Building: Patterns, Links, and Growth

The process of learning feels like a crystal growing, building itself from bits of stuff in the environment. Sometimes it grows in a regular pattern determined by its main constituents. Sometimes it encounters other minerals in its environment and incorporates them as inclusions, which can be very beautiful in their departures from regularity. Sometimes it sends off spiky shoots in new directions, where it can grow unimpeded, becoming more fully itself.

Quartz crystal with pyrite inclusions -- more here

Spiky white aragonite crystals -- more here

A lot of the visible patterns forming here this week are happening with our new set of pattern blocks. P and T use them pretty differently, but both are coming up with wonderful things, and their designs (and mine, when I join in) inform each other, so their creations evolve over time.

T came up with the central design; P added the border.

Besides building freeform, we've talked about the names of the shapes and how many names could apply to some of them (three different kinds of rhombuses, one cleverly disguised as a square...). P gravitates toward designs with reflective and rotational symmetry; I talked with her about those ideas, and she grasps them with ease. Both kids are building designs with translational symmetry. T builds mountain ranges while asking me questions about how real mountains form. T and I have built some collaborative designs that start off with high symmetry but break into more chaotic forms as we go on. P is discovering which angles combine for nice, solid walls and mosaics.

P's first mosaic. I asked if she wanted help moving it so she could finish it,
but she said the opening was intentional -- a door into the house.

The wall has fallen apart a bit, but the mountain lookout is complete.

Both kids have also built things to resemble real-life objects like houses, walls, or spaceships. An argument about what a spaceship should look like led to looking briefly at an update on the Voyager probes, as an example of a spacecraft that's not aerodynamic and has no landing gear, because it's never intended to enter an atmosphere or to land. T's very interested in landing gear. Every time we visit the science museum nearby, he watches the video that shows how the Mars rovers (Spirit and Opportunity) landed and went about their missions, and then asks questions about the replica rover in the museum.

P got out the Cuisenaire rods recently and wanted to do some number exploration with them. We tried using them to find factors, first of 10, then 12. P reasoned well about why various numbers would or would not divide 12 evenly; for example, 5 doesn't, because 5+5 is 10, and since 12 is only 10+2 (making 12 with Cuisenaire rods makes this obvious, but she knows it abstractly too), there's not room for another 5 in 12. After the math play, both kids built house layouts with the rods, and used the white unit cubes as people inhabiting the houses and driving around in their 9- and 10-rod limousines. The garages were bigger than the living quarters in these car-centric houses!

P embellished my star; parts got borrowed for other things;
change happens quickly with pattern blocks.

P's been drawing lots of house (and garage) plans on large paper and using them to play with T with dolls and toy cars. They've made and populated neighborhoods of row houses and played for hours with them, often making home improvements before the next iteration of the game. Since our toy budget has been limited a lot of late by limited cash flow, this is part of a larger theme of creatively making do with what we have to play in new ways. Recently both kids were walking around in homemade waterskis or snowshoes or ice skates (depending on when you asked) made from newspaper, egg cartons, and yarn. There have been pirate eyepatches and daggers with sheaths, superhero capes, cat ears and tails, and more, all made with materials at hand. The craft table and its contents are getting a lot of use.

T puts finishing touches on a design he and I made together

This morning, before I was even up, P got started building a scrapbook from photos she had lying around. I'm glad to see this for a number of reasons, including that these photos have been lying around for a long time with no real home, and it's good to see them safely stored and in use! She's using a binder full of notebook paper I gave her months ago, which has gotten no love until now. P's been telling me occasionally that she doesn't like writing, but she's writing captions for her photos with enthusiasm. There are some themes emerging, like her favorite toys from different Christmases, and she's borrowed my camera to take pictures of some toys that weren't in photos yet. I also love seeing how much she writes about playing with T and loving him. I told her about acid-free paper and archival glue, but she's happy with her notebook paper and giant glue stick for now. We can always upgrade if scrapbooking becomes a passion for her.

One of P's photos for her scrapbook

One evening this week I put on a DVD about the design of castles and the English occupation of Wales by means of castle fortifications. As often happens, though the kids didn't express interest in it beforehand, they were drawn into it quickly. Castles played some part in the floor plans and pattern-block constructions after that.

Also this week, we bought and broke out a kids' magnetic poetry kit. The main action it's seen so far is T lining up long sequences of words and asking me to read them to him. He enjoys it when I try to make phrases out of them, with appropriate inflection, rather than just reading them as lists of words. I tried to paint a piece of sheet metal with chalkboard paint so we could write words along with our magnetic poetry, but we all learned that despite the Lowe's salesman's assurances, we should have used a metal primer first. Soon we'll try it again on the other side, if we can find a metal primer that will support latex paint on top.

