Transportation Projects

transportation projects comparing human-powered wheeled edit2When I think about transportation projects, I remember Kate Keller rounding up approximately a million human-powered wheeled vehicles, so we could try them and compare them and consider the relationship between function and design.

transportation projects humanpowered wheeled wagon and office chair

Transportation involves the movement of people or goods, so these small human-powered examples count, even when powered by very small humans. (See below.)

transportation projects design and function notes cropped

Why do wheels help so much, when we need to move things (or ourselves)? What design modifications help a wheel work well? What about handles? What about the way the weight of the goods is balanced?

transportation projects humanpowered wheeled chartmaking cropped

Kids had time to think about all these questions as they were actively trying out several vehicles at each station, comparing wheelbarrows and garden carts, or several kinds of strollers, dollies for working under cars, wheeled suitcases, even wheeled desk chairs. Then they had time to think about what they were noticing, and add to their notes or charts, before rotating to their next station.

In this activity, unlike some projects time set-ups, everybody tried everything. We would not have been forgiven by the people who didn’t get to try the scooter. Also, we wanted to avoid any suggestion of girl stuff and boy stuff.

transportation projects human-powered wheeled b edt

When I think of transportation projects, I’m bound to think of this photograph of Troy, experiencing the enhanced mobility provided by his very first car, in the form of a paper plate.transportation projects village simulation hWe added cars in the third round of a simulation of the relationship between transportation and trade, usually referred to as “the villages.” A Touchstone alum turned transportation planner (my son, Colby Brown) heard that we’d gotten a grant to develop curriculum about transportation. He said, “You have to do this Touchstone style. You have to model the interactions with a simulation on the playground.”

transportation projects village simulation a editSo Kate Keller, resident genius at translating complex concepts into compelling experience, designed a simulation in which students pretended to live and survive the seasons in three villages, widely spaced on our school grounds–under the gazebo out front, at the back of the rear playing field, and at the bottom of the slide. transportation projects village simulation b edit2

Kate put special care into making sure that none of the villages could be seen from the others, so transportation was also the only route for communication, true to most of human history. In order to conduct a trade, the traders had to travel. transportation projects village simulation c edit

We imagined each village having its own geography–mountains, woods, or a lake in the form of the playing field, which students pretended to cross by pulling saucer-sled boats.

Each geography had its own resources to offer in trade, for example cattails from the lakeside, wood from the forests, or cloth woven from the wool of mountain-tolerant sheep. At first, the villagerstransportation projects village simulation d edit had nothing but their own bodies to carry their goods, but in the second round each group had some additional transportation, such as a wheelbarrow.

Here’s one student’s writing, evaluating how that day’s experience had worked:

transportation projects village simulation eI kept the little note at the side, saying that trading was interesting, because that was such an understatement. The students were wildly excited about trading. In one debriefing conversation, a student said, “It’s hard to take part in the simulation and learn as an observer at the same time, because I get so excited about the trading.”

Looking back, I appreciate more than ever the engagement and thoughtfulness, the serious playfulness at its best, that gave rise to such astute observations about what we were asking students to do. I appreciate also the ways students supported each other in being both participants and researchers, reminding each other of our questions: What impact did the transportation have on the trading? What impact did the need for trade have on the need for transportation?

Village culture evolved very quickly, so magic stones and medicinal pieces of bark were also traded, and one student, writing up the day’s events, wrote as the History Keeper

transportation projects village simulation history keeper edit In the third round, after class discussion about where to take our simulation next, we introduced transportation that involved motors–individual private cars, a toll bridge, and a train route in the tunnel through the mountain of the school. As it played out, students were surprised at the expense of private transportation, at least in this simulation. In one of the replays of the curriculum in later years, a student yelled in exasperation, “This car is making me go broke!”

