Monday, 31 July 2017

ways of knowing: math by hand








































There are ways of knowing.

There are ways of knowing that bypass, if not the brain, then at least the logical, linear, linguistic parts of the brain. There are ways of knowing things with your hands. There are ways of demonstrating ideas because you can use them, or do them, or at least make a model of them.


A crocheted mathematical model of a coral reef.
crochetcoralreef.org





















There are women who make models of coral by crocheting  [Margaret and Christine Wertheim, The Coral Reef Project]. They are able to demonstrate that in the seemingly-random shapes of coral, there is logic. There is order. There is an unwritable formula. In the organic, frilly shapes of corals are embedded straight lines. And they can prove it because they can make it with their hands, manipulate it, fold it, and hold it up or hand it over for anybody else to experience. To my understanding, nobody has been able to reduce this geometry to an equation; although they can reduce it to a pattern. (Eg. “Crochet three, increase one.”)

There is truth in the things we can make and demonstrate with our hands, even if we can’t reduce it to a formula.

As Margaret Wertheim, co-founder of the Coral Reef Project, says: “I can see it. I can feel it. I can touch it. I can play with it.” We can "literally, physically play with ideas.”

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There are ways of knowing.


Ron Eglash. Drawing of the plan of a Ba-Ila village in Africa,
created using fractal geometry.


























There are villagers all over Africa who build their villages in fractal patterns ; not the same fractal pattern, but many different ones across the continent [Ron Eglash, Rensselaer Polytechnic Institute]. I don’t pretend to understand the math or the science of fractals, but I know it refers to a geometry which replicates the same shape at different scales, ad infinitum. Without equations or labels or formulae, Africans have been building communities using fractal geometry for centuries; expressing their social structures and embedding their myths in their architecture. There is a non-hierarchical way of knowing the world which is reflected in how they order their communities.

There are parts of their processes that are quite possibly the earliest visual representations of binary code. (I don’t begin to understand.)

There is even self-organizing (fractal) design in their play.

There are ways of knowing.

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A Mancala board with "stones."
























When I was a kid, I used to love to play this African game we called “Kai”. I now know it has many names, most commonly "Mancala." It’s a game played with a carved wooden board and marbles. Or stones. Or shells. Or even seeds. There are many versions of how to play Mancala; we played a game closely resembling this one. [Michael; Kasao, Ghana]

What I loved about the game was the way the pebbles felt in my hands. The dropping of them one by one has a tangibility and a logic and a rhythm of its own (one-to-one correspondence). The heft of a handful of pebbles, the gradual diminishment as you repeatedly subtract one from the handful (subtraction as loss, as “less;” division as repeated subtraction), the gradual addition to each well on the board, the estimation or mental math of knowing how many pebbles are in each well as they change throughout the play (subitizing, number sense). It may have been Math but it was a Math I understood with my hands. No equations or formulae. No pencil or paper. Just doing it. Just replicating a pattern or formula or a simple set of rules, over and over again.


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A few years ago, I bought a couple of Mancala boards for my first grade classroom, but the pebbles quickly got lost or used for other activities, the boards got used for sorting trays, and — for one reason or another — it fell off my agenda. I’m wondering now if that was a missed opportunity. And I’m wondering: if I made a Mancala board out of an egg carton — and cut it down to ten wells instead of the traditional twelve, and put five stones in each well…. Now the kids would be playing Mancala in a ten frame. And if we decided that five stones in a well was the number you had to have to “capture” the stones, then we would be working with the numbers that are the basis of our number system and our curriculum. And our hands. (Five fingers per hand, ten in all.)

And it would be like planting seeds. A simple, everyday, organic, radical way of knowing. With our hands.



Saturday, 8 April 2017

the butterfly whisperers....

























Every year around this time, I order my butterflies.

The butterflies arrive as tiny caterpillars with jars in which to put a little food (which comes in the package) and one caterpillar. These jars will be their homes until they go into chrysalises. Then they will be transferred to the butterfly box where we will wait for them to emerge fully-winged. We watch them in there for about a week, and then release them outside. (We get Painted Lady butterflies. They are native to this part of the world and many, many others. Monarchs do not like our northern climate, and we are not on their migratory flight paths.)

I could tell you lots more about how to raise the butterflies, but it's all in the package when you order them. I usually order mine from Boreal Science in Canada, but google "butterfly kit" and do your own search. There are lots of people who sell them these days. Similarly, there are LOTS of good materials on Teachers Pay Teachers -- just search "Painted Lady Butterflies." My favourite thing is called "My Painted Lady Observation Journal" by Smart Chick Teaching Resources. It's simple to use and flexible. In Grade One in Alberta, Canada we are not required to teach life cycles, but of course you can't not do it, when these little miracles are happening in your room each day. The real emphasis, though, is on watching living creatures grow, and on finding out that even butterflies need food, shelter, water, space, etc.

