to get closer together as they move off into the distance, and explaining perspective to a child is not an easy thing to do.

There are ways to overcome these minor difficulties, though. For one thing, children don’t necessarily need to understand all these fine distinctions right away. The real thorns in my side are the concepts that are all the way at the hard end of continuum. One of these concepts is large numbers.

Learning to read and write large numbers is one thing. Once you get past the teens, our numeration system has a predictable pattern. But really understanding what the large numbers mean is much harder.

Instincts about large numbers are not something we are born with. When I was six or seven, I had a Dr. Seuss book called My Book About Me. Each page had blanks to fill in. My name is _______. I am _____ years old. I am _____ feet _____ inches tall. I happily filled in all these blanks, and eventually came to a page that asked me to count the number of steps from my room to the kitchen, from the kitchen to the door, from the door to the mailbox, and from the mailbox to the store. I counted the steps in the first three trips, then stopped. I'm not sure if I just didn't want to walk all the way to the store (which was about a mile down the road) or I thought my mother wouldn't let me, but I didn’t go. Instead, I simply wrote 100 in the blank, assuming that it couldn’t possibly be more than 100 steps. After all, 100 was a huge number.

I eventually learned a better sense of 100. There are many ways to visually compare 1 with 100. There are 100 pennies in two rolls, 100 squares in a 10-by-10 grid, and 100 paper clips in a box. If kids are exposed to comparisons like this (one penny versus two rolls of pennies), they will eventually gain a sense of how much 100 is, and come to understand that maybe 100 is not such a huge number after all. Lord knows that, as an adult, I have learned that $100 is not the fortune it seemed like when I was 7.

There are similar ways to help children gain a sense of 1,000. But what about 10,000? What about 100,000? What about a million? When is the last time you’ve seen that many of anything? I think part of the problem is that even when you do see collections that big, our brains have a hard time processing the individual pieces. There are photographs of crowds of 100,000 people, but when I look at such photos, I don’t see individual people. I see one mass of people. I don’t know if that is true of everyone, but I imagine that it is a common difficulty.

I openly admit that despite the fact that I am 28 years old and I have degrees in mathematics and learning sciences, I still struggle to really understand large numbers. My undergraduate alma mater recently received a $100 million gift. Many alumni were very excited about this, but I have to admit that my response was a blank stare. I don’t really understand what this means for the university. I know that they are going to use the money to open a medical school, but will the $100 cover the whole start-up cost? Will there have to me more fundraisers just to erect the buildings? Will it only take $50 million to first open it, so the rest can be used to sustain the school until it becomes profitable? I haven’t the faintest idea what $100 million will buy.

I also don’t have a clue about the population of the United States or the planet. I have heard the numbers before, of course, but they never stick because I really have no idea what they mean. Before I google it, here are my wild stabs at these populations: There are 3 million people in the United States and 2 billion in the world.

Here are the true populations, according to the census bureau: There are 311 million people in the United States and almost 7 billion on the planet. I guarantee that I will forget these numbers tomorrow, because at the moment my brain is struggling to really understand the difference between my guesses and the truth.

While I understand that my own personal anecdotes are not proof of anything, I relate them to illustrate the kinds of struggles that kids (and the adults they become) will face if they don’t develop a good sense of large numbers. This is, in fact, the kind of math that is used in everyday life, and I wish I had learned it better. And that returns me to my original point: This is a hard thing to teach.

There are some curricula and books out there that make a very good start, but I’m always on the lookout for inspiration for ways we could teach a better sense of large numbers. I often count my steps while I’m running, so maybe I will see how long it takes me to run a million steps (not all in one day, of course). I’m not particularly interested in finding out how long it takes me, but I am interested in finding out if it helps me understand just how much 1,000,000 is.

And if any of you would like to donate $100 million to the cause so that I can see what it takes to spend that kind of money, that would be great too. Thanks.

Canadian

“The restaurant downstairs was still cheap, if you didn’t mind the difference between francs and euros. Three-franc wine was now three euros, which was more than fifteen francs, but Harris was not interested in such mathematical calculations.”

--from “Belons” in Edible Stories: A Novel in Sixteen Parts by Mark Kurlansky

In general, I was a rather tame college student. I didn’t drink at all until I was 21, and even after that my bouts of heavy drinking were few and far between. My Friday and Saturday nights consisted mostly of lounging around my dorm or apartment. I just wasn’t interested in the frat party scene or the bar scene.

But there was one aspect of the college stereotype I was interested in: SPRING BREAK! It wasn’t so much that I wanted to go to Panama Beach and wear a bikini and get trashed, but I did want to get the hell out of town and go on a trip with my friends. I spent the spring break of my freshman year at home with my parents, but after that I was determined to go somewhere for the remaining spring breaks.

This was one goal I actually ended up achieving. However, none of the trips really turned out the way I expected.

