Math Through the Looking Glass

All too often, math teachers sit in silent complicity when it is said that math is exact and linear—humanities are not. Math is about answers that are right and wrong—humanities are not. If math teachers don’t interrupt the status quo, who will? Consider sharing this narrative from an alternate universe:

In my humanities class, I learn that there is only one correct way to spell a word—my teacher says that spelling is not a matter of opinion. My teacher tells me to identify the word in a sentence that is a pronoun—apparently there are words that are pronouns and ones that aren’t. I am told that there are fragments and there are complete sentences, and the difference is clear. If I am talking about a novel we have read, I have to tell the facts in the exact order they happened. There are rules for how you are supposed to use commas and apostrophes. I have to capitalize some words and not others—as if that really makes a difference in being Understood most of the Tiime. Those are the rules, I am told. People seem to care that I know what capital city belongs to what country, and you can’t mix those up! My teacher says that some books are too hard for us to read, and some books are too easy for us, because you are supposed to read certain books at a certain age—it’s developmental.

My math class is where I really get to think. Here’s some of the stuff I have done;

--I made a poster explaining when it would be best to say something was “one third” and when it would be best to say it was 33%. It isn’t always clear when you should use decimals or fractions or percents to describe a portion of something. My teacher says understanding how to communicate a mathematical idea is so much about your audience and your intentions.

--I had to look at baseball statistics about shortstops and defend my reason why one of them was the best choice to get a 5 year contract. Wow, that was hard! My best friend and I had very different opinions. My teacher gave us good grades for how well we prioritized the different data. He said there was no one right answer, of course—just like real life!

--My teacher put an equation on the board and said there were a few ways to solve it. He wanted us to pick a way to solve it that would be best if our life depended on getting it right, a method if we wanted to have the most fun trying a wacky way, and a method that was the quickest, even if it might sometimes cause you to make a careless error.

--He showed us a shape we had never seen before. We had to experiment with rulers and protractors and calculators and come up with the area—and then we had to come up with a formula we could remember. I love when he says, “Try more experiments. That’s what math is about.”

--My small group was given a big jar of pennies. We had to come up with 5 different ways we could estimate the number of pennies in the jar. He is giving the same problem to the kids in a class two grades below mine and two grades above mine.

My math teacher says humanities classes could be fun too, but mostly they are taught like math classes that did only number-crunching right-and-wrong drills. He says humanities classes could be filled with opinions, creative writing, lots of discussions, and using evidence to back up our own theories. He even says there are people who have a love of literature the way we have a love of numeracy. Yeah, right.

Don't Be Bored...Or Boring

This is an exhortation, a plea, a pat on the back and a push up the hill. It is meant to inspire and unsettle, and to help you find your passion and determination. It comes as a request and a challenge: Don’t plan to go into class and tell your students, “This is the boring part.”

Haven’t you and the kids been bored enough already!? When we were students in school, when our minds were striving to explore and understand, how often we ourselves were bored, and our teachers looked and sounded so bored themselves. I thought they should say to us, “Learning to be bored in school is preparing you to be bored as an adult. Get used to it. This day will be another exercise in learning to be bored.”

It is not a version of grit to passively accept boredom. It is not a version of grit to be passive. For teachers or for students. It’s a version of submission.

It is good to know how to manage one’s boredom in life without losing one’s mind. It is good to learn to cope with disappointment and failure, and to find inner resolve. And there’s enough boredom and disappointment and failure in the commerce of life to learn those lessons without my actually building it into a task that my students have no choice about and saying, “Here’s something else you’ll find boring.”

We and our students never get back the minutes that accumulate into hours of boredom in a school year.  You read the directions to standardized tests and the students spend that much time listening to you. On the first day of staff orientation in the fall, the superintendent, with all good intentions, reads through the myriad new regulations, and you can’t wait for it to be over so you can get to your class room. It’s in school and out of school: waiting for the bus to arrive because the funding for adequate public transportation was cut; being on hold to a call center half-way around the world where labor was cheaper. There’s a lot of boredom for citizens that is the result of intentional planning. All of that is not inevitable boredom, and it wears us down.