It’s torture to leave out everything I’m having to leave out. I want to describe just one more of our transportation projects. Later in the unit, we split into groups working parallel and reporting to each other–about transportation access issues, or about what it’s like to make a transportation plan. For example, one group designed a bike path from West Upton village to our school.

transportation projects 140 plan editAnother planned several bus routes. No bus could pick up all our students, from the many towns in which they lived. But when we had mapped all our own class member locations, at the beginning of the year, Kate and I had noticed how many families lived near the state highway very close to the school. The bus route planning group spent a lot of time with maps on which they located all the school families involved in the clustering we had noticed. They made two lists, the one I’ve shown, and another of families who lived south and east of the school, in Milford and Hopkinton. Then they designed routes.

transportation projects 140 plan b editOne of the students pointed out that parents might or might not be willing to let their children ride a bus, even a school-sponsored bus. She might have heard about the parent-organized bus to Worcester that ran for a few years, with continual difficulties around poor communication. So she designed the questionnaire to the right.

transportation projects 140 plan cThe bus route planning group had several final products to share, including maps made on Topo software, annotated with the proposed routes, and an article which ran in the school newsletter.

transportation projects 140 plan d

Although the bus routes never did materialize, those Very Young Transportation Demand Forecasters had learned lessons almost impossible with anything less connected to their own experience.

That was true, of course, of the whole deal. In the next post I want to write about the transportation field trips, giant projects time sessions on many kinds of wheels.

Two extra notes:

#1  This post is the third in a series. The first post in this series about Projects Time describes some logistics, considers the social benefits of this format for hands-on inquiry, and takes a flyover of a typical afternoon of outdoor projects. The second compares accountability and responsibility in the context of Projects Time.

#2 Our hands-on explorations of the physics, history, public policy issues and fun of getting from here to there were the Projects Time side of a curriculum called Transportation Choices, which Kate Keller and I developed with the help of funds from the U.S. Dept of Transportation, administered by the University Transportation Center at Assumption College in Worcester.

One of several university transportation centers throughout the country, the Assumption center focused specifically on K-12 learning about transportation and the environment. When the center closed, its website documentation of the various curricula developed by grantees disappeared from public view–but I’ve saved most of what Kate and I produced to record and evaluate our own work, including curriculum plans and maps and a bibliography. I was able to return to that material and use it in subsequent explorations of the transportation theme.

I’ve written elsewhere about Kate Keller’s gift for developing hands-on developmentally-appropriate activities about complicated ideas. You can find more here.

Who Sits Where, or Ahhhhhhhhh-yippeeeeeeeee!

Image

“I’ll tell you the truth,” he said. “If I don’t know the person I’m sitting near–especially if it’s a guy–I keep having the impulse to punch him. It’s hard to pay attention to anything else.”

There it is, laid out as clearly as possible, as only a kid could. He might have felt this unusually vividly, and expressed it to me, one-on-one, unusually straightforwardly. Still, there was some element of his feeling in many of his classmates. Students prefer to be seated near other students they know. Left to their own devices, most kids aren’t particularly eager to reach out to unfamiliar people.

Hooray for the minority who do reach out in friendship, and the huge gift they give to the group! Still, most kids need help with that.

Class life should give them that help. Here’s a corollary of my student’s statement. Students need to get to know the other members of a new class fairly quickly, so they’re not each sitting in the wanting-to-punch-someone condition (or some individual variation of that.) The teacher’s structuring of the situation needs to support kids in creating social inclusiveness, mutual knowledge, and safety, so that other good things can happen, things like learning how to divide fractions, or when to use there, they’re, and their–or the history of immigration policy, which is all about exclusion and inclusion.

Ideally, a teacher works gently and carefully with whatever social chemistry she or he finds, to create a productive balance of secure familiarity and growth-nurturing newness, for every student.

Among the faculty of my small school, all of whom I respected, there were real differences of opinion about how to work this out. Different routines are appropriate at different ages; different strategies work for different teachers’ styles.

Beginning the year

My young adolescent students (aged ten to twelve) spent a lot of their day moving around. Still, their table places were very important to them.

reading at tables

Before the first day of school, I made a temporary seating chart, and signs to put at students’ places. Kids would be seated at tables that held four students, and this usually worked out to be three or four at each table. (Longer ago, these were desk clusters with about the same number of desks in each cluster.)

Before I made this temporary arrangement, I talked with the teachers who were sending kids on to me. I always felt grateful for the help this gave me. I didn’t want the job of inclusion to fall to just a few generous kids. I tried to avoid giving hard jobs to kids with challenged attention, or to kids with sensory integration issues who might be thrown off by classmates brushing against their chairs. I thought carefully about how to handle kids with desperate crushes. (“Please,” a girl said to me when she ran into me over the summer, “don’t put me where I’m looking directly at _____, ” She knew herself, and knew what I needed to do for her.)

