The Daily Texture of Progressive Education

Posted on September 21, 2015 by pollybrown2013

My Year to Think It Over took almost two years, actually. Every week or so I looked through my overflowing boxes of teaching souvenirs, revisited twenty-five years of life in an extraordinary learning community, and returned to these questions:

What did I learn, over time, about collaborating with young adolescents?
What learning adventures were particularly memorable, and what seems to have helped them work?
What am I still learning from the comments of past students, now adults?
What can I give back, out of the gift of all that time doing what I loved best?

When I started the blog, I had stopped teaching. Finally I could write more: savor wonderful moments, and reflect on them; give credit to people who deserved it; give voice to ideas and practices that had guided me; honor students whose descriptions of their experience had transformed mine.

I began writing posts one by one without any realistic schedule–I really thought a year would do it!–and without any overall plan. Very soon threads of continuity began to emerge, willy-nilly, and those stretch across the screen up at the top, below the butterfly.

If you click on those headings, you’ll find an introduction to each strand, with links to posts exploring that strand. You can also click on the topic headings below.

Power in Literacy I worked mostly with kids who were 11 or 12 years old. Often, in our mixed-age class, I spent two years with students. Across any time we had, students developed real and flexible fluency as readers and writers. With increasing confidence, they used reading and writing to explore the world and their own emerging identities. This heading title includes the word power, because that’s what I saw: I watched kids–in a world and at an age in which they can so easily feel powerless–taking up the effectively magical powers of literacy with contagious pleasure.

Being Human Within an interdisciplinary approach, we could draw on both science and social studies–and anything else–to explore our human evolution and the voyage leading to who we are. We could grapple with issues our species still struggles to work out, about how to live together. Eventually, students often dragging me along, we arrived at questions this basic: “Can we come to see each other, all over the world, as cousins? Over time, could that change the way we view the notion of race? Or the costs of war? Or the goals of economies and governments and communities?” If you give them the chance, young adolescents will tackle amazing things.

A Sense of Place What do we mean by “a sense of place” or “place-based education”? What can kids gain from exploring and coming to know the places they call home, and the places they share with others, including school? How far can a vivid sense of place reach, and what skills support that reaching? How can we respect and honor–and take responsibility for–the places that nourish us? These posts explore the teaching and learning of geography in its largest meanings.

Serious Playfulness Here I gathered posts about our explorations of mathematics, various branches of science, and some related matters. Obviously “serious playfulness” is my own wacky term, but it means what it says: we were serious in our goals, but the ways we pursued them were playful oftener than not. Playful didn’t mean games based on television quiz shows. It meant true inquiry; open-ended questions; working together, taking risks, and getting dirty; discovery and surprise.

Together This overview gathers posts that explore social and emotional learning: learning to care for each other, learning skills for working in a group, learning both kindness and resiliency. This strand also includes a series of posts about not using grades, because, in our experience, other kinds of assessment worked better to support authentic collaboration and community.

When I first began this blog, and composed the About page, I wrote out of that clarity that can come from life in the trenches. “The world is full and busy and loud with ideologies about what works in education. I want to revisit some real experiences that worked for real live students, and think about why and how.”

It would be thrilling if my school’s approaches became–soon!–the norm not only in published research results, but also in mainstream practice. None of us should hold our breath. In the uphill battles we still face, I’m going to keep these posts available as long as they seem to be useful. Rereading, I’m deeply grateful for both experiences: to have lived that richly challenging and rewarding teaching life, and to have taken the time to “think it over” afterwards. I’m grateful to everyone who felt that this was an important thing for me to do, and said, “You can do it.” (Alex Brown, you’re at the top of that list.)

Through this writing, things I’d learned from teaching reached forward into my present. Attending writing workshops at UMass Boston’s William Joiner Institute for the Study of War and Social Consequences, I felt again how overwhelming and exhilarating learning can be for the learner. Visiting my dad as he slipped further into dementia and spoke much less, I watched him learn to play a game oriented around spatial relationships. My math teacher self talked to my daughter self, helping her.

Am I done here? I’m not sure. I haven’t explored some topics, or told some stories that feel important. But at this point I am more involved in other adventures.

Meanwhile, however you’ve found this blog, I’m glad. I feel like the host of a fabulous potluck feast. In effect, I’ve spent years working with wonderful cooks. Enjoy! Be emboldened! You can reach me, if you want, at the most obvious email address for someone named Polly Brown. I don’t like to write it out, because robots search for such things–but you’re very unlikely to guess wrong. Or you can share a comment.

From my new adventures, I wish you well in whatever you may be exploring or daring to try, in your own learning life.

Finding the right game

Posted on December 10, 2014 by pollybrown2013

My father, 93 this year, barely speaks now. During the three days my sisters and I recently spent with him, he said little more than yes or no. Even for that he mostly nodded or shook his head.

The exceptions touched us deeply. When our father’s wife asked me to play their small organ, and we three daughters sang together, our father joined in for parts of “Dwelling in Beulah Land,” smiling broadly.

Before every meal, as we held hands around the table, our stepmother prompted our father to say grace. Sometimes he used words we’d heard throughout our childhood (until he and our mom separated and then divorced, and we saw him much less often.) Sometimes he used different words to request the same blessings, ‟living kindly in each others’ lives,” where the original grace asked that we be kept ‟mindful of the needs of others.”

Mostly, though, he listened to us. Sometimes he raised his head at a name, or to watch when one of us grew animated telling a story.

Through our childhood, and for many years after, our father was the most powerful talker we knew. A church deacon who sometimes filled in for the minister on Sunday, he helped to broker peace in a fractured congregation more than once. He sat on the school board in our town, helped build support for a new school, became a leader in his professional organization.

Later on, farm boy turned Green Revolution advocate and diplomat, he spoke persuasively to ministers of agriculture and heads of state all over the world.

We were immensely proud of him, and lucky ever to get a word in edgewise. In fact, the last five years we’ve been glad to have him dominate the conversation less, glad to have him listen more effectively and more appreciatively.

Near total silence felt different, awkward, heart-breaking. That talented, challenging, proud man sat at his dining table, folding a paper napkin along the diagonal and then throwing it into the waste basket. Then he started with another, and folded that one in half the other way, midpoint to midpoint, and then half again. He lined up his knife with the pattern of the tablecloth. He adjusted the position of a box of tissues, making it align precisely with the table’s corner. Looking at a stack of photographs, he positioned a smaller photo under the lower border of a larger one. Then he picked up another napkin and used it to measure the place mat, putting down a pointed finger to hold his place. All in silence.

Without meaning to, I watched my father through a math teacher’s eyes. I thought, ‟He’s practicing spatial reasoning.” Practicing, doing the same thing again and again, to do it well.

I thought back. Our father’s professional and community roles depended heavily on his verbal persuasiveness, but strong kinesthetic and spatial intelligence has also shaped his life. Before I was born, he played basketball, and sometimes refereed. (Years later, reading John McPhee helped me appreciate the way a really good basketball player knows where every other player is, and where the ball is, moment by moment.) All of us had watched our father build boats, plan and create gardens, play pool, dance.

As I watched him now, adjusting objects edge to edge, experimenting with fit, I thought about pattern blocks, math manipulatives beloved by many of my students, which they used occasionally in math, and often during rainy-day recess.

Where could we get some? On an errand at a nearby mall, my sisters and I saw a toy store. No pattern blocks, but we found something called Imaginets, from MindWare. Small flat wooden shapes painted in five brilliant colors, with magnets on the back, filled a wooden suitcase lined with shiny white magnetic surfaces.

The set offered cards with designs to reproduce. By unanimous consent, we hid those right away, sensing in them an invitation to fail. That afternoon we just took out the box, and opened it on the table where the four of us sat together. After some fuss opening the plastic packages of shapes, one daughter set a purple rectangle in the middle of the white space. Another added to that shape a blue semicircle, lining them up the way our father had been lining up place mats. The third daughter added a green shape that became one of my favorites, an irregular pentagon.