It’s time to rebel against the forces that conspire to make us passive. We are teachers! When we stand in the class, we are the most influential force in the lives of our students. In that time and place we are potentially their hero, their role model, their hope. And because we are teachers, we know something very important, almost mysterious in its power: all information is potentially interesting, every skill acquired broadens our potentials, and all impassioned activity leads to learning. Our best teachers showed us over and over that life is not a struggle against boredom—it is a wonder to be apprehended.

I don’t have control over many boring and draining things in school I wish I had control over: I have to proctor standardized tests; I have to cajole and demand that students wait quietly when it is so hard for them to do that at their age; I have to stop mid-sentence for announcements and bells.

But I don’t have to walk into class and tell them that “This is the boring part.” That’s in my control.  In my work with teachers for over 35 years, I have heard almost all of them share promises they made to themselves: I will never hit a kid; I will never ask a student to sit in the corner as punishment; I will never tell a student that she is bad. Yes, yes, yes. That’s how it should be. And I ask and challenge you to consider, “I will not bore myself today because I will not plan to bore the kids.” Let’s not watch more of the sands of our own professional lives slip away in boredom that we can avoid.

As much as I have had that as my intention (and not only in the classroom, but in faculty meetings as well, and wouldn’t you like your principal to have the intention not to bore you at meetings?), I know I have sometimes bored students. It wasn’t in my plans, but a class would end and I knew Edgar over there was missing in action. But I didn’t plan it. I’d have to check in with Edgar and find out what didn’t work for him, because I didn’t see a boring part in my lesson plan. Edgar might have something to teach me about my planning. And because so much of my career has been spent with challenging students, who are often barely holding on to their motivation, if I didn’t communicate the worth of the lesson, they were unlikely to find whatever little motivation was left in their tank.

Perhaps we could translate our phrase, “This is the boring part,” into “I have no idea how to make this interesting,” or “I can’t figure out why this is in the curriculum guide,” or “I know this is truly worthless to you,” or “I too am but a fallible person trapped in a system that is slowly killing my passion and I am so sorry that you have to bear any of the burden of that.” Since we won’t be declaring those things, here are some preventative steps to take when you look at your lesson plan and say, “This is the boring part”:

1)      Seek the links—When the information in the required curriculum seems so far from their lives that you assume it will be boring (why else would information be boring?), offer them the challenge to make the connections. Don’t do the hypothetical, “You never know when you will be building a shed and need to use the Pythagorean Theorem” if you yourself have never used the Pythagorean Theorem. Tell them how the information truly impacts you as an adult.  Consider how the information may impact the lives of their families, or their community. Have them survey members of their community: “Tell me why you think I should learn about the three branches of government?” The class can send emails to professional organizations that are impacted by that information. Invite in a local professional.

2)      Develop cognitive challenges using Blooms Taxonomy—Thinking is inherently interesting, even if the facts may seem irrelevant. Throughout the year underscore the types of thinking you are asking of students: “You have to do some powerful analyzing today to see what are the most important pieces to this information;” “As we do this, let’s evaluate whether we should add this to the list of essential information;” “The challenge today is to find a way to translate this information so that your younger brother or sister would understand it.” One of the benefits of applying higher-order thinking to information is that it is far better remembered.

3)      Time it—“Class, I am not sure if any of you will find this interesting, so let’s set the timer for five minutes, and then stop and talk about what you think of this.”

4)      Look at the task through multiple intelligences—Graphs and pictograms offer various perspectives on what may at first seem dry data. Giving a dramatic reading to a list of historical names and dates is not boring to either try or to watch. Asking students to verbally free associate with rules of grammar is hilarious. Chanting as a class the chemical symbols on the Periodic Table of the Elements is sublime.

5)      Encourage and allow for creative note-taking. –Teachers often identify note-taking as a boring part of the class. Of course it is, if the students have little inherent interest in the material and note-taking is condemned to be only for the test coming up. Start making note taking interesting with two column notes, which offer students a space to make their own connections and rhymes, drawings and stick figures. Have students share with the class their most interesting note-taking creations. Try it yourself, watching or listening to the news at home one evening, and see how idiosyncratic and engaged you can make note-taking.  Celebrating how students employ arrows and underlines and boxes and shadowing and parenthetical commentary can make note-taking a collectively enriching opportunity, dare I say one of the best times you’ll offer students in class.