In related events, a few days ago when T was having me ask him questions from a Brain Quest kindergarten question pack (one of his favorite "stories" for bedtime), he read his first word! There was a question asking him to pick out, from several words in a picture, the one that matched a circled word. He found it correctly. I asked him if he knew what that word was, and he read it: "ON." He's seen that on many a radio-controlled or other electronic toy, and he's also alert to phonics, so there's no telling whether he sounded it out or recognized it as a sight word.

Other highlights from this week:

• After taking three beginner classes at a local mixed-martial-arts dojo (rooted in Tae Kwon Do), and watching a higher-level sparring class, P and I decided neither of us was very interested in pursuing martial arts if sparring was to be the high-level goal. Sparring is required starting at intermediate levels at that dojo, so it's time to move on. We have friends who take classes at a local aikido dojo, so we may go watch classes there soon. We're taking a break for the moment.
• We took a trip to the small museum of natural history at our local university, which is free and convenient by bus. Arriving after a nice lunch at a campus-area taqueria, we tried on a beekeeping veil, saw a model beehive, and touched honeycomb and a paper-wasp nest. We looked at the dwellings and tools of Pueblo Indians in this general area, from antiquity through current times. T liked looking at and hearing about the variety of houses; there were great dioramas of pit houses, row houses, and cliff houses. We compared the teeth of carnivorous and herbivorous dinosaurs. We touched bison bones, a skunk's tail, a cow hoof, and assorted fossils. P bought a coloring book of Mexican folk art in the gift shop; T chose some crystals in a little pouch. I bought some sun-print paper for us to try when things warm up a bit.
• Today we did an extended problem-solving session about sharing of toys and rooms. We came up with some possible solutions, including sharing space and toys differently, using timers to limit sharing time so there's a clear time boundary, and other possibilities. They're trying one of P's ideas as I write this bit: They trade rooms for a limited time, with a timer set, and can play with each other's stuff during that time. When the timer rings, they'll both help clean up both rooms, unless they agree to set the timer for additional time before cleanup. [Note later: More work needed here. UnschoolerDad says he thinks the answer is to make T's room cooler than it is. I think he may be at least partly right.]
• We played with gelatin, dissolving gelatin capsules to release the spongy animal shapes inside and also making Jell-O, so we got to see the creation and dissolution processes.
• One day when we pulled our car alongside a semi, T wanted to know how to hitch and unhitch the trailer. I had guesses, but really didn't know, so we found some YouTube videos from truck-driving schools showing the process -- not in great detail, but enough for now. Both kids are psyched about the prospect of having a video chat with a friend of mine who is a long-haul trucker; I'm working on setting it up with him, which is tricky since he usually doesn't know in advance when he'll have down time (waiting for a load or unload) with a good internet connection available.
• We finished reading The Friendship Doll out loud. P and I linked the phrase "chewing the fat" to an Inuit story we read months ago, in which a special kind of fat was saved for sharing while talking with visitors. We looked up the phrase origins and found related and unrelated, likely and apocryphal possibilities. We also read about car tires that could be repaired as bike tires can be now, the dust bowl, the shoddy welcome given Okies arriving in California, the hundreds of thousands of letters people wrote to Eleanor Roosevelt during the depression, and more. After finishing the story, we read online about the real 58 Japanese friendship dolls, and we found out one of them is in a museum near us. Perhaps we'll visit soon!
• We started reading Hattie Big Sky, also by Kirby Lawson, who wrote The Friendship Doll. P is totally intrigued by this story of a 16-year-old girl, orphaned at 5 and bounced around from one distant relative to another, who inherits a 320-acre claim of dubious value from an uncle in Montana and tries to prove up the claim on her own.
• We finished reading The Hobbit out loud. P wants to see the Lord of the Rings movies. We'll see; they're so graphic in their violence that they give me nightmares. We might try the books first, though those didn't hold my attention until I was in my teens.
• P told me she doesn't want to read any more of the slim chapter books in the Rainbow Magic Fairies series; she has outgrown them. She's still game for the bigger "special edition" books in that series, but she says that mostly she wants to read "bigger stories," like The Hobbit or Hattie Big Sky. Perhaps she's ready for Susan Cooper's The Dark is Rising series, or The Chronicles of Narnia, or Lloyd Alexander's Chronicles of Prydain. 
• P has been enjoying reading newpaper comics, and she devoured her first Garfield book checked out from the library. She read some of it aloud to T, who enjoyed it as well.