We all held our breath. Would our wordless father join in?

With the exquisite care of a ferry pilot approaching a dock, he steered the piece he’d chosen into the position he had chosen for it. When we oooohed and ahhhhed with appreciation, he beamed.

Gradually, as we kept playing, our father joined in with increasing confidence. He had his own sense of fit and appropriateness, in this completely non-competitive, non-verbal, intuitive game we were all inventing together. Until recently, we realized, he might not have been able to do anything this loose, this unconcerned with winning. Here he is, to the right, with one of our completed designs, which fulfilled our goal of using every piece in the set.

When we started letting the curved shapes be tangent instead of fitting closely, he went along for the ride. We grew more and more relaxed about taking turns, particularly after our father added seven shapes one after another, in a run of brilliant yellow, and looked up, pleased with his own sophistication.

I turned away, not wanting him to see tears. Transcending everything that made it hard for us to communicate, we were having a kind of conversation. A man in hand-to-hand combat with dementia, losing one capacity after another, our father was learning.

I wrote the first draft of this post riding north again on the train (a happy little link to the previous post about riding trains with my students.) As I watched the eastern seaboard slide by, creek by creek and cove by cove, I kept mulling it over. My daughter, by phone, suggested the string of words I might use for an online search about spatial / kinesthetic / sensory experience for the elderly. (And I’d welcome leads from any of my readers.)

Already, I can say this much. Unlike the students I observed and fell in love with and learned to support both verbally and non-verbally, my father does not have years of growing and learning ahead. He’s in his last chapter, no matter what right games we find. But he, too, needs and can savor the experience of learning. He is still one of us, a human, seriously playing.

In today’s email, I found a photograph our stepmother had taken, shown above, in which our father builds designs with the Imaginets on his own.

This photograph, taken by one of my sisters, captures the image in my heart. I wanted to focus this post on my father, but I come to the end of it needing to thank not only my father but also my funny, creative, wise sisters, and my brave and patient stepmother–all the hands in this photograph. Also our mother, blessing this visit from her distance, and our families, giving whatever they can to the dispersed village we are together.

I think also of my students, from whom I learned so much that is still with me, about all the ways to be alive and aware–and learning–in this world.

Time Claps, Part II

Posted on April 8, 2014 by pollybrown2013

The paragraphs go by much faster than the learning did. If you let each paragraph equal a day, or a week, or maybe even five years of our own process, alternately scrambling like mad and sitting back soaking it all in–then you might have just about the right scale.

Kate Keller’s genius invention of the time claps was partly about time, but also about scale: using the small as a window on the huge. Of course, sometimes we make scale models in which something made large is used as a window on the small–much larger models of the DNA helix, for example. But here, we were definitely trying to grasp huge, and the time clap model was a way to compress very long periods of time into periods of time we could experience.

The time claps were also about changing the scale. The 5,000,000 years of hominid evolution we considered for the first time clap (and the previous post) are a drop in the bucket compared to the history of life, or an infinitesimal speck compared to the history of our universe, which we only waved at. Hello, history of universe, we are breaking off a tiny chunk of you, which seems enormous to us.

Five million years is one hundred times as long as the 50,000 years of our own species’ wanderings across the continents. When our class went from the first time clap to the second, we were thinking about one-hundredth as long a stretch of time all together, and each clap was worth one-hundredth as much time as before.

Our species had been around for a while before some of us took the chance of leaving Africa, almost certainly unaware that we were switching continents, but meeting considerable challenges to expand our territory. Following Spencer Wells’s account, based on research with Y chromosome mutations, we tracked our way from continent to continent.

At each stage, through weeks of learning, we investigated some of the remaining indigenous peoples, again following Wells’s lead and using his video, The Journey of Man, in which he visits Aboriginal Australians, people from remote villages on the Indian subcontinent, central Asians, Chukchi people from eastern Siberia, and Navajo in North America.

The time clap itself was a way to summarize what we’d learned: about genetics, about the challenges of human expansion into new environments, about ways the human body had evolved to handle those new places.

Clapping and counting together–clap, two, three, four–we let each four-second interval, each clap, be worth 500 years. Each student, or a pair, was responsible for moving onto the map at the right time, and placing one of our crepe paper streamer lengths. He or she placed one end in the area where that y-chromosome mutation is thought to have arisen, then carried the streamer following a simplified, summarized version of that mutation’s spread.

We worked hard to figure out all the logistical problems in showing these things. Here’s a detail from the photo I used in an earlier post, so you can see that Russell is poised to do his job as the time line person, responsible for showing at each clap where we were on the time line. The pieces of brown paper on the floor are continents.

I folded the first section of this time line, so I could show two labels almost in focus.

Here’s a detail from a map in The Journey of Man. which we used as our way of timing the spread of groups of Homo sapiens across our own paper continents. Each arrow is a schematic representation of the spread of the y-chromosome mutations that have let scientists reconstruct this sequence of expansions.

Here’s the map key that helped us connect mutation numbers with times in our time clap and on our time line:

Because I’m a nearly total failure at throwing things away, I still have some of the crepe paper streamer lengths we cut and used to represent the paths. The photo below shows two rolled-up streamer lengths for M130. These were placed beginning at the northern end of the short length for M168 (the Y chromosome shared by all men not indigenous to Africa.)

One student carried one of the M130 streamers by the coastal route around the Indian subcontinent, and then through southeast Asia to Australia. There was much less water to cross, in the time this happened, because the sea level was so much lower, with lots of water locked up in ice. Much more of southeast Asia and the nearby islands stretched in one long continuous land mass. But still, there were many miles of open ocean to cross, to get to Australia. Somehow people did it, spreading around the perimeter of the Indian Ocean astonishingly quickly.

Another student carried the second M130 streamer northeast to Siberia and then to North America–a very long expansion into harsh conditions, that took a much longer time.

JOM M130 cropped This whole field of human population genetics is moving fast. M130 is now designated as C-M130, and on Wikipedia you can find an excellent, very technical article about the C-M130 lineage, or haplogroup. I love the labels on these streamers, made by students, full of pride in their own technical knowledge at that point.

JOM multicolored mutation streamer I’m not sure about this streamer with its many colors, mutation group leading to subgroup, leading to further subgroup, but I think it has the earliest journey on the outside: out of Africa leading to the Middle East, to south central Asia, to central Asia, to Siberia.

If you want to start a fight at a meeting of the folks who pay attention to such things, just ask about how we arrived in the Americas. Increasing numbers of scientists now say that boats must have been involved, small boats made probably out of walrus or other large marine mammal skins stretched over frames, like the ones coastal Chukchi people still make and use. Spreading across the northern edge of the Pacific Ocean west to east, we probably kept fairly close to the coastline or ice pack, and in each new venture moved only far enough to come to an ice-free coastal area that had what we needed. Alice Roberts describes her own take on this in her video called The Incredible Human Journey.

Because of lower sea levels at the time, that ancient coastline is far out to sea now. Boats wouldn’t last to be found, and coastal settlements would currently be under many feet of water–so there’s not much archaeological trail of any kind, so far. The evidence is all circumstantial: somehow we arrived in places that involved crossing wide stretches of water, no matter how low the sea level had dropped.

However they did it, some very small percentage of my own ancestors made that ancient journey into North America. Still, that’s not why I say “we.” I’ve come to feel that all of this story belongs to all of us.

The rest of the ancestors of our class (including most of mine, and Kate’s) came to North America more recently. We wanted to end this thematic study of who we are and how we got here by learning about our recent immigrant ancestors, and the patterns of goodbye and hello that shaped their lives.

So we changed the scale again. In our preparations for the third time clap, we looked at just the last 500 years of immigration to North America, and focused on stories we had gathered, about people related to us and about family friends. Those included Pilgrims who traveled on the Mayflower, representatives of the huge influx from eastern and southern Europe in the early 20th century, and more recent immigrants from Latin America, some with mixed African heritage.