6)      Offer to summarize essential ideas—If the next two pages of the textbook are deadly and likely to destroy momentum, tell the students your summary, ask them to summarize what you said in their own words, and move on. You can do the same for sections of movies. Let’s not confuse what takes effort with what is worth the effort; e.g. digging a deep hole in the ground and immediately filling it up again takes effort, but it’s not worthwhile. Laboriously reading boring textbooks should be kept to a minimum, and identified for what it is— a challenge, if you have no alternative (you probably do). Don’t undermine your relationship with your students by using your teacher power to coerce them to do really boring tasks because it will be “good for them.” It’s not good for any of you.

7)      Don’t teach it—Integrate a few of the main ideas into another lesson.

The last item above might put many of our colleagues into risk with their school administration. We are in an era of imposed curriculum, in which our wisdom as teachers to make decisions about how to bring our very real students to mastery is not being honored and trusted. Too many of our colleagues are trapped in systems in which they must rigidly check off that they have “covered” items on a predetermined (and not critically assessed) pacing guide. The standardized test demands that students be exposed to information at such a rate that meaning and depth are often false advertising.

So do what you can. One of the seven items above can usually help you avoid, “This is the boring part.” And then consider digging into your own professional soul for some grit to join committees, professional associations, political campaigns, contract negotiating teams, letter writing efforts, and public hearings, adding your voice to the others who are exhorting us, on behalf of our students and ourselves, not to passively allow the work of schools to be boring. Your students will love you for it.

PS--if you have a lesson that you can''t get around being boring, write about it in the comment section and I'll brainstorm with you ideas.

Lines of Thinking From the 2014 ASCD Conference

The ASCD annual conference took place in Los Angeles from March 14-17. It was consistently thrilling to be among a diverse group of 12,000 educators. Everyone had stories to tell, aspirations to share, and good work to do. You just had to sit down next to anyone and say, “Where are you from? What do you do?” and an hour later you had another colleague.

I heard competing narratives about our students and the schools they need. One narrative concerns poor kids of color who come to school from the earliest elementary years already behind in basic skills. They need schools structures and teachers who are strong enough and sensitive enough to stand with the kids, and who have a pedagogical skill set attuned to their students’ particular needs—especially in reading, writing and the traumas of poverty. If we don’t provide a more rigorous and high-end curriculum of health care and basic skills for these kids, they’ll never catch up; the lack of resources to more predictably turn these communities around is further proof of the institutional racism we still must fight. There is much call from these communities for longer school days and longer school years to bridge all the gaps.

Another narrative is that our schools are overwhelmed with mind-numbing standardized curricula tied to standardized tests, and kids need to be freed up to be creative, to follow their interests, and to make mistakes as they are preparing to take democracy into another generation. We don’t need longer school days or longer school years to just do more of the enervating sameness—we need a grander notion of what education means.

One more narrative: schools alone cannot heal all the wounds of poverty and racism, no matter how long the school day, because there is a limit to how much remediation of basic skills you can ask a kid to tolerate in a given day. All students need recess, the arts, advisory, vocational exposure—not just the prosperous kids whose basic skills are secure. At our best we’ll still have to prioritize the options. As a mentor of mine said to me once when I was struggling with all the needs of my school: “You can do anything, but you can’t do everything.” Schools operate in a world of infinite need and finite resources, and you make hard decisions about what you can do.

The synthesis of these narratives compels much thought. Is it as simple and ultimately complex that different communities of children need what may look like significantly different schools?

These overlapping and at times competing narratives contribute to a shared dilemma: we are fragmented in our struggle against the forces most of us identify as a threat to democratic schooling: privatization that diverts the limited funding already available to the most needy school systems; undermining of the teacher as a professional; over-reliance on standardized testing. It’s a sad fact that thousands of parents in the Boston schools are trying to get their children into charters--the love of their kids understandably trumps long-term political theory.

At one point in L.A. I am in the audience for a panel discussing the whole child initiative. The members of the panel are articulate and deeply critical of the status quo of schooling, and the audience members are the choir, and everyone who speaks says, “WE should…” or “THEY should…” or “THEY shouldn’t…” I started getting antsy. I remembered back to an organizing meeting of my youth when my buddy and I realized that as long as people spoke in “We” and “They” terms, nothing was about to happen. We decided to say, “Here’s what I am going to do, and if you want to do that too, come see me.” Not sure what I am going to do now.

