Dear Satellite Dodgers,

Did you see the news about the falling satellite? It weighed six tons and was the size of a school bus! When it re-entered the atmosphere, it broke into smaller pieces, but scientists said it had a 1 in 3200 chance of landing on a person. What do you think the odds were that it would have landed on you?

This week we’ll talk about probability. When you learn to think probabalistically, the world lets you in on its not-too-well-hidden secrets, you make better choices, and you don’t waste precious time worrying about 6-ton satellites falling on your head.

Look at the globe or the map. Where do you think the satellite probably landed?

Let’s have a great day.

Sincerely,

Mr. H.

August 15, 2011

Dear Students,

I love numbers. Some of you probably do as well. If you don’t, I hope by the end of the year (or maybe earlier) you will. If you haven’t been “good” with numbers in the past, withhold judgment and give them a chance to enchant your life. Numbers are not some foreign language that only certain people have been given the skills to understand. Numbers exist in a system that you can learn and find meaningful. I know you’ve mastered many other systems in your life. This is just another one that you’ll learn.

Numbers don’t really do anything. People are always talking about real world math, applying math, or making math relevant, but I like numbers for the same reason I like poetry: it’s not good for much beyond itself. Sure, scientists use math. Programmers use math. Rocket scientists and doctors and architects use math. While these fields use the same number system we’ll be learning about, they use structures that have been built out of that number system. My hope is that by learning about the number system you will be able to use these structures and maybe build up some of your own structures for making sense of the world.

I can hear you already: “When will we ever use this in our real lives?” When you learn math, you learn how a system works. In our case, we’re learning about the number system. This number system is governed by a few rules and operations. Within the confines of those rules, there’s an infinite world of patterns we can create. Those patterns, coincidentally, are close copies of patterns in the real world. That is what makes the number system so useful for scientists, engineers, and other fields that use number system applications. However, the real power in learning math is in learning how to manipulate things within a system. When you play with numbers enough to discover some sort of pattern, what you’re doing is making an observation about the entire number system. You’re discovering the “rules” that govern the system.

Intelligence isn’t what you know, it’s what you can figure out. If you understand the universe as a bunch of overlapping systems, your job as a human being is to figure out the “rules” that govern each of those systems. Once you do that, you can start thinking about how those systems impact each other. Once you do that, you’ll discover more systems and more ways that systems interact. Because human beings concoct these systems as a way of making sense of the world, many of the rules governing systems are similar. And because humans create these systems, the rules governing them are provisional, incomplete, and always being better understood (but never completely understood). As you start thinking deeply about systems, you’ll find new rules within systems, instances in which the rules don’t hold seem to hold up, and times when it all seems so perfectly beautiful that you can just barely stand it.

We’ll learn about many systems beyond the number system this year: body systems, systems of government, systems of classifying things, systems of measuring things, water systems, carbon systems, solar systems, systems of structuring society, systems of moving money around the globe, and many more. There really are too many systems to name, and there are more emerging every day. Lucky for us, we can practice our systems thinking with the number system, the most exquisite, useful, and widely thought about system that human beings have ever created. I’m looking forward to it.

Sincerely,

Mr. Heimbuck

Today I was looking through a cupboard and found 150 googly eyes. Motherlode! I taped those things to as many surfaces as I could think of: a student’s desk, the filing cabinet, the wall directly above the in-box, the back of my projector cart. When fifth-graders see them, they laugh and laugh. You cannot stare into a pair of googly eyes without joy.

Humans see faces wherever we look. Why not let the eyes be googly?

This is the week I’ve been waiting for. Every week our spelling list has a pattern. Usually it’s something phonically boring–hard/soft ‘g’ and ‘c’, changing ‘y’ to an ‘i’ to add -ed, open or closed vowels. This week, however, all of our words are portmanteau words–two words put together to form a new word, which encases the meaning of both words.

While such words have probably been around for a while, Lewis Carroll gets credit for coining portmanteau word in Through the Looking Glass when Humpty Dumpty says, “You see it’s like a portmanteau–there are two meanings packed into one word.” Words on this week’s list include bash (bang+smash), smash (smack+mash), glitz (glamour+ritz), motel (motor+hotel), scrunch (squeeze+crunch), chortle (a Carroll original of chuckle+snort), and humongous (huge+enormous). A recent piggy-backing off of the last one is the word ginormous, which I suppose is a combination of gigantic and enormous but also includes the double entendre by emphasizing the ‘gino’ part as ‘gyno.’

In Academic Instincts Marjorie Garber cites a study that claims 1 out of every 12 words that Shakespeare used were of his own invention (or innovation). I hope my students learn this week how dynamic language is. It’s constantly being revised, reinvented, refuted (refudiated?), and realigned. And despite claims from English teachers and purists (DFW called them Snoots), it cannot be ruined, despite the best efforts of the cast of Jersey Shore.