For this time clap we made a very simplified geographical representation that could fit in our classroom. Simpler props–but we were moved and focused by representing individual real people whose stories we knew. Clapping and counting, holding signs, we showed their individual arrivals decade by decade.

What do Kate and I think about, looking back at all this?

I often recall a memory that is uneasy. A girl who had been adopted from China represented herself in our third time clap, and “traveled” east to North America. She joined us from another class, and we were proud and excited to have her take part. Only afterwards, and with regret, I realized that she was embarrassed, unhappy to have been identified as a recent immigrant.

Kate remembers worrying that we were all focused so intensely on our parts in each time clap’s execution, struggling to move and do the right things at the right moment, that it was hard to pay attention to the whole as it happened around us. At least for us, for Kate and me and the invaluable parent volunteers who helped us pull it off, each of those not-quite-seven-minute stretches went by in a blur. So we might be tempted, doing it again, to change the scale and make each time clap last longer, not in what it represents but in how long it takes in the present. Of course, then we might lose people in the long stretches with not much happening. Trade-offs. Probably we’d let the kids decide.

For sure, the value was not so much in the observed performance, but in the experience from the inside–all the preparation, and that immediate sense of taking part in something huge.

Lucky-and-a-half, both grown-ups and students, we felt like explorers ourselves, opening up new knowledge, sharing that with our families and with each other, imagining eyes focused on new horizons.

Time Claps: the first 5 million years

Posted on March 31, 2014 by pollybrown2013

The enigma of time

In a new novel by Kirkpatrick Hill, Bo at Ballard Creek, a gold miner who loves rocks, shiny or not, tries to tell Bo how old they are.

“They’ve been here since the beginning. Before plants or animals. Before the oceans. They’re billions of years old.”

Bo…looked hard at Peter’s kind face to see how old that was. Billions must be terribly old, but she couldn’t even imagine being twelve or fifteen, so how could she think of billions?

Bo is just five, but kids twice her age, or more–adults, even–have the same trouble. Trying to grasp the idea of deep time, billions of years of time, is like thinking of the depth of the universe—something always there, but mostly invisible to us, unreal even when we try hard to get our minds around it.

We need to grasp the depth of time in order to understand the role of evolution in biology, the impact of the speed of light in astronomy, any explanation of rock origins in geology, and the long span of cultural evolution in anthropology–just for starters. How can young adolescents begin to grasp this essential ground for so much learning?

Kate Keller, curriculum genius, on the case

Having grown up with multiple brothers and multiple sisters, Kate is interested in everything. (Even football, I think to myself as I write this.) The daughter of two architects, she is always alert to purpose and design wound together. Planning curriculum, reading everything she can find, Kate becomes a sort of settling pan (notice the gold-mining image) for the most powerful, most fertile, heaviest ideas in a thematic study–from some points of view, the most adult understandings. Then she comes up with active, playful, open-ended, deeply kid-centered ways for students to connect with these ideas.

All of us who work with Kate–colleagues, students, parents–feel smarter when we’re working with her. We try harder things, and try harder while we’re doing them. Not all geniuses have that effect.

We called our thematic study The Journey of Man but wanted it to encompass more than Spencer Wells’s book by the same title. We’d begin with a relatively brief overview of the past 5 million years of hominid evolution in Africa. Then we’d look at the past 50,000 years, focusing on the spread of modern humans, Homo sapiens sapiens, across the continents, using that as a chance to do a lot of geography work. Finally we’d look at the most recent 500 years of immigration into North America.

In other words, to think about all this, Kate and I wanted our students to imagine millions of years, thousands of years, and hundreds of years. How?

Modeling time and space

Harvey Weiss map of Australia cropped In order to make maps or scaled blueprints, we model large quantities of space by using smaller quantities of space. We let an inch equal a mile, or a centimeter equal a kilometer, or three, or a thousand. Here’s a very basic example from a favorite book about maps, by Harvey Weiss.

When we’re making time lines, we use small amounts of space to model large amounts of time. If a meter is a century, for example, then each centimeter is a year, and 10 meters can be a thousand years, a millennium. Need more than a thousand years? No room for a timeline 10 meters long? Change your scale. Let every millimeter represent a year, say, so that a whole meter stands for 1000 years. On the sample below, students made each 4 inches equal 100,000 years.

One way or another, a time line lets space stand for time.

Time lines can be very powerful. Here’s a memory I treasure, from another study. We’d been working on a time line of transportation innovations, and it had gotten so long that the students working on it had to lay it out down the school’s longest hallway. As I helped them carrying it back to our classroom at the end of projects time, some younger students walked by. “What’s that?” one asked. Without missing a beat, one of my students answered, “Ten thousand years of human history.”

On beyond time lines: letting time stand for time

Still, time lines aren’t made of time. Kate asked, “What if we let small quantities of time stand for longer quantities of time?”

Science videos sometimes present this in words. For example, at the beginning of the video The Journey of Man, Spencer Wells represents the evolutionary history of apes as one year, with the emergence of our own species, Homo sapiens sapiens, on December 28. This compression, in which we leave Africa on New Year’s Eve, can give kids some sense of the comparative brevity of human experience. But what could help them really feel it?

Suddenly, Kate came up with an idea so brilliant that the students who were involved still say it with an exclamation point: the time claps!

We would all clap hands, as a group, to represent time ticking away. The interval between claps, a few seconds, would stand for a much longer amount of time–a different amount of time in the time clap for each section of our study. Meanwhile, individual students would stand and move around and hold signs or other props, to represent what was happening within that time. We would all be participants, and all be watchers.

Some overall nuts and bolts

We did three separate time claps, each with a different scale and its own companion paper timeline, for the three parts of our study.

We worked in many ways to prepare for each of the time clap “performances.” We created paper continents and paper timelines and other props. At one point we arranged our desk groups into a very rough representation of the continents and their relation to each other, to help with that part. We made plays about the indigenous people of some of the continents, and investigated some of the requisite technologies for leaving the tropics. (In another post I need to write about the incredible contributions of parent volunteers, in all this hands-on work.)

Although we gave students the responsibility, as usual, for figuring out workable scales for the paper time lines, Kate and I figured out the scales for the time claps behind the scenes.

Here’s a chart I made as we were talking and considering:

The first time we tried it, we realized that counting 5 seconds again and again was much too awkward. (Try it–you’ll see.) The rhythm of “clap, two, three, four” worked much better, so we refigured:

Five million years

For the first time clap, we looked at the past 5 million years of evolution of various hominin species. With everyone clapping together, we clapped and counted four seconds–clap, two, three, four, and repeat. Every eight seconds, or every two claps, counted as one tenth of a million years, 100,000 years. So we represented 5,000,000 years in 8 X 50 or 400 seconds, or 6 minutes and 40 seconds.

Meanwhile, different kids represented different hominin species. When the fossil record indicates the beginning of a species’ time, a student would stand up, holding a sign with that species’ name. He or she would stay standing for as long as that species is thought to have been around, and act out some of the behavior scientists agree we had evolved at that point: creation of stone tools, use of fire, ritual burial of the dead.

So, for example, the student representing Homo erectus stood up around 1.8 million years ago (represented on the time line as 1.8 MYA, and in the clapping as 65 claps in, since we began with a clap.) Then he or she sat back down at roughly 27,000 years ago, two seconds before the end.

On the time line, the kids put the label for Homo erectus about halfway through that species’ time, and used a yellow line to represent the whole Homo genus.

In that first time clap, long stretches went by, during the first few million years, between the emergence of known hominin species. A lot happened pretty quickly in the last 200,000 years, represented by the last 16 seconds.

Kate wanted students to feel the way a simple list of events doesn’t give a true sense of their relation in time. It takes some way of making the intervals proportional to the actual intervals, to get a real sense of the depth of time we’re talking about when we look back that far.