I am thinking of the notion of working upstream and downstream: those of us in human services are working at a river, pulling drowning people out to safety as much as we can; we need some of us heading upstream to find out who and what is pushing all these people into the river. How do I find other hands to link with up and down the river?

My most hopeful notion is that the work of the 12,000 passionate educators surrounding me in L.A. was but a fraction of our larger community. We are a huge reservoir of  potential and kinetic energy—for now keeping the educational system functioning as well as it can, perhaps just a decisive moment or two away from cleaning up the river.

from the introduction to "Hanging In"

There is never one thing that defines a challenging student, never one cause, never one life event, never one disability. If it were one thing, the solutions would be simple. One of my own teachers confronted me with this important and demanding advice: “Keep the complexity as long as you can.” My stories in this book invite you to hang in with the complexities of our challenging students and to take action with no guarantees of immediately observable success. The only guarantee is more evidence that you can use with the next challenging student—because I can guarantee you, there will be another one who challenges your capacity to hang in.

Once, in a meeting convened to develop an intervention with a particularly idiosyncratic student, I said, “This is a lot like our work with Harry a few years back.” No sooner did I offer that bit of wisdom then hands shot up around the room with a chorus of, “No, this is not like Harry at all.” We had never shared our various conclusions about what had caused Harry to be so challenging; with the passage of time, the team was unable to reconstruct the events in Harry’s story in order to craft a shared understanding. Our stories are valuable only in as much as we collectively construct their meaning and articulate a shared wisdom. Set time aside to tell stories. The learning must be made explicit; we hang in collectively.

I have learned so much from working with our traumatized, neglected, and remarkably alive students and with their teachers. What I learn, the gift to me, is how this student and this student and this student are coming to understand this lesson in the varied and unpredictable ways the human mind can work. To be fascinated with the thinking and growth of each student is a formula for lifelong learning as an educator. Small classes are prime real estate for such adult education. The teachers in our schools who embody this accumulated education should be treasured and exalted, but too often they work without the resources and support their challenges demand. The admiration they get is often in the form of “I don’t know how you do your work,” but rarely are these teachers asked to say how they actually do their work, as if the teachers of our most challenging students are in a different profession or possess superhuman qualities. This is a loss for us all, because the accumulated stories of hanging in with our most challenging students are vital to maintaining a diverse and just society.

Schools That Work and Work and Work

Let’s agree that we are not pouring money into public education without wanting a return for our investment. We need our kids to grow up to pay taxes, enough taxes to pay the government back for their schooling, or what’s the point?  To pay taxes you need a job—the purpose of schools is to make sure our students are employable. We need to teach them to behave like good employees. And that’s where we can really start savings some big bucks on educating these kids, and get an even bigger return on our tax dollars.

To make them good employees, schools need to reflect the world of work. We live in a capitalist economy and the kids need to learn right up front that we are all about competition. They can start learning this by competing for their teacher’s attention and competing for grades. This is why we keep class sizes big—but they could be even bigger and save us more money. We could probably reduce the number of teachers if we hiked class sizes up to about 50 kids in a class—or maybe even 75, or 100. It’s said a lot that class size doesn’t matter; it’s the teacher that matters, so we can cull from the ranks of teachers the very best ones, put the best ones in the cafeteria with a lot of kids and let them go at it. Once we get class sizes over 20, we might as well face the facts that we could jack the numbers way up. Big savings right off the bat!

This is why standardized tests are so important! Once you have enough kids in a class that competing for grades and the teacher’s attention is an important skill (which is happening already in most schools), you have to use tests—you can’t expect a teacher to know what every kid can do and then evaluate that in a personal way—that’s far too costly! The tests quickly divide up the class into those who are special and those who are just going to be your run-of-the-mill employees—and we need a lot more of those types of employees than we need bosses. With standardized tests you can safely measure only what is important for most kids to be good employees, and really put an end to the illusion that many of them and their parents have that they are special. For years schools have been implicitly giving kids the message that we don’t need them all to be special, so let’s just be explicit it about it, because we don’t have the time or the money to play around. Keep it simple; keep it as big as we can; keep it uniform.

The special ones can come from the expensive private schools, which seems like great models of education—so many of their graduates go on to college and leadership roles! But those schools cost way too much to consider for every public school kid, and we don’t need every kid to be a leader. The private schools can keep churning out our leaders; we’ll save our bucks on the public schools, where we really need to stock pile our next generation of employees. It’s a good differentiated system of education—let’s keep it that way, as differentiated as we can.