[There are scads of books -- fiction and non-fiction to support this learning and extend it into the Language Arts. I often use this moment in the school year, to review and teach the kids to read the days of the week, using The Very Hungry Caterpillar by Eric Carle. This ties into calendar work in Math, as well as some simple measurement activities. And there are more art activities than you will ever be able to do in one school year! But here is my favourite.]

Raising butterflies never gets old. I have had so many, "Drop whatever you're doing and come watch this" moments with our butterflies -- watching them go into chrysalis, and especially watching them emerge as butterflies! It is so exciting; the kids are all "in." It's one of the best things I teach all year.

The butterflies actually get used to the kids, so that by the time we release them outside, they are in no hurry to fly away. I tell the kids that they have to stay still as we unzip the butterfly pavilion and let them go. But often the butterflies will land right on the kids. By this time, the kids have become little butterfly whisperers....

I know there is more to teaching than making memories, but I don't know anything that is better!

These two butterflies went straight for the fake flowers on one of
the girls' sandals!




































































































Thursday, 23 February 2017

flying colours....

















I've got to admit it: this is one of my favourite art projects.

It borrows from Science (making observations, and learning about "living things" more generally). It uses simple materials (oil pastels and construction paper). And it introduces the art concept of mark-making.

We begin by looking at lots of macro (close-up) photos of butterfly wings. We look at all of the little scales that coat the wings and create the colours and patterns. These scales make up the "fairy dust" that comes off of the wings when you touch them; or sometimes when the insect's wings move violently. Typically I will show the kids a dozen or so photos in a slide show.

A small selection of close-up photos of butterfly wings.

























After that, I let each of the kids choose a close-up photo (printed) of a butterfly wing. All of them are different, so no two kids will be drawing the same picture. I let them choose a coloured piece of 12x18" construction paper, and show them how to draw the big shapes of their wings with white chalk. Then I show them how to "colour" in their shapes using short lines for marks, in imitation of the scales themselves. It's not quite pointillism, but it's far from just "colouring in" the shapes as well. It creates texture, and rhythm and movement.

At some point, I stop the class and show them how they can "blend" colours (without blending them) by overlapping or intermingling their pastel marks. Adding yellow to an orange area to make it lighter, or adding green to a turquoise area to give it depth and interest. (This is an Impressionist technique.)

Here's a selection of butterfly wing pastel drawings from several classes of Grade Ones.
















































leaping tall curriculum objectives in a single bound....









































Every teacher has that moment in May (or June) when he or she realizes how many things he/she still has left to teach before the end of the year!

(Or so I hear.)

For me the Health curriculum section called "Life Learning Choices: Life Roles and Career Development," is always one of those things that gets left until last. If I'm honest, I have to say it's not my favourite subject. Grade One students often can't remember whether they've had lunch yet, and whether it's first or last recess. So starting a discussion about "career development" seems a little bit abstract.

Happily, the central thing the kids need to be able to say is: "I can recognize interests, strengths, and skills I have."

So... in order to leap tall curriculum objectives in a single bound, I decided to ask my kids who they would be if they were superheroes. What would their super powers be? And what are their real-life superpowers?

(This seemed like an easy way to get them to think about themselves and their skills.)








































I had to laugh, though, when one of my kiddos (who doesn't particularly like to draw) drew two houses and an empty sky. (See above.) "Where are you in this picture?" I asked. "I'm right there," he said with all seriousness; pointing at a large blank area in the sky. "Where?" I questioned, skeptically. "Right there! I'm invisible! Invisibility is my super power!"

Bahahaha! Using his imaginary super powers to get out of real life work! Bonus points to that child!

Here are some of my other super heroes....



















children, children, what do you see?







































Sometimes a photograph is a provocation.

It can be an image that elicits a conversation. That tells a story, yes. But also, one that asks a question. That asks the viewer to respond, to bring to it what he or she knows. To synthesize existing information with new.

Showing a class a photo of something in their local environment, allows the students to show and tell you what they know. To share it with the other kids. To be the experts. To be the teachers and the storytellers.



















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Years ago, I realized that I couldn’t teach very much of the Grade One Social Studies curriculum through text books or other ready-made media, because so many of the objectives are specific to the community my students live in. And there’s no text book for that. I would have to create my own resources; letting the lived experience of being in Peace River, Alberta, Canada — a very specific place, at a very specific time — be my source material. The natural and constructed environments would be the “third teacher” in my students’ lives. (After their parents and myself.) (That’s a tenet of the Reggio Emilia approach to primary education.)

So I started taking photos that could provoke conversations around the curriculum objectives.

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1. Local Landmarks

One fall, I went out and took pictures of local landmarks in my small town of Peace River, Alberta. Places the kids would know, like the school, the swimming pool, the gymnastics gym and the hockey arena. Places like the movie theatre, the fast food restaurants, and stores. Places they should know, like the library and the museum and the town hall. I compiled these into a slide show, and we spent about a week discussing all of the landmarks; one or two slides at a time.