It takes the passage of time to help us imagine the passage of time.

Speaking of which…

Writing a blog resembles teaching in some ways: everything takes so much longer than you think it will, and personal excitement can make it take even longer. We all loved this work; we felt proud to be doing something we’d never heard of students this age doing. I saved lots of notes and lots of artifacts. I want to share some of them, but I also want room for some thoughts Kate and I had when we talked about all this recently. In other words, this post has become, itself, a time line for which I have no adequate hallway.

So, I’m throwing my hands in the air, and stopping here. Next post: 50,000 years, and 500 years, and what we think, looking back.

I also want to mention that when I searched through those artifacts I found a copy of our picture book about the Chukchi, and added some wonderful samples of that to the previous post. The benefits of boxpile archaeology.

Ancestor Pies

Posted on February 11, 2014 by pollybrown2013

A few weeks ago, Chrissy Danko and I met for lunch. Every time I’ve thought about it since then I’ve started grinning. She is the oldest of four siblings, and I taught them all, sad to say goodbye to the last of them and to their parents. (‟Wouldn’t you like to have more?” I asked Joe and Joan, impertinent as ever.) It was a huge treat to sit and talk with Chrissy, and hear about them all, and hear about who she’s becoming as an adult.

When she came to me, Chrissy was so shy she barely spoke in front of the class. My fierce protection of turn-taking, especially for the turns of the quiet, didn’t work for everyone, but it helped Chrissy. She opened up; she began to appreciate herself more. Now she is writing her dissertation, for a PhD in philosophy, about Hume and Kierkegaard–and about what it means to be an individual, to have a self.

Here’s a photograph of Chrissy, when she was in my class:

Here’s another, at Halloween. I have no idea who’s the alien, and who’s the pumpkinhead, and would love to know. (At a place that really values creativity, Halloween can be pretty amazing.)

I don’t know how it is in your life, oh patient reader, but in mine, right now, there are many mysteries, treasures that lie somewhere unknown in still-pretty-tall stacks of boxes. Some absences I can live with cheerfully for a while more, but some feel like serious deprivations. For example, although I saw it some time in the last year, I can’t find Chrissy’s ancestor pie. Hers was one of the most unique of the circle graphs of background and heritage that I assigned in the early years of the immigration theme.

Here’s Aaron Goodman’s ancestor pie, made that same year, also quite wonderful:

Pretty soon in the evolution of the immigration theme, I stopped assigning ancestor pies, realizing that they could be problematic for some kids. While it was an assignment, though—and later, when it was a choice—we considered fractions as small as sixteenths, one sixteenth for each of a child’s sixteen great-great-grandparents. Two parents; four grandparents; eight great-grandparents; sixteen great-great-grandparents.

(When I heard that a cousin in my father’s Maine hometown had said that his great-grandmother had been two-thirds Indian, I knew that couldn’t be quite the case. Ancestry denominators come in powers of two.)

Aaron didn’t need sixteenths; fourths did it for him. Ben Redden needed eighths, and managed to line up the eighths from two different grandparents, to show that he added up to a fourth English.

For Chrissy’s ancestor pie, unique and memorable, she made one big pink circle, on which she wrote, ‟I’m all Polish.”

On one of those trips back from Ellis Island described in the previous post, Chrissy’s dad’s stories intrigued me. More accurately, I was struck by his lack of stories. ‟They won’t talk about it,” he said. ‟None of them will, or ever would.” The memories of life in Poland too dark? Or still too much sense of rupture from that other life? Maybe both—since those feelings seem able to coexist, in all of us.

Another parent had spent years coming to understand that her mother’s grimness could be traced to her own mother’s very difficult immigration experience. She’d been left behind as a baby, then finally came over to join her family, and was ridiculed for being slow to catch on to America; her bitterness affected her daughter. ‟I’m where it stops,” my student’s mother said. ‟I’m not going to keep living out that hurt, and I won’t pass it on to my daughter.” (I may not have the family history details quite right, but I will never forget the mother’s resolve.)

Even the stories we would definitely call successes seemed often to have a shadow.

Beyond those individual stories, looking at the community story, I began to see the melting pot project as very much unfinished, at least in our area. A friend of mine in Marlborough went to have her children baptized. ‟Wrong church,” they told her. ‟You’re Irish. This is the Italian church.” Several Worcester parents in my class described lingering enmity between Irish Catholic and French-Canadian Catholic colleges.

These and other stories convinced me that we can all be tribal, insular, distrustful. We seem to be nowhere near being able to handle racial differences; we can’t even handle ethnic ones.

(All of these, of course, being cultural constructs, not biological. Inside that designation of Polish there could be many variations, given Poland’s history. And we are all Africans, in very recent time. But that’s for another post, somewhere down the road.)

The ancestor pies told yet another story. Sarah Tonry’s, one of those mysteries hidden in the boxes, had nine colors, as I remember, for nine different flavors of European heritage. Most of the kids in our central Massachusetts population colored in at least three or four different cultural origins, and when we located all our collective countries of origin on maps, the class list ran to nearly twenty, easily.

Willy nilly, we were the melting pot, and the ancestor pies showed us that.

I myself have to go to fractions smaller than sixteenths to show anything other than one big circle. Growing up, surrounded by people with ‟interesting fractions,” I felt the lack severely. At some point, our mother helped my sister and me calculate that we were 1/2048th French. An exhilarating notion. We spent a whole crossing of Long Island Sound gloating.

Family legend in my father’s family said that we were 1/16th Native American, and recent research by family genealogists indicates that my generation probably really is 1/32nd Abenaki. I’ve learned since that brutal treatment of Native American Indians in southern New England led survivors to flee north. So Judith, my great-great-grandmother, could have been any combination of tribes, along with whatever portion she had of what we call white.

I’ve thought about Judith a lot, remembering this again and again: inside our historical selves, the selves we bear through the changes and patterns and stories of history, there are wars. There are hurts unassuaged, that convey hurt forward without ever being named. For all of us, one way or another, things got thrown overboard; loved people were left behind.

Publicly, we may celebrate our emigree identities, whatever they may be, and the melting pot project, the meetings of differences. Privately we still seem to carry a lot of grief, more than we usually let ourselves know.

That’s one of the things the community of a class can do together: we can honor each others’ historical selves, whatever we know and share of them. Honor them with knowledge and wide understanding of the historical context; celebrate them with respect and joy. We can be gentle with the unnamed mysteries inside the tall stacks of unsorted boxes that are each of our identities.

One year, Kate Keller (wearing her aide hat) suggested that all of us take our just-finished immigrant mini-posters outside. (Each mini-poster gave the basic information about one immigrant, relative or friend, for each member of the class; Kate and I each made one, too.) Outside, we all stood together on the wide steps below the classroom windows, holding our posters and making a human timeline, century by century. A fairly boisterous crew, we stood there quietly for a minute or so, honoring all those reasons to have left and reasons to have arrived, all those ways of persisting afterwards. We called all those people, a few still living, most gone, to be present. Neither of the adults had dry eyes.

Living with each other, hearing each other’s stories, we might have looked pretty homogeneous to an outsider, but we were honoring difference, discovering commonality, keeping an old project alive. Nothing else we did mattered more.

Ellis Island Stories

Posted on February 4, 2014 by pollybrown2013

On one of my first trips to Ellis Island, with my family, we were part of the annual surge of people into the national parks, on the day after Thanksgiving. (‟Highest attendance, nationwide,” the rangers told us.)

Moving from exhibit to exhibit in that throng, I overheard an older woman telling her companions about her own father’s journey to America, alone, at the age of 12. As she stood above the Great Hall, where people were sorted–allowed in or refused and sent away–stories she had heard all her life took on new shape.

On the ferry back to New Jersey, listening to all the languages around us, I leaned over to my husband and asked, ‟How many?” and he listened for a few minutes and said, ‟Maybe twenty?” We were surrounded by another pilgrimage, a pilgrimage of new immigrants, come to honor that shrine of the old immigration.