When I was a sophomore, six of us piled into my friend Stephen’s dilapidated minivan and made our way down to Myrtle Beach, SC. We had high hopes for beaches and sunshine, and the memories of the drive down there are some of the best of my life. But two things happened when we got there that really put a wrench in the trip. First, turns out that Myrtle Beach is not warm and sunny during the first week of March. The week was rainy, windy, and cold. We got so frustrated that we actually got back in the van and drove to Florida one day. Second, during our first full day there, I caught some kind of Godzilla virus that made me cough until I choked, and most of the time I was barely able to keep my eyes open. While now, looking back, I would not trade my memories of that trip for the world, at the time it was a big let down. I wish I would have enjoyed it more. As it turned out, it was the only trip I would ever take with that group of friends.

When I was a junior, I was studying abroad during spring break. When my friends were on spring break back home, I was in Rome, walking until my feet felt like they would fall off and spending a night in an airport with some random guy doing tai chi. During my own spring break of sorts, I was in Russia, eating last night’s moldy desserts for breakfast and getting ushered into Russian Orthodox Easter services by armed military personnel. Again, I wouldn’t trade those experiences for anything now, but they were their own kind of bizarre and not the kind of spring break I had imagined.

So, my senior year came around, and I really wanted to go on a trip. It was complicated, because some of my friends had different spring breaks than me because they were doing teaching internships at the time, and others just couldn’t be away for other reasons. I would not be deterred, though, and I begged three of my available friends to go somewhere, anywhere with me. Somehow, I talked them into driving to Toronto.

I don’t remember a lot of details about what we did in Toronto. The only thing I remember clearly is how much we were annoyed with the process of converting prices from American dollars to Canadian dollars and back. Most places accepted American money, but it was hard to tell if you were getting the right amount of change back. Some places would give you change as if you had paid in Canadian dollars, and since the American dollar was worth more at the time, that was a total gyp. So, it was a constant mathematical battle, and it turned into a running gag.

Every time one of us said something about money, another made a point to say, “Canadian or American?” even if the context made it completely clear what we meant. Then we started asking the same question about any number at all. One person would say, “They said it was a 20-minute wait for a table.” Another would answer, “Canadian minutes or American minutes?” Someone would point out that the next attraction was 10 blocks away, and another would ask if they were Canadian blocks or American blocks. It sounds lame, but it was all extremely funny.

Being college students, stayed at a cheap, dingy hotel. We spent some time in the pool, and we were always the only four people there. The pool was pretty large, and if two people were in the water at one end and the other two were talking on deck at the other end, we had to shout to hear each other. Yet, on the wall, there was a sign saying that the maximum capacity of the pool area was 15 people.

This made no sense, of course. It could clearly fit many more than 15 people with room to spare. So what was the deal? I don’t remember which one of us said it, but I should have known it would come out eventually. “That must mean 15 Canadian people.” And the rest of us answered, “Oh, yes, Canadian.” And we cracked up.

Like I said, I know it’s a stupid joke. Yet, it’s what I remember from the last of the spring break trips I so coveted. It was odd and untraditional the way my other spring breaks trip were, but it created a joke that no one but the people who were there will find as funny as I do. In that sense, I have to believe that the true essence of spring break-ing was accomplished. We got the hell out of town and came back with a gem of an inside joke.

I went on one more spring break trip while I was in grad school. We went to New York City for a day, then on to Montreal. Oddly, I don’t remember any difficulties with conversions on that trip to Canada. Maybe in Montreal, all the numbers were in French Canadian, and that’s why I didn’t notice.

Shut up. I think that joke is hilarious. But I only expect Candace, Matt, and Carl to understand.

Alien

“They were, I now saw, the most unearthly creatures it is possible to conceive.”

--from The War of the Worlds by H. G. Wells

When I was in middle school and high school, I had a science teacher by the name of Mr. Barker. Because I went to an arts and sciences center, I was lucky enough to have three classes with Mr. Barker: earth science in eighth grade, biology in ninth grade, and advanced biology in twelfth grade. I say this makes me lucky because as a teacher, Mr. Barker was truly extraordinary.

His classroom was full of amazing things. There was a tank of hissing cockroaches that we were allowed to pick up and handle any time. There were pipettes of every size and measuring scale and kits for making gels that separated out strands of DNA. There was a polygraph machine and a seismograph and a weather station. Because of his elaborate set-up, Mr. Barker was often on the news talking about some random scientific phenomenon. He was labeled everything from “Local Science Teacher” to “Seismology Expert” when he gave his sound bites. Everywhere around him, there was science, because Mr. Barker was, at his very core, a scientist.

He was also a skeptic; in fact, he was the most emphatic skeptic I have ever known. He took significant amounts of time out of his classes to show us videos that debunked psychics and mind readers. He had us measure the various parts of a pair of scissors and manipulate the measurements until we found patterns, just to see how easy it is to find them. (He made us promise not to be astounded and go off and start a scissors cult.) On his wall was a larger poster of Occum’s Razor: “When you hear the sound of hoofbeats, think of horses before you think of zebras.” It was his mantra.