I’ve been avoiding news coverage of Wikileaks because it doesn’t fit into the neat political boxes I prefer. To understand an issue, I read responses from pundits with sympathetic opinions. In the wikileaks case, many of the responses from these people were ambivalent. Rather than take a simple pro/con stance, many of the articles I read about Wikileaks used the topic as a jumping off point to detail larger social and cultural changes, not just in the digital world but in our everyday lives. These changes–in how we get information, how we consume it, how we share it, and how we turn it into knowledge–have been in my mind for the past few months. Because they have been so central to my thinking, they are the prism through which I view almost everything, including the Wikileaks case. The conclusions I’ve come to have little to do with the details of the Wikileaks case and everything to do with our assumptions about information, the tools we need to understand information, and my role–as a teacher–in helping to forge these tools.

Lawrence Lessig’s article “Against Transparency” used the Wikileaks case to discuss how our shrinking attention spans have undermined the value of transparency. Transparency in government and corporations creates lots of data. Delving into that data requires time and patience. Rather than do that, we prefer to pick choice bits of the data that support our preconceptions about the institution that leaked the data. Not only has this been the response to the limited leaks from Wikileaks but it’s the stated intention of Assange and his supporters. Assange aims to support the individual at the expense of the institution. Rather than see the institutions as a body that serves the individual or even as a collection of individuals, Assange (and many of his supporters) assumes a central conflict between institution and individual.

Because we assume the institution to be bad, we automatically assume that the “raw information” will be damning. We believe that the information will speak for itself in a universal language that will condemn the actions of the institution as objectively immoral. We can agree that murder is immoral, but when the killing happens on a battlefield where identifying friend and enemy is difficult, the question gets a little murkier. This is where context gets added to the information that was just text. Wikileaks believes that the “raw information” they leak requires no context, but all texts (and the leaks are just another text that we humans read) require context. Without context, we cannot fully understand text. What Wikileaks is doing is providing their own context to the information. They do it implicitly with their assumptions about the institutions they are leaking about, and they do it explicitly in how they produce the video footage they release. Ravi Khatchadourian’s article “No Secrets” detailed Wikileak’s production of the video leak of civilian killings in Iraq and shows us how the production controlled the context in which viewers would see those videos: “Assange saw these events in sharply delineated moral terms, yet the footage did not offer easy legal judgments.”

The world is a collection of texts. The only means we humans have of understanding the world is reading those texts. To do so, we need context. Books help us discover context, not just in their physical form–title, page numbers, the structure of stories, and text structures–but in the way they are published and marketed. Furthermore, ever since we were read our first story, parents and schools have taught us about uncovering the contexts of texts. In the past, institutions have been major teachers of context. Institutions taught us how to understand texts whether they were religious texts, political texts, legislative texts, or literary texts. The Internet has allowed an unprecedentedly large avenue of rebellion against the authority of these institutions and their power over context. On the Internet, content makers can release their content on their own terms and try to control the context.

The problem with much of the “raw information” on the Internet is that people are apt to believe it is context-free. Videos, photographs, audio, and leaks are things we often believe can be understood objectively without context. What’s happening, however, is that the power of context is being ignored. We can extend Lessig’s argument about short attention spans to this case. Reading and understanding is about discovering the contexts of a text. Doing so requires time, attention, analysis, and discipline. There can be no such thing as raw information. Information is always understood in a certain context. We need to be vigilant about asking who is controlling that context, because context-controllers have a lot of power.

Even though we live in an age where information looks different than it used to, we as citizens and humans must read this information, not just for its content, but for the context in which that content is nestled. The skills of reading are centrally the same as they ever were: use our human tools to make sense of the world as a collection of human created texts.

Every morning, the students read a morning message. I try to use the morning messages to get them to think about the essential questions underlying what we’re learning. I think of essential questions as those that have historically created new paradigms of thought–questions that still remain after these paradigm shifts and spur on new ones. Really, the question behind all of our learning is this: how do we make the world more comprehensible?

Here was yesterday’s letter:

Dear Model-Makers,

Humans understand the world by making models of it. When we make models, we decide what the important parts of a thing are and how those parts are related. Today, we’re going to make models of big numbers. Humans’ brains aren’t very good at understanding the difference between millions and billions. Maybe by making a model of these numbers we’ll better grasp them.

Sincerely,

Mr. Heimbuck

Later in the day, we converted 1 million seconds to a more kid-friendly unit of time. To represent it, we drew 12 days on a calendar. Then, we converted 1 billion seconds to a more friendly unit of time. We represented it as a birthday cake with 32 candles on top.

Albert Bartlett said humanity’s greatest shortcoming was our “inability to understand the exponential function.” If my students didn’t gain much in understanding the exponential function, I hope they gained a little respect for the world’s ability to amaze us.