None of our own close relatives came through Ellis Island—his mother came after the island was closed; my ancestors, like the rest of his, came centuries ago, when nobody was counting or checking or manning the gate in any way; when people just came.

Still, the story we felt around us is universal—all those people, in all their languages, were saying so—and we were deeply moved.

The parents of my students helped me figure out how to get us there, from our distance in Massachusetts. The first time, Gail Epstein and David Tapscott arranged for us to stay with relatives near New York City, taking over their rooms in a giant sleepover. (Thus the comment–in the recording below, that shows part of our debriefing session once we got back–about not stepping on anyone.)

Another year, Carol Bedrosian, now the editor of Spirit of Change, arranged a bus for a day trip, and helped the class throw a car-wash to defray some of the costs. It was a very long day. We left from Grafton at 5:30 am, and returned about midnight. Still, it worked, and we used that way of getting to Ellis Island many more times.The trip book–a combined guide and workbook, the sort of thing teachers can create and use in the wonderful age of photocopying–included games to play on the bus. We chose a video to watch on the way home, and the few kids who didn’t pass out cold in extremely odd positions watched along with the adults.

The bus had more room than we needed, and cost a fortune, so we invited parents and grandparents to join us and help cover the cost. Making this a multi-generational field trip had all sorts of benefits. Kids got to know each others’ parents; parents got to know their children’s friends. Especially on the way home, as children slept, parents told each other (and me) their own families’ stories, deeply moving, often full of sorrow and darkness along with hopes fulfilled. With all those generations bearing witness, we settled more deeply into some truths of our history.

When I decided to post here that debrief of the very first class trip, I knew I would have to tell the story of the guy reaching over the railing.

We were exploring in our small groups. My group was in the room with what I called immigration math, huge colorful 3D graphs and interactive maps, showing immigration trends across time. I had designed a day that would echo our day at school: math time in the math room; reading and writing time in the galleries full of photographs; sketching time in a gallery full of the actual objects immigrants had brought with them, candlesticks and prayer books, christening dresses and lockets. Recess time we spent outside, looking for our own relatives on the wall of names, watching the seagulls. All of this was meant to help us feel ourselves mid-harbor, mid-history, mid-melting pot.

Lucy Candib, medical doctor and mother of Addie, was with me there in the math room with our group of four or five kids. Suddenly, we heard the terrible sound of someone’s head hitting the stone floor in the entrance room behind us. A young man from another school had leaned out over the stair railing too far, reaching to a friend, and had tumbled down to the floor below. Lucy was the first person at his side. I saw him on a stretcher, apparently unconscious, as rangers waited for a helicopter to fly him off the island.

All of us, every single one, including me, had to tell that story first, before anything else, when we got home late that night. I had to get past the ghost of that story in order to go back to Ellis Island with kids again. That incident made me tighten my organization for the trip, and recruit kids to be mindful of everyone’s safety. It forced me to think through (again) all the risks teachers take when we leave the classroom with kids, and all the reasons why we should, anyway—because the story of the young man who reached too far was not the only story we all had to tell when we got home, just the first.

Inspired by that woman on the balcony of the Great Hall, imagining her father, I had designed the immigration unit around true immigration stories of family members and friends, people still alive and people known only by the stories still told about them. Kids called uncles in California who knew that stuff; they interviewed their babysitters; they often found family artifacts and brought them in to share. In our work at school, students gathered these stories, distilled them into file card versions to put on a huge timeline stretching around the room, and chose one to write in full and revise for publication.

Always, in any particular class, a good portion of the kids, as many as half, had family stories that linked to Ellis Island–but the assignment didn’t specify that.

At Ellis Island, I asked the kids to make up a fictional story, also. In a room full of giant portraits of immigrants, near the entrance to the Peopling of the Americas exhibit, each student chose a person from one of the photos: boys and girls, women and men, from several continents.

Then, as students moved from section to section in the exhibit, the trip book led them through the corresponding stages of the immigrant experience: a section about saying goodbye, when they left their old homes; a section about finding work; a section about communities of immigrants giving each other comfort and reassurance. After reading some of the text on the walls, looking at the photographs, and listening to recorded accounts on phones placed around the exhibit, each student wrote a journal entry in the voice of his or her chosen person, bearing them through the experience, stage by stage. To the right, Ian Wills and IanTapscott have found a comfortable piece of floor. Below, Mike Costa reads what he’s already written.

Sometimes a kid chose a photograph that could be a stand-in for a great-great-grandmother or grandfather. Sometimes they chose photographs that could be stand-ins for themselves. Stefan Cunha chose a newsboy yelling out across a street–and for all these years since I have remembered the clarity and power of his writing in that situation.

By the time we got back onto the ferry to leave Ellis Island, each of us was like a set of Russian dolls, with other lives nested inside us: the boy who discovered that the immigrants had come to earn their way into this country with unbelievably hard work; the girl who was let through Ellis Island but had to say goodbye to her father; the aunt who could never fully emerge from the trauma, the shadow, of the pogroms; the teenager who became the family’s translator exactly at the age when he wanted independence; the mother with her children held close all around her, hollow-eyed, all of them hungry and hoping to be better fed.

Ellis Island was hard hit by Hurricane Sandy; it’s only gradually being reopened, and I’ve worried that exhibits I treasured, as a teacher, may have been lost. Even before that, security arrangements put in place after the World Trade Center bombings had so lengthened the process of getting onto the island that it no longer worked for us as a day trip. Meanwhile, I had been learning about Blackstone Valley immigration stories, and had discovered the Museum of Work and Culture in Pawtucket, Rhode Island–not at all the same, but fascinating in its own way. The focus of our work in the fall gradually shifted.

It’s fair to say, though, that all my curriculum work afterward was affected by the Ellis Island field trip experiences, and by the thematic study that grew around them. Looking back I can see shifts: in my sense of what is at stake in curriculum choices; in my sense of the huge and complicated realities young adolescent students can stretch to embrace; and in my sense of the importance of combining, carefully and respectfully, both research and imagination.

Below, Adam Curley and I are too excited to sit down, while various parents huddle and talk in the October wind across the harbor.

You’d have a hard time tracking people down with these photographs, from several of the earliest trips–so I decided to just go with them. Thanks so much, to everyone who helped these wonderful field trips happen!

Five More Thoughts About Grading

Posted on January 11, 2014 by pollybrown2013

The story so far: If the product of a learning experience takes the form of a grade, other possible products and outcomes have less reality and less power for the learner.

Voices speaking out against grades want to shift the focus of learners and teachers, to give priority to those other products and outcomes. I’m going to focus on just a few.

# 1 Teacher support, and student goal-setting, guided by targeted, individualized, meaningful assessments

Focused effort matters, and thoughtful assessment can support that. Very briefly, here are some of the kinds of feedback individual kids could come to expect in my classroom, in place of grades:

one-on-one working conferences to look at pieces of writing, reading comprehension progress, math quiz outcomes, etc.;
group mini-lessons based on common confusions or not-quite-there efforts or emerging possibilities or spontaneous break-throughs, acknowledging and moving forward from all those;
quick skills checks in the form of miniboard warm-ups;
written responses to specific assignments;
long narrative progress reports twice a year;
conversations in preparation for portfolio sharing, and the portfolio conferences themselves;
feedback from classmates, students in the wider school community, parents, and other adult audiences.

The previous post has examples of some of these. The feedback for students in younger classes varied from this in developmentally appropriate ways, but always with the same goals: not judgment, but celebration and support.

Each of these activities provided an opportunity for student and teacher to observe patterns in comprehension and skill, or difficulty, and to set goals both short-term and long-term. At the same time, each of these assessment activities was an opportunity to revisit, share, and reconsider the important questions inherent in our content.