I quite vividly remember one of the times he got worked up about alien abduction stories. To begin with, he hated, hated, how movies all show aliens to be these greenish, humanoid forms with big heads and big eyes. “Those aren’t that different from us!” he said. (Of course I am paraphrasing here.) “People think these silly descriptions of aliens are so otherworldly and different. So if I described something that had legs that bent in different directions, tasted through its feet, and breathed through its butt, people would say it’s an alien for sure, right? Well guess what? That’s not an alien. That’s an insect!”

If life on other planets exists, he argued, surely we have not begun to imagine the forms it could take. There’s no evidence to suggest such life exists elsewhere in the universe. “But even if it did,” he said, “why would the aliens go to Nowhere, Iowa, beam up Bubba, leave depressions in the crops, and leave?” He did not believe in alien abductions, and he made it quite difficult for his students to believe, either. I haven’t known anyone to be so passionate about anything, before or since.

Mr. Barker’s purpose in all of this, I think, was not so much to make sure that we did not believe in aliens. What he really wanted was for us to use science, not hearsay, to draw conclusions about the world around us. Or, more simply put, he wanted to make sure we thought for ourselves. Once we did that, he was pretty confident that we would discover that he was right about everything else.

Those stories give you an idea of what Mr. Barker was like as a person. Above all else, he was a scientist and a skeptic. Those are the things I immediately remembered when the quote above reminded me of him. Ten years ago, if someone had asked me why I thought that Mr. Barker was a truly extraordinary teacher, I probably would have listed those same things. I do still think his passion for science and truth made me sit up and pay attention, and that’s no small thing. But now that I’ve been a professional in the education field for a few years, I find myself thinking of different ways in which Mr. Barker was different. Three new things renew my belief that he was a world-class teacher.

First, Mr. Barker’s tests were hard. Every student in my math/science program lived in fear of his tests. In fact, the difficulty of the tests turned some students away from his classes altogether. You couldn’t cram for a Barker test. You had to start getting ready for them as soon as you started a new unit. I’m not sure I really understood this at the time, but now I realize that Mr. Barker’s tests were hard because doing well on his tests required not only knowing the material, but understanding it. The questions required some significant thought and problem solving. Nothing was simply regurgitated, and there were definitely never any multiple-choice questions. Mr. Barker taught us things, and then he expected us to apply them. That expectation alone raised the bar and caused me to learn more in his classes than in most others.

(As an aside, I’ll also note that he drew pictures on the board during his tests. They were cartoons meant to depict some person or thing associated with the material on the test. If we could guess what they meant, we got extra credit. I remember him drawing a picture of a large toe and a large letter O, each with faces, handbags, and necklaces. Off to the side, a speech bubble proclaimed that someone’s sisters had arrived. The answer (did you guess?) was my-oh-sis and my-toe-sis, or meiosis and mitosis. Mr. Barker’s ability to come up with these on the fly was a sure sign of his brilliance.)

Second, Mr. Barker did not teach to standardized tests. His advanced biology course was considered Advanced Placement, but the curriculum was heavily focused toward genetics, as this was Mr. Barker’s particular interest, and the lab equipment at the center allowed us to do some pretty amazing things with DNA. Finally, about two weeks before the date of the AP test, he did briefly go over some other topics that would be on the test, but he made it very clear that it would take a lot of outside studying for us to do well. He knew he didn’t prepare us to pass the test, but he didn’t apologize for it. It simply wasn’t important to him—and he didn’t think it should be all that important to us, either. I wish teachers today had the luxury of expressing that attitude to their students.

Lastly, and perhaps most importantly, Mr. Barker treated me the same as any other student. I don’t mean that other teachers pushed me back; I mean quite the opposite. I was an academic star for most of my school life, and almost every teacher I had put me up on some sort of pedestal. I was always the favorite, the one who knew all the answers, the never-do-wrong class pet. But to Mr. Barker, I was just one among many. Being smart and having my homework done were not things to be rewarded. They were just expected.

I studied my butt off for Mr. Barker’s tests. I usually did well, and when I didn’t, I knew it was my fault for slacking. I also studied for the AP biology test, and I managed to barely scrape a passing grade. But even if I hadn’t passed, I would not have traded Mr. Barker’s class for a better score. And I always checked my attitude at the door when I entered Mr. Barker’s classroom, forgetting the pedestal I was usually perched on elsewhere. It wasn’t a conscious choice so much as a necessity. My feet had to be solidly on the ground if I was going to do well.

Now, looking back, I know that these are the things that set Mr. Barker apart as a teacher. He was brilliant, passionate, and dedicated; those things made him an exceptional scientist. But it was his high expectations of everyone and his refusal to be driven by outside forces like school boards and the Advanced Placement tests that made him an exceptional teacher.

Mr. Barker retired the year I graduated high school. He absolutely deserved the rest, but I can’t help but feel sorry for the students who came after me. Still, I know there are other teachers out there to are great the way Mr. Barker was great. Someday, if I have children, I hope they have teachers like Mr. Barker.  He was an alien of his own sort, and I’m grateful that I got to be one of the Bubbas that Mr. Barker beamed up.