A river runs through it. These photos opened up discussions about rivers, islands, hills, valleys,
 and bridges. The top photo was taken by my husband, Tom Tarpey. The other two are mine.





























































































The kids had lots to say. I added bits of information to fill in the gaps. I added context for some of the landmarks using Google Maps, to show where they were. We used the satellite view to look at our local landscape; the map view to identify streets and bridges, and the street view to “walk” down the main street of town. I asked the kids to give me directions (verbally) from one place to another. “If I am looking at the Town Hall, which way do I have to turn to go to A&W?” “If I walked across this bridge, where would I end up?” And so on.


The old train station.


















Wooden sculpture of "Twelve Foot Davis" -- a gold miner,
and the stuff of local legends.



















The Peace River town hall. Note the Town of Peace River logo on the
near end.



















I printed some of the landmark photos we had looked at on card stock, and cut them into the shapes of postcards. The kids dictated a sentence or two about the landmark on their postcard to myself or a teacher aide, and we wrote them on the reverse sides of the cards as letters to their moms and dads. Then we addressed them and mailed them. Along the way the kids practiced reciting their addresses. (Not because this is curriculum, but just because it's important for them to know.)


Top: The MacKenzie Museum and Archives.
Middle: An artifact that lives outside the museum. It's the axle from the old paddle-wheeled
boat that used to be the main way in or out of Peace River.
Bottom: local mural of the paddle wheeler.

To extend the concept of local landmarks (because the landscape is a landmark), I taped a map of our town to a tray, and put out blue and green plasticine. I asked the kids to cover the water with blue, and the land with green. If we hadn’t run out of time, I would have added Lego blocks and centimetre cubes for the kids to make houses and restaurants and bridges, etc.


























And finally — on a slight tangent — we looked at the logo of the Town of Peace River. It is a symbol the kids come across in their movements about town, and knowing about it contributes to their visual literacy and sense of place. Signs and symbols are also a part of the Social Studies curriculum. Our logo, happily, is a simplified image of the river that runs through our town and the hills on either side of it, which form our beautiful valley. So the logo is closely connected to the landmarks in our region.


Miriam Gair. Peace River Valley. Watercolour. 2004


We took some time to look at a watercolour painting by once-local artist, Miriam Gair,  which depicts the same landscape as the town logo — layered hills, receding waters, the sun as the focal point — talking about what is the same between the two images, and what is different.

Then we recreated the town logo on paper plates, using plasticine. I cut out “stencils” from sturdy dessert-sized paper plates, and placed each one on top of a whole plate. We squished plasticine into the holes of the stencils, using blue and yellow mashed together to make green (which tied in with our Science work on mixing colours). Then we lifted the “stencil” plates off, and — voilĂ  — we had created images of the town logo, and by extension the local landscape.


Town of Peace River logo project: plasticine landscapes on paper plates.
Finished piece above and lower left. Stencil, lower right.


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2. Long Ago

The history of Peace River — at least in terms of European settlement* — is a short story. Our landscapes are still dotted with the remains of the homesteaders’ cabins who first cleared and farmed the land in this area. We drive by them every time we leave town. So this seemed like a good place to start the discussion about the “long ago” past of this area.

I took a photo of a fallen-down homestead. (I have since taken more.) We looked at it and talked about its size and configuration (one room), what it was made out of (wood), and where the people would have gotten their materials. Who lived in the house? How many people? How did they keep warm? What did they eat? Where would they have gotten their food? Their clothing?



















We talked about gardens and barns and outhouses. (Oh, my!) We talked about roads and churches and schools and, eventually, stores; all of this “development” organized around the central concepts of basic human needs. (A topic which is relevant to the Social Studies, Science and the Health curricula.)

The kids drew pictures of what it might have looked like here “100 years ago.”


























































All of this became the jumping-off point for other activities about our first farmers.

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* We had been discussing the Aboriginal peoples in our region (long, LONG ago and now) since much earlier in the year. 

Saturday, 18 February 2017

what makes a city....


















I teach Grade One in a town of 6000-and-some people. The nearest city of any size is 500 km away. Most of my kids have been to the city at least once, but most likely just to the (West Edmonton) Mall. Or maybe to see family.

Our Social Studies curriculum calls for an understanding of rural and urban communities. We spent quite a bit of time looking at pictures of cities and talking about what it means that a city is "bigger" than a town, working on the general concept of more. More people, which means more houses and apartment buildings for them to live in, which means more roads for the houses to be on, which means more cars, buses and trains. And so on. More stores. More gas stations. More signs. More traffic lights. More parking lots. You  name it.

For our "Building Things" unit in Science, we learned to make pop-ups. So we used our pop-up-making skills, markers, scrap paper, and small yellow stickers (for windows) to make little three-dimensional urban landscapes.



































Then we did some writing. The kids drew cityscapes, then finished the sentence: "A city has lots of ________." (Or wrote a sentence of their own.) It seems that lots of cities have super heroes, by the way. And other people standing on the tops of high buildings. With parachutes.

(Not sure if that is in the Social Studies curriculum, strictly speaking.)


















"I saw one of my cousins at the hospital."