#2 Learners who belong to themselves

I remember a conversation with the high-school-aged daughter of a friend. She told me about her classes for that year by telling me her grades. She couldn’t tell me what was interesting to her; couldn’t say what she wanted to learn next; couldn’t describe anything about her learning process. Her grades were high overall, and she assumed that the subject in which she was getting the highest grades should be her major in college.

This young woman didn’t belong to herself as a learner; she belonged to her grades, and to the people who were giving her those grades–even the people who were celebrating those grades.

Especially once we were able to keep students until they were ready for high school, people observing the graduates of my school have been struck by the way graduating 14-year-old kids belong to themselves–how clearly they know and understand and respect themselves as learners.

Instead of pinning their student identities on their GPA, students in ungraded situations learn how to work with their real identities as learners. They learn how to choose meaningful and sustainable challenges for themselves. They know how to manage their own attention, and what to do to sharpen their memories. There may be passages through which they struggle, but a lot of the time they’re having a blast. Above all, they know, for themselves, why it matters. To the left, checking and graphing temperatures.

#3 Authentic and rewarding group learning

Teamwork flourishes best when grades are out of the picture. When I’ve talked about the amount of group work happening in my class, people have often asked, “Don’t kids get distracted by working together? How can you tell who did what?”

I’d have to be crazy to deny that distraction happens sometimes, or that timid students can become dependent on others. Still, young adolescents are ready and eager to learn how to be teams.

At Tsongas Industrial History Center, these girls are constructing a working canal system model. As usual, museum educators commented on how well students worked together–incorporating everyone’s ideas, sharing the dirty work on the floor.

At any age, effective group work doesn’t happen automatically. In order to get the huge benefits of several minds focused on the same task, complementing and helping and challenging each other, kids have to learn how to be task-focused and team-focused both at once; how to do the social work, the intellectual work, the creative work, and the procedural work all woven together.

Kids exposed to plenty of group projects in an ungraded situation get a terrific head start. Without grading to tell them they’re competing instead of collaborating, they learn how to stay balanced within the group process, and how to help the group stay balanced so it keeps on working for everyone.

If you want an argument against grades, focused on future success, you could start with that.

Above: Working with a parent volunteer, students help each other figure out which direction the rivers are flowing on topographic maps.

Meanwhile, freed from generating grades, I could put time into helping groups design and choose tasks that would engage them, with topics and audiences that mattered to them. The resulting energy helped their bicycle built for two (or three or four) keep momentum.

Often, when sharing work in a portfolio conference, students mentioned their partners and teammates, and told about what each of them had contributed, as I set off quiet internal fireworks of celebration. Yes!

# 4 Deep meanings held in community

As humans, we seem to have evolved to construct meaning, and experience meaning, collectively.

Many groups of students have been inspired by the collective power of the communities that built Stonehenge, and archaeologists’ ideas about the community events held there.

Archaeologists and paleo-anthropologists have found evidence of the power and importance of community life and community understanding, deep in the past history of our species–and even for the other hominin species before us.

Young adolescents work hard to begin to understand huge things: life and death, economic reality as they observe it, the concept of scale, the notion of one image symbolizing whole realms of experience. Whenever I asked groups of students what they’d like to understand better about the world, I was astonished anew at the ambition of their questions, knowing this at the same time: the really heavy lifting they can’t do alone, any more than adults can.

In my own most emblematic image of this, a group of learners listens to a challenging novel read aloud. As I write, I realize that I’m thinking particularly of Lizzie Bright and the Buckminster Boy, a novel about racial prejudice in early 20th century New England, beautifully written by Gary Schmidt. Sharing a novel like this, the students build understanding together through their various comments and questions. Sometimes I sense their collective bravery in their silence for a tricky passage, or just after.

If somebody out there knows a way to assign grades to the quality of a shared group silence, let me know.

Now hold that in contrast to this: When individual achievement is the only test of an experience; when shared learning is considered cheating; when it’s constrained by the “level-playing-field” concept that requires teachers to do exactly the same things for every student; when teachers face such large classes that they have no way of knowing who’s doing what without completely isolated graded assessment–the deepest and truest parts of learning are hobbled, compromised, or outright lost.

It’s not impossible to nurture community, and the deep meanings community can hold, in the presence of a grading system–just harder. In fact, in my experience, over-emphasis on individual outcomes in any form–either grades or some supposedly benign substitute–works against the development of community, and the construction of shared meaning.

#5 Powerful connections with content

When grades aren’t the focus, content itself–the world!–gets more attention. The world is alarming to young adolescents–and to all of us–but also fascinating. Grades wind up being a smokescreen in the way of that fascination.

That’s what broke my heart about my friend’s daughter, mentioned earlier. She was experiencing very little actual engagement with the world and how it works and what we make of it. Her grades were like junk food, no fit substitute for actual encounters with the depth of time, or the mysteries of prime numbers, or the relationship between surface area and heat loss, or the way human history offers such contradictory evidence of both altruism and cruelty.

I think of a student long ago who wanted to read novels about the Holocaust. She had no assignment. She just kept coming back to me for more books, and talking about them to her classmates and parents. She was choosing her own path to a deeper understanding of the world.

Or I think of a student, now grown to a man, who used his sketchbook, during morning sketching time (which was completely open, unassigned), to make a very long narrative map, which continued from one two-page spread to the next, and the next, for months. The map as a whole incorporated everything that kid was noticing about the world through which he traveled: about geography, transportation, and the designs of buildings and other systems; about humor; about continuity and discontinuity.

Looking back, I remember now that this student’s family had just gone through an unusually messy divorce. His rehearsal of continuity in the built and natural worlds, page by turned-over page, feels tremendously poignant to me now. At the time, I was focused on his thinking and processing and creativity. But it seems likely, now, that the mapping was working for him on levels I couldn’t even guess. He gave himself the assignment that let him live in his intellectual strengths, and use those strengths to help him live through his family’s troubles.

Although he made me copies of some of the pages, I have no idea where they are. Hooray for memory so vivid and dear that it doesn’t need props. Hooray for learning so rich that no grade could encompass it. Hooray for the safe haven, also a highly effective launching pad, in which such work could happen.

I have a feeling I’m still not done with this topic…

Never, Nada, Zip, Zilch: No Grades

Posted on January 3, 2014 by pollybrown2013

In the teaching and learning I’ve written about for this blog, some things never happened–things taken for granted in most schools. I was lucky.

For starters: because my school didn’t require me to, I never summarized my assessments of students’ work using grades. No number grades; no letter grades; none of the judgments about mastery (not as clear a concept as you might think) summed up in terms that are just grades thinly disguised. None, never, nada.

Like all my colleagues, I gave plenty of careful attention to student work. The students received many kinds of feedback, and even more kinds of support. Above all, in ways small and large, we celebrated the culmination of authentic learning. But not with grades.

I was still a kid myself (and getting A’s) when I decided that grades were meaningless and dangerous. As an adult, I’ve been known to refer to grading as institutionalized child abuse.

Still, I’m used to the fact that people I respect may disagree. Occasionally, Touchstone families have decided they wanted grades, going somewhere else to get them. Other families have wished for the crispness of grades, but stayed for the quality of their children’s learning. Almost all our graduates have gone on to schools that use grades, and almost all of them have continued to belong to themselves and care most about meaning.

If you want to read essays about the uselessness (or outright harmfulness) of grades, track down the writings of Alfie Kohn. I think often of a less famous heroine, Meghan Southworth, a working math teacher and trainer for the Maine Mathematics and Science Alliance. She wasn’t able to eliminate all grades, because her school required them at the end of every quarter. In order to have some basis for those grades, she had to administer tests and other graded assessments, and record the results.

Here’s the kicker: she had stopped showing her students the grades they received through the term.