I turn the objects in my hand into the digits on my hand,
and with the tongue that’s in my head I count them out to you.

We dole out what we have; you keep your two eyes on the piles,
and as they heap into the sky your face cracks with a smile.

But as we keep counting out by 2′s and 3 we near the end
of the communal pile, which sits between, from which we send.

Because you are so bright you see it long before I do:
there’s 13 fingers left and there’s only just us two.

You make arrays in your mind that stretch across the sky.
The stars are only fingers that we measure heaven by.

And there’s one little star–I swear it shines so bright–
it hangs out by itself; it has no partner in the night.

Take that little star, put it in the pocket of your jeans.
We’ll never know what that point of light really means.

We’ve taken the one and we’ve turned it into two.
We’ve taken the real and turned it into the true.

There have been many recent news reports about school districts banning the “I Love Boobies” bracelets from the Keep a Breast Foundation. The bands are meant to raise awareness about early detection and prevention of breast cancer, but school administrators disprove of their provocative wording. I had a 5th grade boy wearing one of these bracelets earlier in the year. I thought I recognized the font from some news articles I’d read about the bands and sure enough, when I looked closer, there was the word boobies. I asked him to put it in his pocket, and I haven’t seen it since. Silly Bandz are another wrist accessory that some school districts have banned. I’ve also seen these in my classroom, but I haven’t yet made any rules about them.

Most of the news reports about these school bans, and many other past school bans, take an incredulous tone, like “Can you believe how unreasonable these school districts are?” In the past, we’ve read similar stories about schools banning tag, fluffer-nutter sandwiches, and hot Cheetos.  In the wake of Colmbine, zero-tolerance policies came into effect, and when schools had to enforce them, they looked pretty silly–a first-grader suspended for bringing a butter knife to school.

While people who aren’t in schools may scoff at these bans, when you work with kids, you realize that there are two words that you can never say to them: “Be reasonable.”

Humans’ brains don’t fully develop until we’re in our 20s, so kids lack the equipment to make proper decisions. Asking them to “be reasonable” is asking them to make poor choices. Growing up is a process of figuring out all the unwritten rules of life. When you’re asking someone to “be reasonable,” you’re asking them to follow these unwritten rules. Kids don’t know them. That’s what makes them fun to be around and sometimes distressing to be around at the same time. That’s what makes it necessary to tell them, in excruciatingly painful detail, what to do and what not to do.

I’ve been reading Paul Lockhart’s Mathematician’s Lament, and loving it, nodding my head in constant agreement, and occasionally setting the book face down and open on my coffee table while I wander around my living room thinking about how I could apply his thoughts into my own teaching.

And they’re radical thoughts. When Lockhart says, “There should be no standards and no curriculum,” I think “My director wouldn’t like this,” and I think, “That would be a lot of work for me.”

But when he says, “Mathematics is the music of reason,” or “Mathematics is art,” I nod my head vigorously. Like all endeavors of human knowledge, math is a creative endeavor, created by human minds and hands and passed down through the ages.

I always hate it when we treat math as a static body of knowledge that seemingly came prepackaged from the gods. No, curious minds created it out by asking questions and playing around. We should explore and retell the narrative of how these minds came to these conclusions. I think that’s an interesting story, and learning it will build the foundational mathematical skill, which Lockhart elegantly boils down to “solving problems.”

But what Lockhart really tries to do is debunk the myth that math is necessary. When teachers try to find the practical applications for math, my skin crawls. No one under 50 balances their checkbooks (I don’t even know where mine is most of the time) and few people use algebra or trigonometry after high school.  Heck, few people use simple arithmetic in their “real-lives.” Calculators do the trick.

The reason we do mathematics is because it’s a chance to play around in a fantasy world. It’s a chance to be imaginative, creative, and have fun. I don’t think that’s something that we need to justify with real world applications.

Here’s a link to Lockhart’s original essay.

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Mesofacts. I’m glad to finally have a word for these facts that constantly change. As a sports fanatic child, I intimately knew mesofacts–think world records in the 100 meter dash, most homeruns in a season, most career rushing yards. These are simple mesofacts because they are the results of human creation. They are things that are undoubtedly going to change because humans will build taller skyscrapers, run faster, hit more home runs, etc.

Arbesman uses Mt. Everest as an anti-example of a mesofact, but I once wrote an essay in college arguing that the quantification of Mt. Everest was just another example of human construction. The number we agree upon as the tallest point in the world has changed (albeit slightly) through the years. So I would argue that the highest point in the world, the largest body of water, the number of planets in the solar system, and other seemingly “natural” facts can fluctuate as well, but these fluctuations aren’t the result of human creation as is true for mesofacts. Natural facts change as a result of human quantification and changing human criteria.

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