To close, here's a different bit from Marge Piercy's poem, "The Seven of Pentacles," which I've quoted here before. I can imagine, from her underground roots and brambles, sudden explosions of upward growth when conditions encourage it.

          Weave real connections, create real nodes, build real houses.
          Live a life you can endure; Make love that is loving.
          Keep tangling and interweaving and taking more in,
          a thicket and bramble wilderness to the outside but to us
          interconnected with rabbit runs and burrows and lairs.

Of Contour Maps, Candy, and Cargo Cults

Whew! We just came back from a two-week road trip as a family; I'll write about that in a different post. This material is from notes I made before we left, which preparations for the trip kept me too busy to write up.

I forgot to write before that when we were on our way back from our trip to see the elk bugling, we were driving down a winding mountain road that roughly followed a river. P asked "Why do you think this road is so curvy?" We got to talking about why it's good for roads not to be super-steep, and I said the designers of the road were trying to follow the elevation contours as closely as they could. Earlier that day we'd seen a map of the national park, with contours shown in relief. If you looked closely, you could see that the contours were built up with actual flat layers of material (or perhaps the map was made to look as if it had been built up that way) -- so the contour lines were obvious in the fine texture of the map. We looked at some contour maps online when we got home, relating the concept to places familiar to us.

Also on that trip, P asked whether it was hard to tell aspen apart from pine in the summer, when the aspen weren't gloriously gold as they were on that autumn day. We talked a little about the lighter shade of green, flatter texture, and tendency to flutter in the breeze as distinguishing qualities of aspen leaves.

In an unfortunate example of experiential learning, P accidentally swallowed a peppermint hard candy whole while we were coming home from a restaurant. She was quite miserable with that big, hard thing stuck in her esophagus. We had her drink sips of water. She reported that each sip hurt as it reached the candy, but then the pain level went back to normal. When we got home I gave her some warm water to sip, and she said that seemed to speed up the process of dissolving the candy. In a little while the candy slipped into her stomach and stopped hurting, though her esophagus was still sore when she ate or drank for the rest of the day. We talked a little about the process of dissolving, and why P wouldn't see the whole mint in her poop. The next time I went grocery shopping, I bought a bag of peppermints. Then, as we were finishing lunch one day, I set up three bowls of water -- cold with ice, room temperature, and hot -- the kids got very curious as I did this without explanation (I answered their questions rather than laying it all out) -- and put a mint into each. We stirred each about the same amount with a chopstick and watched what happened until the differences were clear: the one in hot water was dissolving a lot faster. There didn't seem to be much difference between the cool- and cold-water bowls. We ate the mints and drank the water from the bowls. P noticed that the mint flavor in the water tasted strong in the ice-cold water. We wondered whether the cool tongue feel of the menthol was intensified by the cold of the ice water.

One day, P was pretending that she lived in a pre-electric society, but that she had heard of electric lights and had made something that looked like a light fixture and stuck it on her bedroom ceiling. This reminded me of cargo cults, so I told her about them and pulled up some photos online of pre-industrial Pacific Islanders who, after WWII ended in the Pacific, had built control towers, runways, and (nonworking) radio gear out of locally available materials, hoping that doing so would bring back the airplanes and their useful cargo. We talked a little about how, when people don't understand a technology or phenomenon, they sometimes try to replicate it in an attempt to make it work for them anyway. Richard Feynman described "Cargo Cult Science" in one of his famous talks.

This playing may have been related to another recent event. There were some great rebates available for energy-efficiency home improvements, so we had our home checked out by an energy auditor. As a result we've made covers for the swamp cooler vents and had insulation added to the attic and some sealing of our home done. I explained what was going on to P, who was annoyed at all the racket in the house (though she and T loved coming up with games to play with the leftover mylar/plastic insulation from the vent covers). We talked about how getting our house better sealed and insulated should allow us to spend less on energy and have less of a detrimental effect on the environment. After thinking about this a bit, P asked if sometime soon we could go a week using no energy. We talked about what that would mean -- we wouldn't be able to heat the house, use our electronics, turn on lights, cook food, etc. She was still interested in a more limited version (no electronics/lights for a limited time), so we may try that soon.

A few times recently, P has asked me what I was doing when I was looking at online petitions, trying to decide whether to participate. Some recently have been very general online petitions, without enough detail about how the organizers wanted to achieve their goals. P was curious about what petitions were for, so we talked about online petitions, recall petitions, and other means for lots of ordinary people to try to effect change in things beyond their direct control. The particular petition that sparked her questions was about student loan forgiveness, and P wanted to know about student loans, so we talked about those and loans in general. P wanted to know why I wasn't sure about the petition, so I talked about my concerns about where the money would come from, and how current and future college students could plan. Would they expect their loans to be forgiven also? It might make more sense to increase government funding available for education in a way that would allow realistic financial planning for all involved.