I tried to build in unfamiliarity along with familiarity. For example, I wouldn’t put three close friends at the same table–not good for them, not good for the group. I wanted everyone to have some safety, and some reaching to do.

projects time group with plantsAs the year moved forward, the groupings for academic work often built social connections. For example, projects time groupings were generated by kids’ choices of the various activities, expressed in rankings on sticky notes (which I could easily move around to arrange the groups.) It’s a tribute to the social education of my students before they reached me, that they could almost always handle this. For two afternoons a week, they could work in a small group with anyone, and make it productive. It was enough to have shared interest in a topic and a hands-on activity, with a little support from me or from a parent volunteer.

Very often, new friendships came out of these projects time pairings or groupings–if not close over-each-other’s-houses-frequently friendships, at least I’ll-put-this-person-on-my-list friendships.

The list

About a month into the year, sometimes less and sometimes more, I followed the seat assignment ritual I had learned from Kate Keller.

First we talked about the guidelines:

  • List at least two people of each gender. It’s fine to list more than two.
  • It’s okay to say “any boy” or “any girl” but you have to mean it, and that will count as meeting your conditions.
  • You can’t say “any girl (or boy) except _______.”
  • It’s fine to say “anybody.”

Kids wrote their preferences on 3 by 5 cards, with their names at the top. I learned that I needed to talk about anyone who was absent, so the card-writing kids wouldn’t forget about that person. It was helpful, especially early in the year, to have all the class names visible. Students folded the file cards and brought them to me, and I treated them as if they were top secret files from the CIA.

On the same cards, kids could also write requests involving placement in the room. I tried to honor those requests, if I could, since I wanted to encourage the self-knowledge that often went into them.  I explained ahead of time, though, that I couldn’t make promises, because good social mixing had to stay my main priority.

I promised just this: to give each student one person from his or her list, seated nearby. One safe presence.

That was hard enough to do, sometimes–to make all those interlocking choices work out. Usually, I started making the arrangement by placing kids who were least chosen by the others, or those who weren’t chosen by people they’d chosen themselves. They needed support, and this was one way I could give it.

One year, by the end of the year, every single file card said “anybody.” Thrilled and impressed, I threw them an ice cream party over the summer to express my high regard.

A sociologist could write a book about how these table-mate choices evolved through the year, with a chapter about how friendly, undemanding students tended to be chosen by almost everyone, time after time, and another chapter about how a child working hard to enter what he perceived as a popular group would fail to list any of the ordinary kids who had listed him and might treat him better. We don’t come automatically equipped with social skills for classroom life; we have to learn them, together, with some detours and lots of support. The information on the cards helped me know where support was needed.

Occasionally, a student thought she was designing the table group of her dreams, and reacted with shock when she didn’t get all of the people she had listed.

How to avoid any open expression of shock or dismay:

This sounds goofy, but it helped. Before I announced the seat assignments, or projects time groups, or any situation in which kids were placed in groups (almost always with their input) we went through the Ah Yippee ritual. This is very hard to describe in words. If you’re lucky enough to know a student from the past ten years, he or she may be willing to demonstrate, but it’s pretty silly.

Following a hand signal, we all said Ahhhhhhhhhhhh Yippppppppeeeeee! (Do you know what I’d give for a tiny video of this?) The collective tone swooped around, down and then back up. In the process, each child expressed his or her disappointment and excitement about the grouping–before knowing it.

Why in advance, before they knew? So the actual groupmates, or others not in a welcomed group, wouldn’t feel dissed.

We switched table places four or five times through the course of the year. Meanwhile, there were more frequent switches of math partners and projects time partners. All this in addition to various group-building activities I’ll describe another time. They helped, too–but my best chances at constructive social engineering were mostly under the students’ radar, in careful decisions about who sat where, and who partnered whom.

One way and another, there were lots of opportunities to decide that the unknown person you thought you wanted to punch might actually be someone you could trust and enjoy.

Hooray for the everyday bravery of kids in classroom life! Hooray for all the rewards it brings them!