Instead, she continued to give her students written comments. I didn’t see hers, but I’m guessing they were a lot like mine: suggestions for ways to rethink problems, ways to improve quality control, ways to balance carefulness and momentum–along with acknowledgement of the kinds of engagement and effort, no matter how tentative, that can help a student move forward. Here’s a small sample of comments on a test:

$math quiz comments cropped$ This student was working to overcome test-taking anxiety, and needed to focus on how close she was to the full answer. Thus “almost” instead of an X.

Like most teachers everywhere, Southworth wanted her students to improve, not just stay at the level of achievement they arrived with. She had noticed that they wouldn’t really absorb or use the support embedded in her comments, as long as the shortcut of a grade was available. She quoted a student who caught on to her new system very quickly: “Oh, you want us to read the comments instead of just looking at the grades!”

Southworth also cited research describing most students’ response to grades: “Is this what I’m used to getting?” If the student is used to getting A’s, and this is an A, no need to stretch. If the student is used to getting C’s, and this is a C, no need to worry.

To put this as harshly as I’ve sometimes felt it: If it’s a teacher’s job to sort kids into levels, grades make sense. If a teacher is meant to be a gatekeeper restricting access to future opportunities, ensuring a scarcity of qualified applicants for those opportunities, then grades make sense.

But if a teacher’s job involves paying attention to learners, understanding them, and working with them to help them grow, then grades aren’t worth much, and can actually get in the way.

Think about what freedom from grading meant for me and my students, as we worked together:

$math work and progress cropped$ Freed from grading, I could put much of my energy into assessing what each child needed in order to make the best possible progress. I took lots of notes, and reviewed them less often than I thought I should, but often enough to keep my concerns and hopes for each student fresh.

We could make frequent and thoughtful use of student self-assessment. That’s awkward to incorporate into a grading system, but really important in helping students move forward.

$math self-assess and my response cropped$ Written quickly on the back of a math quiz, this is part of a student’s routine reflection on test-taking strategies and skills, with my response.

Here are some of the sentence starters for a reading journal self-assessment, leading up to a portfolio conference.

My students and I weren’t in the more-or-less adversarial relationship that grading so easily encourages. Kids tended to be fully invested in the goals we had set together. So I got to hear them say things like this: “Something in me just rushes right through instructions, because I want to get started on the answers. So I’m trying to build the habit of stopping myself and reading the instructions again.” Or: “Now I can really understand what I’m reading, I get involved in what’s happening, and hate it when you say that reading time is over.” These are kids realizing what they need–habits of rechecking, reachable books–and figuring out that they can provide that for themselves.

Freed from grading that would imply class standing, we didn’t have to worry about an “even playing field.” I could help kids make individual choices of topics and materials comfortable enough to encourage confidence, interesting enough to inspire excitement, and challenging enough to nurture flexibility and pride. Like our physical education teacher, I aimed for “challenge by choice”–and I found that well-supported students motivated by genuine interest almost always aimed high.

There had been a rage for home-made marble chutes, in a run of rainy-day recesses. This student worked on his own to explore a new idea, incorporating a toy vortex.

At a professional conference, another teacher asked me, “But why do kids work, if there’s no grade as a reward?” I didn’t actually burst into tears, but I felt some despair. We are in real trouble when teachers themselves have been conditioned to forget the intrinsic rewards of learning, the joy of feeling powerful as a learner, the genuine appetite kids bring to their mutual effort to understand the world.

What about my own reward? Immeasurable. My students grew like weeds, not just physically but intellectually. They bloomed! That was the real delight, for me, in teaching at a school that disavowed grades: I got to watch kids learning like mad, bright-eyed and working tirelessly, full of the meanings in their learning and full of themselves, taking off and flying for their own reasons.

I wouldn’t trade that for nothin’. (Nada. Zip.)

I could not fit this topic into anything resembling my 1000 word target. So I’ve saved some aspects for another post: the relationship between grading (or not) and group work; ditto the development of class community. Also: in the absence of grading, kinds of feedback students could come to expect–and my continuing fascination with learning that happened in odd little corners (like rainy-day recess) where feedback wasn’t a factor.

Afterthoughts, Afterlinks, Resolutions, and Thanks

Posted on December 27, 2013 by pollybrown2013

My most recent post, about math mentors and math fun, was the 25th on this blog. The calendar year is about to turn; I’m a little less than halfway through my year to think it over. Time for a mixed salad of quick thoughts, including some resolutions.

More math fun

First, it turns out that 2013 is not prime. All year I’ve wondered. Finally, this morning, I started scratching calculations on the back of an envelope. Then I went to the web to double-check, and found a prime factor calculator. That confirmed it, just in time:

I also checked 2014. That, too, is a product of three primes, but I’m not telling. (You know right off the bat what one of those primes has to be.)

After reading the previous post, Kate Keller said some really nice things, including, “Wait! You left out the birthday ritual!”

Kate’s remembering something we did whenever a birthday happened in my class. I started by writing the child’s new age on the big whiteboard: 11, or 12, or occasionally 13. Then I’d ask, “What can we say about the number —?”

Students responded in a variety of ways:

with cultural uses of the number. (“It’s a dozen!”) (“Some people think it’s unlucky, but they’re crazy…”)
with expressions that equaled the number: 3 x 4 = 12, or 14 plus -3 = 11, or much more complicated expressions coming out of our experience with Lloyd’s Game (described in the previous post.)
with a magic number sequence that started with the number and returned to the number.
with words that describe other properties of the number: it’s odd (or even); it’s prime (or composite); it’s a palindrome; it’s deficient or abundant or perfect.

These various statements, written on the whiteboard, both documented learning and provoked it. Although we focused on the same numbers again and again, the activity was repetitive only in the way ritual has to be repetitive: a pattern similar in every iteration, but never actually identical; a shared dance in which roles can change and change again; a bowl or basket or web for both familiarity and innovation.

If I forgot to include the number ritual in our celebration of someone’s birthday, or if we ran out of time before dismissal, the kids insisted that it be carried over to the next day. Remembering my students’ affection for the ritual, and remembering the way every student participated, I feel like I’m holding some important key to who they were, and are; something hard to put into words; a treasure.

For still more math fun, check out the YouTube channel of Vi Hart. Here’s a link to one of my favorites, the first in a sequence of three about plants and the Fibonacci sequence. “Ow!” one of my younger students said. “My head hurts! Play it again!”

More My Place

I’ve been tickled to have the posts about My Place get a steady trickle of hits from Australia, so I did some behind-the-scenes backtracking. In the process, I found a wonderful collection of material relating to Nadia Wheatley, with an author interview, curriculum plans, and reviews of some of her other books–and a link to my own post about My Place, down towards the bottom. Great stuff!

If I were teaching right now…

I would read aloud The Higher Power of Lucky, the first in a series of three novels about a girl named Lucky in a town named Hard Pan, in the Mojave Desert.

Living in a very small town, Lucky has memorable friendships with both kids and grown-ups. She eavesdrops on twelve-step anonymous meetings, hoping to hear the advice she needs. She hopes seriously for an afterlife, because there are some questions she would like to ask Charles Darwin. (She has a dog named HMS Beagle.) She’s cranky and impulsive and imperfect and worth a million dollars, and she’s part of a new sub-sub-genre of realistic contemporary fiction for young adults, in which characters think about biological evolution and what it means, and interact sympathetically with adults who can’t or won’t.

“If” thought # 2: I would figure out how a class could use the latest book by Alice Roberts, the charismatic anthropologist and medical doctor who narrates a BBC video series (which we did use in class) called The Incredible Human Journey.

Alice’s new book (we pretend to be on a first-name basis with her, in my household), published by Dorling Kindersley, is called Evolution: The Human Story. It uses narrative, model reconstructions, photographs, illustrations and charts, to take the print medium’s slower-paced (but thrilling) look at the history of our species, starting with the Big Bang. Such a rich resource for a class to use!

A third “if” thought: I would explore the idea of privacy, which matters a lot to 11- and 12-year-old people, and keeps coming up in the news.