Also, employees don’t read books on the job, so we can save a bunch of bucks by stopping the buying and reading of novels; the kids can do that on their own time. They should be reading manuals and instructions and guidelines, which exist by the thousands on the Internet already. This is where technology is going to really help us. With our electronic whiteboards, we can project the owner’s manual of a toaster oven for all the students to see, and save on paper and shipping costs and deterioration of the books. Along similar lines we can save money by cutting out most literature, and certainly any poetry, because poets don’t make enough money to pay taxes. And what are you going to test? Same for most of the arts, right?

The move to the Common Core presents some risks to our hopes of developing good employees. The Common Core may actually lead to a bit of analytical thinking, but luckily not critical thinking, in which students might actually be supported to be critical of their schooling. We are not going to have a stable workforce if kids learn to be critical of their conditions. Luckily, we are not letting students or teachers have any say in what is in the Common Core, and we’ll keep them all in check by tying any curriculum to our standardized tests. Don’t worry—no thinking, and certainly no acting, outside the box. Teachers will still be doing what they are told.

So this is where teachers’ unions are a big problem for getting our kids ready to compete in a global economy. The type of manufacturing jobs good employees get have gone overseas, and not to Finland, by the way—a place many people are touting as a good example for our schools, but it’s not where the jobs are going. They’re going to China, where there are no independent unions!!! That’s why the Chinese work-to-school model is so effective: their kids don’t have any illusions about organizing for their rights, because that would cost them their jobs! If we are going to compete with the Chinese for jobs, unions are a problem; our students don’t need role models of adults thinking they know better than the bosses above them—that’s not the mark of a good employee. My proposals here don’t give kids any opportunities from day one to think they should do more than follow directions. The teachers should be following the direction handed down by the companies that make the text books and standardized tests, and the kids should be following their teacher’s directions, and then we’ll have the good employees we deserve. And it will all be so much cheaper.

I Still Love Being In Schools

I love to watch Tucker when he is learning. His eyes widen, his face lights up, and he cannot contain himself, shouting out answers—no, not answers but ideas and concepts and “ah hah”s—and he often gets in trouble for being insensitive to his peers who are still struggling to do their work, for being self-centered, and there are times he is frustrated by the trouble he gets into, and other times he seems to accept it as the price he is paying for his education. He grimaces for a moment and then reinvests his energies into his school work. He is eleven years old.
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 One of my first mentors believed, and so have I, that education is healing.
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 When I have expressed frustration to my friend Adam that life for so many seems mean and filled with pain, when it could be filled with so much more joy and kinship, he says he admires my idealism. He is a doctor who works with the elderly poor. He says that life is that mean and painful—not that it seems so—but that it is so, which is why he marvels and takes solace that humans can achieve great moments of transcendence in the midst of our suffering as a species. He and I share the exuberant sweat-filled passion of basketball, the rock band that hits a groove and sends an entire bar into a pulsing mass, the books we are reading that are keeping us up late. My friends and I are junkies for transcendence.
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 Adam is a member of a very liberal synagogue. My only religion is education. Tucker is my proof.

​ I practice my religion, education, in schools. I don’t care about prescribed academic content, and I abhor standardized tests. I abhor the industrialization of education, the ridiculous over-crowding of young people into narrow hallways, the regimentation of bells ringing, the hyper force-feeding of irrelevant textbook tasks that leads to cognitive indigestion and shut-down. Most kids shout for joy when they are released from the building.
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​ I’ve observed affluent suburban high schools. The students go through their paces. They seem less distracted than kids in the city. As rarely as all students, few of them ask interesting questions and a decided minority show passion—some for art, some for physics, some for writing. Their teachers are more relaxed than their urban counter-parts. The pain of the world is less palpable. Here education evokes not religious fervor but a ritualized ennui.
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​ Despite the boredom and enforced pass-fail monomania of schools, I still love being in them. I see when students experience, despite all the barriers, the moments of joy for having their minds opened and their neurons firing in unexpected patterns and, in those moments, transcendence.  I fear my friend Adam is right that those moments are exceptions to our suffering. And I hope my friend Adam is wrong that such moments are the exceptions to our suffering; I am an idealist: schools can provoke less pain; they can inspire more transcendence.