Journeys, again

Last month I wrote about the Journey of Man thematic study, looking at the routes used by our species, Homo sapiens sapiens, as they colonized all the world’s land except Antarctica. Recently I was thrilled to find a cache of student work samples from the first year of that study.

It’s timely. Over the next few weeks, some of the kids from that first Journey of Man class will graduate from college. They’re dancing in their last undergraduate dance concerts; giving senior voice recitals; helping younger students prepare to take over the leadership of campus organizations; getting ready to go off and be teachers themselves.

All of you from that class, wherever you are in your journeys, should have that buzzy feeling that says someone is thinking of you, because my mind has been full of the journeys I watched you make, from question to question, draft to draft, project to project.

Although I’m in touch with some of you, I’m not sure how to find others. So I’m going to hide names and identify you, if at all, only by first initial.  I’m assembling these samples out of the impact of the whole stack, in which I read every word. So in some sense all of you are reflected here.

JOM evidence stack

Over the summer before we started this study, I asked students to find and read a book related to the journeys we would be examining: the evolution of hominin species over millions of years; the travels of modern humans colonizing the globe; and the immigrant journeys that populated New England. Students could choose books relating to any of these topics, and I asked them to copy a passage that had been particularly meaningful for them.

Many students read about relatively recent immigration. Here’s one student’s heartbreaking choice of passage, from Ellis Island: Gateway to the New World by Leonard Everett Fisher:

JOM passage from Ellis Island bk editJOM copied passage geneticsI had offered genetics as a possible book topic, knowing that we’d be doing a side-trip into some learning about genes. We needed that to help us understand the role of Y chromosome genetics in the book by Spencer Wells from which we had borrowed our thematic study’s name, The Journey of Man. One student read Why Are People Different? from Usborne Publishing, and copied a fascinating passage.

 

JOM copied passage evolution

One faJOM copied passage evolution p2mily found a beautiful picture book about evolution, Our Family Tree: an Evolution Story by Lisa Westberg Peters. It’s become one of my favorite nonfiction books for people of any age,

I’ve scanned both the copied passage and the student’s explanation for why she chose that book.

 

Other students jumped right into paleoanthropology. The passage below came from The Origins of Man, by John Napier.

JOM copied passage origins editReading through these, child by child, I am so moved by what grabbed them, when they were just sampling our topics to create an overview for each other. All four of those kids, J, J, S, and J, were drawn to story interpreting evidence–historical evidence, evidence from biological research, evidence from paleoanthropology and archaeology–all of it warmed and made coherent by a little bit of storytelling.

The first part of our exploration, about the evolution of species increasingly like us, focused on the first time clap, which I’ve already described. Here’s one student’s species sign, scanned to show the directions on the back.

JOM Homo erectus directions

I love that two word direction at the bottom, probably written by one of the students who carried copies of the sign. Those two short words take sides in a controversy still not fully settled by the interested scientists. Clearly we decided, for the purpose of the time clap, that Homo erectus really was able to control fire and use it at will–and that the dramatic growth of brain volume in Homo erectus fossil skulls indicates something revolutionary: cooked food. (You can watch this video to hear some of the evidence.)

Once we turned to the voyages of early modern humans, we were all grateful for Spencer Wells’s own effort to give his genetic evidence a human face and a story line:

JOM hunting with San

JOM target practice with SanJOM Spencer learning P editLike some of the other pieces I’ll include, these were quick pieces of writing done overnight for homework, in response to an open-ended invitation to write about something that stood out for each student. They had a word limit–probably no more than 60 words, judging from the ones that show a word count. Sometimes pairs or small groups of students shared what they had written; sometimes volunteers read theirs out loud to the full class, as a preparation for watching the next chunk of video.

Much of The Journey of Man is based on genetic evidence involving the Y chromosome. We did some other work to help us understand this, isolating DNA with help from parent volunteers, making models, reading other books. But all the kids were really taken with Spencer’s own treatment, using monkey oranges to lay out a big graphic on the ground near the San Bushmen camp.

JOM monkey oranges R editThe crosses indicate a second mutation; so R’s diagram would have been even better if he’d shown that second mutation happening in an individual who had already inherited a first one. Overall, though, he showed real understanding, and like so many Touchstone students, he didn’t hesitate to critique and appreciate Spencer’s teaching technique!