Resolutions

One of my most faithful readers wants to know why I haven’t yet written about some teaching and learning that was central to my teaching life:

about the evolution of life in general, and about human evolution more particularly;
about animal behavior and archaeology and the history of technology;
about immigration, both chosen and involuntary, in the history of our country and our communities and families;
about Islam and the Arab world and the history of Arab Spain;
about The Voyage of the Mimi, both the first and the second;
and about the making of Voyage to the Sea.

Instead of writing about evolution, I guess, I’ve been evolving. (I know; I’m using the word in two of its different senses.) Somehow I’ve had to work up to those topics, and also work down with them. They’re all so huge for me, giant human artifacts around which I’ve spent all these years crawling, like an ant in the jungle, climbing up and looking around whenever I felt brave, or whenever a student was nudging me onward.

However, I’ve just made that list. I’ve included some of it sideways, in this mixed salad post. I’m pledging myself to figure out ways of exploring those giant thoughts in 1000 word packets, before my year to think it over is over.

I welcome, and probably need, suggestions from readers who shared those themes with me as student or parent or colleague or cheerleader. If you were writing this blog, how would you tackle all that big stuff? Just askin’.

In an activity so solitary (except for the joyful throng of co-conspirators in my memory), tiny encouragements from the rest of the world mean so much! A quick note in an email, a side comment in the aisles at Colella’s, a post on a website generated on the other side of the planet, devoted to a much-admired author–each of these remind me that I’m really doing this, and parts of it matter to other people. Some of you have recommended the blog, or a particular post, to friends and relatives and colleagues, or on Facebook; some of you have written comments on the blog itself, invariably thought-provoking, nudging me and lifting me forward. For all that…

Recently, my daughter has been sharing a website or movement called Lean In, which encourages women to lean into their ambitions, to overcome fears and take risks, with each others’ support. I take a big breath and “lean in” every time I publish one of these posts, and I’m inviting you to lean in with me, women and men (and girls and boys)–whatever that may mean for you.

Math Mentors and Math Games

Posted on December 23, 2013 by pollybrown2013

Early in my graduate education, I took a Lesley University summer school course about teaching mathematics, with a genuine, fresh-from-the-trenches middle school math teacher, Lloyd Beckett. Authentically–and contagiously–he had come to believe in the power of math conversation, and in the rich gifts students with different approaches could offer each other.

Lloyd’s course woke me up as a math teacher and as a mathematician. For years I had assumed that my relatively decent math grades rested completely on my ability to memorize. As it stood, that was largely true. When I did particularly well on one of the New York State Regents exams, my teacher, Augustus Askin, whom I adored, looked at me and said, “How did you do that?” Although I don’t think he suspected me of cheating, he had seen the puzzled look I often wore in math class.

Memorizing was okay for the test, but the effects never lasted very long. Real understanding, for me, required experiences that math class rarely offered–that I couldn’t even imagine math class offering.

On the other hand, in secret, generating that puzzled look, I’d spent years figuring out my own approaches. I could hold onto math concepts, and work with them comfortably, if I experienced them pictorially or concretely, or told stories about them. This was in a time, though, before math manipulatives, at least in my country schools, and before the wonderful math videos I was able to use with my own students, decades later.

There were exceptions. A little girl for whom I babysat had one of those balance toys with numbers weighted to add or subtract properly. If you hung a 5 and a 2 on one side, and a 7 on the other, the balance came to rest with the pointer in the right place to mean yes.

Here’s a sample of a similar balance still on sale.

$math Plastic-Bear-Shaped-Digital-Balance$

Other, purer versions make more sense for older kids, but I spent a lot of time playing with that balance, savoring it. It was what I needed.

I’m also stubborn, and I hated subtracting. All on my own, with no support from the rote-memory approach in school, I had figured out a way of subtracting by adding, doing a sort of mental algebra: what plus 5 will equal 7? Or what plus 9 will equal 17?

In my earnest little heart, though, I suspected that I was cheating. I thought I was making up for not being good at math.

Years later, when I spoke with parents at math curriculum nights, I sometimes called myself a “born-again mathematician.” Teaching math with new math tools and toys and approaches, and with new respect for many kinds of math minds, I found that I loved math, respected my own math learning style, and got a huge kick out of helping all sorts of kids come to understand new math ideas and feel new math power.

That marked me for life, evidently. In my current pause from teaching, any time a math idea sails into my day, I grin and go with it. So, for any of you who feel math deprived, just through the holiday, or in your everyday life, I offer a few math games.

The first two aren’t really games, just reflexes.

When I tear myself out of whatever book I’m reading, I play with the page number as I walk away. 139. Hmmmm: is that prime? It might be, since none of the proper factors of 100 overlap with the factors of 39…

When someone in our family has a birthday, I figure out the prime factorization of the new age. My father recently turned 92. Let’s see: 2 x 46, or 2 x 2 x 23. Suddenly I feel, inside the 92, an 80 (4×20) and a 12 (4×3). Oooh, cool.

Last year, my daughter’s children were both prime, 3 and 7. As of a few days ago, they are both powers of 2, having turned 4 and 8 (or 2×2, and 2x2x2.) Abe is now twice as old as Julia, and that will never happen again.

What official-sounding thing can we call this? A mathematical storytelling impulse? It works for me.

But other things can work, too. I’ll never forget the day my kids and I stopped by Kate Keller’s house for a quick visit, and learned now to play Set, from watching her play it–because she refused to tell us the rules. Obsessed, we came home and made our own version out of file cards. Later on, watching my students play Set was like giving them a diagnostic test. Some kids were quicksilver zippy at Set, and slow at everything else that happened in class. Some kids were slow, as I am, but warmed up as they went along. Clues, clues. And hilarious fun: in math choice times, I had to limit the number of kids who could play Set together, because that corner would get so loud.

This is not a Set:

Neither is this:

But this is:

and this is:

…and this is a particularly delicious Set:

To learn more, you could track down Kate Keller, my all-time-most-important math mentor, who has more fun with math than anyone else I know. She also perceives and nurtures students’ math individuality with something I can only call math compassion, a power almost magical.

Or follow this link to the Set Wikipedia entry; it’s fascinating! There are ways to play Set online now, too–a discovery that could sharply curtail my future productivity.

Finally, Lloyd’s Game. Of course, he probably called it something else. I’ve sometimes imagined Lloyd just up and quitting when one of his best whole class math games no longer worked. 1999 was a great year for this game, but the very next year, 2000, was hopeless.

In Lloyd’s Game, you have access only to the digits in the Gregorian calendar’s count for a given year. You combine those with math symbols (no quota on those) to create expressions equaling the numbers from 1 to 100. You must use all four digits in each expression, and you may not use two-digit numbers made from combinations of digits (although I remember resorting to that a few times when nothing else worked.)

Generally, in class, we used the new year’s digits to create the numbers of the days in January, catching up with a burst of activity when we came back from the holiday break or weekends, but mostly targeting each number as it came up, day by day. We used the basic operation symbols, + — × and ÷, along with parentheses, the fraction bar, the square root symbol, and the exclamation point meaning factorial. We were allowed to use a number as an exponent, so 1 to the 9th power was an excellent way to dispose of a superfluous 9.

Here are two examples, using 1989:

The best fun came in class, as we compared multiple ways of arriving at the same target number. Gradually, as January progressed, we watched and cheered breakthroughs for kids who had initially feared the game’s challenge.

Here are three ways of making 5, from one of the posters we hung up around the room, again from working with 1989:

After 2000, a flop for obvious reasons, we sometimes used the year in which the largest number of kids in the class had been born. Sometimes I chose numbers relating to our themes: the year Charles Darwin was born, the year the Blackstone Canal was first opened, etc.

Try it out, alone or with some pals. You can use the birth year of your favorite politician—they’re all still creations of that wonderful (for this purpose) century past.

In any case, life is short. Go ahead and feel human. Play with math while you can!

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a year to think it over