It has been one of those weeks where I look back and think, did we do any schoolwork? We did a bit of reading and writing practice and a little bit of math, but other than that, did we do any? What counts as schoolwork anyway?

Reading a chapter of Penrose the Mathematical Cat about impossible shapes led to some drawing practice, trying to copy the shapes and also to draw impossible shapes of our own. Drawing impossible shapes is actually quite fun and I think it a great way to explore drawing three-dimensional objects. To draw a shape that looks almost possible but not quite possible you have to really think about what you’re doing and what each space is supposed to represent.

I wanted to expand the topic of things that don’t quite make sense, so I sketched out something like the image below and talked about how it is similar to the impossible shapes. Each sentence is a correct sentence but put together they don’t make sense. They are like Escher’s stairs leading always down yet somehow always back where they began.

So then we gathered up examples of Escher’s pictures and looked at them. In the library we found a few other books with similar styles but directed at children. My favorites were Switching on the Night and Imagine a Place.

Switching on the Night by Ray Bradbury is a story about a little boy afraid of the dark until he stops seeing night as the absence of light and starts seeing night as the presence of all sorts of wonderful things. The illustrations of the book are drawn with Escher style with no clear focus of up or down, but the story itself is in some ways more like the Escher pictures of Metamorphosis or Encounter where what is just the space outside of the object becomes an object in itself.

Then there is the book Imagine a Place by Sarah L. Thomson and Rob Gonsalves with beautiful pictures and short descriptions. Roadways transform to waterways. Curtains turn into dancers. A few of the pictures lend themselves to discussions of figures of speech.

I encouraged both children to sit down and draw their own transformative pictures. My four year old jumped right in, the older hesitated a little. While they were drawing, I sat and drew some of my own. I found it helped some to have a homemade stencil and attempt to trace it over and over on a page and then slowly focus more on the outline of the negative space between the stenciled image, and slowly set aside the stencil and draw that outline and let it become the focus.

An old geography textbook pointed our next step in this crazy line of exploration. The book Geometry by Harold R. Jacob’s interested my seven year old because of its abundance of cartoons. After letting him skip around and read all the cartoons I summarized the first few chapters, which explain about Euler diagrams, equivalent statements and deductive reasoning. (I pointed out that the Euler in Euler diagrams is the same one who figured out Euler circuits.)

The book used an excerpt of Alice in Wonderland in the section on equivalent statements so I dug out my copy of Alice in Wonderland and we used that as our reading practice for the next few days, stopping every so often to discuss the examples of flawed logic. The edition we were using was the Michael Clay Thompson edition which has little “language illustrations” in it, pointing out how Lewis Carroll uses grammar and punctuation to flow with the book. I tend to note when movies use camera angle and editing to build suspense, show confusion or other emotions but it is easy to miss that good authors use their sentences in the same way. Looking at the grammar of Alice’s Adventures in Wonderland fits with the content of Alice, since so much of the story is about word play.

My kids had memorized Carroll’s poem How Doth The Little Crocodile a few years back and were exited to see it in the context. I wanted to show them even more context to it, so I searched online for How Doth the Little Busy Bee, on which Lewis Carrol based his poem. The original was meant to encourage productivity and responsible use of one’s time so it led nicely to discussion about what Lewis Carroll might think of that message. Is Alice using her time productively? (Yes!) Why are daydreams important? How is the story of Alice in Wonderland like the story of Gedanken in Uncle Albert’s Space and Time?

When we finished Alice’s Adventures in Wonderland we moved on Alice Through The Looking Glass. Chess pieces feature prominently in the story so I pulled out our chessboard and we reviewed how to play it. Playing chess with children is interesting because my goal is not to win but to teach them how to play. It feels weird throwing my chess pieces into positions from which the children can needlessly slaughter them. I talk outloud to myself while playing chess with them to demonstrate how I decide to make my moves. Over the next few days I want to play chess more with each of them, but I also want to have at least one game where as we move the pieces we make up an Alice-like story, about where the creatures are moving and what they are doing. I’m trying also to think about how to draw out or play with a chess board shaped differently, or perhaps to play on a board that morphs into different shapes (hexagons instead of squares, perhaps?).
I want to talk further with the children about transformations and the question of what quantity of something’s qualities have to stay the same for something to still be the same. I’ve been thinking about ways of doing this. One would be drawing, if I drew a little picture and then I drew the same picture with a detail changed, and then a picture of that with a detail changed, talking with the children as I go about when the new picture ceases to be a variation of the original or if it does. I want to tie it in with Alice wondering whether she remains the same person after going through so many changes. We’ve talked a bit about that already, about how the qualities of Alice changed (her ability to remember poems, perhaps, and her size) but she was still Alice. What is the defining feature of Alice? Is there any number of changes she could go through after which she wouldn’t be Alice? Perhaps I’ll use playdough in discussing this. If I made a playdough Alice, to what is the name Alice attached? Is it attached to the particular pattern of indents and such that shape the lump, and thus my Alice ceases to be Alice when I alter the pattern? (And then how many or what types of changes make Alice not Alice, and which chases are simply changes in Alice’s position, expression, etc?)  Or would the name refer to the lump of playdough so that when I reshape the lump into a duck it is Alice-shaped-like-a-duck-but-still-Alice? What is a name?

In Alice in the Looking Glass there’s a joke about Alice seeing “Nobody” on the road, and how good her eyesight must be to be able to see Nobody. The joke ties in perfectly with the Escher pictures where the negative space of one picture becomes something of its own. Is nobody just an absense of something, or is it something in itself? It ties in beautifully with the book Switching on the Night, mentioned above. It also fits with the poem

“Yesterday upon the stair
I met a man who wasn’t there.
He wasn’t there again today.
I wish that man would go away.”

We haven’t done much schoolwork this week. Instead we’ve been chasing the fanciful. We’ve been trying to unwind concepts and connections for which we barely have the language and in trying to produce our own pictures we’ve gained in appreciation for the skill of others. Meeting some familiar poetry in books we had not yet read re-enforces for me the importance of including poetry, art, and music in our studies. Sometimes children are ready to learn one poem, one picture, one song when they are not yet ready to learn about a full piece of literature, or much background about a particular author, artist, musician or time period. Learning the one little bit still gives them something to recognize later. It’s like the poem becomes a friend from another city, and when you visit the city later it has more meaning because you can say “this is where so-and-so is from.” You’re already connected.

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