P, T, and UnschoolerDad went to a fall festival at a local farm. Not much learning of any schooly subjects was reported to me, but the kids had a lot of fun climbing on stacks of giant tractor tires, driving pedal-powered race cars, and screening pails of mud for semiprecious stones. (Size, not density, was the screening method, so there wasn't a chance to relate this to panning for gold.)

But speaking of schooly subjects, P continues to read chapter books on her own, and the other day when we were doing a very rushed set of errands, she went through a pile of coupons as I drove, looking for the one for the store we were headed to. She found it on the first time through the coupons, so I'd say her reading speed is doing great. She's also been asking occasionally to "do math." I ask her what kind of math she wants to do, and then write some arithmetic problems to suit her desires. If they're challenging, we do some together, and I gradually pull back until she's doing them mostly or completely on her own. For stuff that's more familiar, she likes me to write down several problems and then sit nearby while she works them, checking her answers when she asks me to. Our most recent problem set was addition facts to 20, including doubles and problems with unknown addends (e.g., 3 + ___ = 11, or subtraction/algebra in disguise). She's done more advanced, multi-digit addition and subtraction, but she seems to be recognizing that stuff like that is easier if you have many of the more basic facts memorized, and she's actively working on them.

T is learning to add small numbers (up to five or so) and read 2-digit numbers. He asks frequently how to say a 2-digit number (such as the page number in a book being read) and how to write particular letters, and he's enjoying some Android phone games I've downloaded that let him practice some of these skills.

In a happy accident recently, T chose an early-generation Transformer toy on a thrift store trip with UnschoolerDad. He thought it was just a car, but when he showed it to me, something about it seemed to want to move, and I started the process of making it into a robot. We discovered its full range of moves over the next day or so. This is just about the perfect toy for T, who really enjoys figuring out how things work and then making them do their thing, over and over again.

P continues to spend her allowance on things she wants, mostly small toys. On that same rushed set of errands, though, we were at the fabric store, and I told her I'd buy her some small pieces of fabric for her sewing/crafting. She picked out a couple of holiday calico prints to make holiday dresses for her dolls.

Here are some highlights of learning from recent media, from the PBSKids iPad app and library DVDs:

• What a metal detector is and how to use it (Curious George)
• What "scrub the mission" means (Curious George; I paused it to check if they understood, and then I looked up and shared the origin of the term, from when lists of plane flights were made in pencil and could be erased or "scrubbed" when canceled)
• "Leaves of three, let it be" (Curious George; I added and explained, "But if it's hairy, then it's a berry")
• Dentists and what kinds of things they help with (Berenstain Bears; this was new material to T, who's been along for P's visits but hasn't yet been himself)
• Why people move house sometimes, and what's good and hard about the process (Berenstain Bears; P remembers a little bit about our last move, but not much; T was only 6 months old then)
• Snobbish/arrogant behavior and its effects on social relationships (Berenstain Bears)
• Ways of looking for different perspectives when things look bad (Berenstain Bears)

And finally: P wants fish. She's been asking for lots of different kinds of pets for a while now, most of them likely prey to our two cats. Fish, though, I think we could manage, with good precautions to keep an aquarium lid secure. P wanted fish NOW, before our road trip, but I said we could look at it seriously when we returned. P decided to make a fake fishbowl in a mason jar, with some rocks, tap water, and a fish made of aluminum foil. First she cut out the fish shape from the foil, but it just floated on the surface tension of the water. I suggested she try molding a 3-D fish from foil, and that floated because of trapped air inside. We tried squeezing it tightly, but it still floated until we poked some holes with a skewer to let out the bubbles. Then it sank to the bottom, but rested on its nose there, almost neutrally buoyant. The next morning, it was floating again, and we saw that there were tiny bubbles all over it. Shaking the jar dislodged those, so it went to the bottom again. During all this, P started showing some insight into buoyancy, and we talked about Archimedes' principle (a floating body displaces its own weight in water). We tried floating a small glass bowl in a larger bowl of water, which worked fine. We imagined crumpling up the glass bowl into a hunk of solid glass and decided it would sink, as indeed the bowl does when you put it into the water sideways. But if you put it in bottom first, it displaces more water, since the airspace inside that's below the water line also displaces water, so it floats. In a tie-in with her recent pottery lessons, P noted that a hunk of clay would sink in water, but if you made it into a pinch pot, it could float.

I'm still trying to decide whether to bring up the real fish again, or wait until P mentions it.