How did I handle informational errors in this kind of writing? Case by case. Sometimes I talked with the individual kid, or wrote a comment (which I’m cropping out here, mostly.) Often, I let signs of widespread confusion guide what steps the whole group would take next.

I found one page I’d written when I was disappointed with an activity,  brainstorming and evaluating ways we could approach the material differently. After all, I wasn’t doing this to grade students on their various levels of understanding; I was aiming for the greatest possible understanding by everyone–and all of us were being pioneers, including me.

Sometimes I asked kids to write about what they thought, before we watched the video or explored the evidence:

JOM ice bridge A editClearly this student had heard about ice bridges as a part of human migration from one continent to another. But as a way to get from Africa to Australia, an ice bridge couldn’t really work, and he realized that as we moved forward. Later he wrote again:

JOM to Australia new idea Here, K argues for her version using a terrific sketch map:

JOM Africa to Australia with map

JOM time clap 2  plan sheetI’ve already shared some artifacts from the second time clap, in which we worked intensively with material in the book version of The Journey of Man,  to recreate early modern humans’ routes from continent to continent. For all of us, I think, when we say “time claps” we’re remembering that one, because it was so intense. Finding additional materials from that second time clap, I was thrilled by evidence for what I had remembered, that kids themselves did most of the organizing and preparation. So, to the left here’s a planning sheet that is pretty difficult to decipher if you’re not one of the kids at work on the plan. (I know that the numbers refer to Y-chromosome mutations, and that the colors refer to colors of streamers carried on the routes.)

Here’s one student’s individual sheet, to help her know what to do when:

JOM time clap 2 indiv sheet editThe learning spiraled; it was cumulative. We reviewed in a variety of ways, acted things out in a variety of ways, made obnoxious comments about guest scientists having bad hair days, and reached a point of intimacy with the material that was extraordinary, given its challenges.

No Unit Test. Instead, kids wrote final pieces that we revised to a pretty good polish. Here’s part of one:JOM final essay E first paragraphs

Later, we carried these ideas into the work we did in the spring, thinking about the history of human technology and the evidence of archaeology, in connection with The Second Voyage of the Mimi.

Nothing I’ve ever learned about has fascinated me more than this big picture view of human history, and I couldn’t have had better learning companions. Writing about it, organizing my own artifacts, I’ve started rewatching videos, reading books and blogs. I’m excited by new evidence, and also by new attempts to convey the story as a story.

I’ve also been struggling to understand online blogs and comments written by people who dismiss the Out of Africa evidence, for reasons that often seem transparently racist.

At any moment, on my bicycle, folding laundry, driving to the other end of the state, I’m liable to be thinking:

  • How did we get from Africa to Australia as lickety-split as the genetic and archaeological evidence indicates–not just traveling but colonizing? Just what role did bamboo rafts play? Is there any way I could wrangle myself an opportunity to make a bamboo raft?
  • And what about the evidence that even Homo erectus, much longer ago, used some kind of transport across water?
  • But also: what can be done to heal the increasing polarization between people who are excited by scientific evidence–even when it’s confusing or contradictory–and people who are threatened by it? How will my past students navigate that crossfire?

Ultimately, for me, this is the question: How can we build and share a new evidence-based story of our origins? Part of the answer, of course, as always: together.

Time Claps, Part II

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.

across the continents time clap croppedWe 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.

folded timeclap section

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.

JOM map detail

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

JOM map key cropped

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 croppedThis 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 streamerI’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

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 croppedIn 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.

hominid time line detail 2

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:

time clap notes 4The 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:

time clap notesFive 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.

JOM timeclap 1 timeline detail edit

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

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:

Chrissy projects timeChrissy with two heads

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:

immigration ancestor pie Aaron

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, thoughand later, when it was a choicewe 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.immigration ancestor pie Ben

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.

Afterthoughts, Afterlinks, Resolutions, and Thanks

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:

goofygraphics2013I 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!”

vihartfib

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.

higherpowerofluckyb

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.

alicerobertsevolutionbAlice’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…

goofygraphicsthanksRecently, 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

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…

thinkingabout139 cropped

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:

not set aNeither is this:

not set b

But this is:

set c croppedand this is:

set a…and this is a particularly delicious Set:

set bTo 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:

Lloydgame27and2 cropped

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:

LloydGame cropped

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!

In Praise of Colleagues

When I reread my last post, it hit me like a ton of bricks: I had left out something important. It’s easy to overlook something so pervasive that you come to take it for granted. My mother goes to a new doctor, and forgets to mention the mobility and visual impairments that define so much of her present life (along with her continuing eagerness and whimsy.) I write about resources for understanding student writers, and don’t actually mention the sturdiest resource of all–my peers.

After school, teachers gather in each others’ rooms and talk shop. Not every day—there are a few other things to get done: meetings and parent conferences to attend, notes to write on the whiteboards, math manipulatives to locate, photocopies to make, plain old ordinary messes to clean. Still, at the end of the afternoon, for many grateful years I could go stand in Susan Doty’s doorway. ‟Help!” I could yelp. ‟What’s going on with this kid? Why is he so afraid of writing?” I knew she would stop and think carefully about her answer, giving me the same kindness she gave children.

farmer in Crete croppedWhen Marian Hazard taught her own class, before she became the school’s garden wizard, she would wander down to my room and share insights provoked by the most recent book she was reading, about how to help children move forward as thinkers and writers. She often had more patience than me, for reading about education, and, later, for the work of cultivating both plants and gardeners. I gained, always, from sharing what she discovered.

For a while, Kate Keller taught in a room very near my room. When she was trying to describe a breakthrough in the writing of one of her students, she could easily invite me across the hall and produce evidence. ‟Look!” she would say, pulling a file from a pile of folders. ‟Can you believe this?”

four potsOur endeavor, in teaching writing, and in all things: to meet kids where they were, to travel with them as far as they could travel, to help them recognize and celebrate triumphs, and then move forward again—all that was collaborative, in a way not necessarily visible to students or parents.

A thriving faculty conversation is a living thing, like yeast in good bread dough. Over the years I came to see how hard it must be, how delicate, for a principal or head of school to trust and support and strengthen that conversation–and how essential.

three gourdsI also learned that I had to nourish myself, because any individual teacher has to punt, again and again. On the September day when I guided a new class through their first writing fluency exercise, and one child sat in her place at one of the tables and wept for the entire five minutes, and beyond, while everyone else counted the words they’d just written—on that day, like most teachers most of the time, I was the only adult in the room. The student had only recently entered my school; nobody knew her well. So she and I shared something: both of us were stumped. I wasn’t just stumped; I felt awful.

I didn’t scold, since I knew that she was doing the best she could. We talked briefly in the privacy of the hallway. I told her that I wasn’t worried. (I lied.) I told her what was true: that I would ask her to do the same thing again the next day—to brainstorm ideas, to choose one, to write for that little chunk of time that I knew could feel like forever. She would have another chance to try.

redblue turtleI also told her that she could do what I’d done in college: write about why she couldn’t write. If she had to—and she wouldn’t be the first to resort to this at least once—she could write one word again and again, until the second word came to her, and the third.

The next day she did brainstorm and choose; she did write. Not a lot, but some, and that was all the exercise asked for. She went on, that year, to write some pieces that took my breath away. ‟Look!” I said, to whatever colleague I shanghaied that afternoon. ‟Can you believe this?”

I’m telling this story, before I really describe that exercise (next time, probably), because I don’t think there’s any guaranteed approach, exercise, bypass strategy, or technological support for writing difficulties–and because, in my experience, the best source of wisdom, the best source of quality control, came from my fellow teachers. Also the best source of energy to keep going.

Knowing the results of testing or external observation can help, but parents and teachers both can easily make too much of such things. We need to know, by asking the child and by intuiting with all our senses, what challenges a child faces; we also need to offer the bypass strategies that can help. Ultimately, though, we have to do the same basic thing again and again: ask a child to keep trying, and give her credit for everything it takes to try.

I loved my school and my colleagues because our support for each other, so consistently, was support for our highest mission. We supported each other not by blaming the child—even though that’s sadly common in situations in which teachers are hard-pressed (and teachers tend to be hard-pressed.)

pinecone with mushrooms croppedWhen Julie Olsen, having seen me in the hall with a student, asked what was going on, she wasn’t looking for a chance to commiserate about those awful kids we were stuck with. If she knew the child, she always helped me see the world of the classroom from that child’s point of view. If she didn’t know the child, she asked questions that would help organize whatever I’d been able to observe. She laughed her wonderful raucous laugh with a particular twist that acknowledged the profound challenge of teaching—but it was never a laugh at a kid’s expense.

The colleagues I’ve named taught near me, literally or in the sequence of the school’s groupings, for many years. Others, not named here, taught older or younger children in other corners of the school, and helped me understand where my students were coming from, and where they were headed.

We supported each other by honoring each others’ efforts to know each child; by holding firm, together, on the issue of class size, so that knowing the individual child was possible; and by understanding, always, for each other, that all our hearts were doing hard work.

Last but never least, in moments grabbed from the ongoing intensity of our lives, we cheered each other on by sharing our euphoria about progress. I could not have asked for more.

wire sculptures narrowerThe sketches are in thanks and praise for another teacher, Marjorie Weed, who came to volunteer at Touchstone after a long career as a public high school art teacher. She helped me encourage my students as creators and composers, by working with them herself, while I watched and learned along. Mrs. Weed inspired me to give kids time for sketching during our settling time, almost every morning. I was her “oldest and most improved student,” one of many who still value her influence.

Hummanacrafts and the spirit of invention

It’s not some fictitious contraption. The drawing below, made by Justin McCarthy sometime in the fall of 1990, advertises something real. It represents a retooling, a chopping and channeling, of a small paperboard tray, the kind in which take-out french fries used to be served. It’s a design for a hummanacraft, a vehicle that could hover gracefully, thrillingly, along the updraft  from our classroom air vent.

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That classroom’s air intake occupied a shallow metal box under the windows along the outer wall, like an over-sized radiator. The grated vent on the top, about 6 inches wide and 6 feet long, worked perfectly for hummanacrafts.

What gave the hummanacrafts direction along the vent? What kept them from just getting blown off?

Justin now lives in California and works as an engineer, a developer of ideas. If you knew him in his hummanacraft phase, you are not surprised. Colby Brown, another hummanacrafter, grew up to be a transportation planning technologist—obviously as a result of this early influence. Recently, Colby heard the word “hummanacrafts” and had a lot to say.

We’d cut one of the short flaps of the little tray, and bend it up or remove it. The air flowing out that end, the back, propelled the craft forward. The front end just barely touched the top surface of the vent, and that provided stability.

Colby went on to remind me that this particular class had operated as a design workshop for years. For example, several years before the hummanacraft phase (and before organized paper recycling) members of the class had engineered long cardboard chutes to carry crumpled waste paper to the wastebasket.

That group of students were entrepreneurs, also, with a thriving economy on the playground, buying and selling real estate, using all sorts of natural objects as currency. (Kate and I had to ban the indoor stockpiling of pine cone currency in paper bags under desks, because they got buggy.)

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Not everything these kids made involved a cash exchange. Colby made and gave as gifts a whole series of ducks carrying marbles. (Nobody remembers why.)

The hummanacrafts fit into a proud tradition.

I’m pretty sure the kids first invented hummanacrafts with Kate, in the mornings. She would have been the one to ask, ‟What if you make the vent flap smaller?” Or ‟What if you add some weight?”

Justin and Colby were both talkers. Some of their classmates weren’t, at least not in the same way. Watching the evolution of the hummanacrafts in all their hands, listening to their explanations, triggered my first deep awareness that some kids make a lot more sense in motion. I’d read Howard Gardner. I knew, from the experience of my own family, that there are many kinds of intelligence. But hummanacrafts, crazy little paperboard crafts for imaginary drivers the size of mice, convinced me, to the soles of my feet and the outer margins of my plan book, that kids could be smart in ways that had nothing to do with my own.

In fact, some of my students, I saw, would do their best work only if I arranged (or permitted) the sort of learning experience that might have terrified me, or at least intimidated me, when I was a student myself.

And that was the beginning of many stories.

Hooray for hummanacrafts! Hooray for their engineers and operators! Hooray for many things slightly illegal, happening off on the edges of classrooms; things that can teach the teacher, if she’s lucky. (And I was.)

I’m going to try again to get other people to commit themselves in writing. (It’s free, after all, and it can be really short.) (Or long, too.) Did you ever invent or create something on the edges of  classroom culture? What was it? And–I always want to know this: then what happened?