parabolas, brain doodles, and steering the boat

I think I've mentioned before that Wednesdays are a wild card for us.  Sometimes we are in synch and the flow is sa-weet! But many weeks we are tuckered out from Tuesday's coop and Wednesday finds us in our separate corners.  It is reminding me that long ago we quit a coop for just that reason: instead of coop taking one day of busy and out, it really took two days from our week - the long day out and the long day of recuperation.  That feels like too much time to me! We lose our rhythm and struggle the rest of the week.

I keep thinking that rhythm is hard won, because that has so often been my experience, that if you interrupt the rhythm of your days it takes so much energy to get it back.  I wonder if some would argue that in that case, it would mean the rhythm ain't really there...I tell you, this business of  - what? shepherding? guiding? I can't find an analogy I like here...steering the boat? Anyway.  Trying to facilitate a good day for three people is a bit mind-boggling. When I'm rarin' to go, they are deeply focused on Something Else and vice versa.  Case in point: I had my shoes on to run to the store for supper supplies and Ani bounces down the stairs singing, "I'm ready for piano!!!!" Turns out, she had a lovely practice, without me. Good for both of us...

So, to celebrate the successes of today inspite of no rhythm...Eliza launched herself into sewing together the pieces she cut during sewing class yesterday, to make a beautiful little "clothespin apron".  I'll have to get a photo of the finished product to share.  She is still doing a good bit of winging it, rather than being sure to check the pattern and the instructions, but I'm seeing big improvement in her craftsmanship, which was one of her goals.  I love that she forges on and does it, rather than thinking about it for a few months before starting (Ahem. I am intimate with this approach).

Ani and I butt heads a bunch today.  Just couldn't really see eye to eye on most things.  I finally went and lay on her bed and apologized for the ways in which I'd been pushing her to do the things I wanted her to do today.  What I wanted her to know was that I really deeply value her ability to tell stories for nigh on three hours, that I don't think it is a waste of time for her to cut out every piece of clothing her paper dolls have so that she can tell her story and that I remember not wanting to practice piano, and I thanked her for getting to it when she was ready.

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Wednesdays tend to be a math art day.  

We made parabolas a few weeks ago, and today we made more parabolas and Eliza and I stitched some, while Ani got out the compass and made a circle to string on.  I mostly enjoyed that we were all at the table together, Doing.

oh! circles! so many circles!

Ani tried the stitching, but was easily frustrated and went on to something else. Eliza made the sweet butterflies below.

My triangle. I can see why these were popular in the seventies!

My friend Molly sent me a link to this and it got me traveling down a few rabbit holes and thinking about how I could use this method of thinking "out loud" to encourage Ani to put more thoughts to paper.  The girls attend an off-again, on-again poetry class with a poet we love, and Ani participates in her own way, but does not often choose to write during class.  I've offered to be her scribe, but she feels pressured by time and is a bit intimidated by what she perceives as the ease and skill with which her friends accomplish their writing. (Some are impressively skilled and some are willing to accept some scribe help to get past the mechanics and are able to contribute to the class.)  

So, we doodled.  We chose to think about our cats, and to draw and write what came to mind as we talked and giggled and thought.  

I think we might be on to something.

the week

Last week was our first week consciously trying to fit a few things into our days - you know, something other than watching Dr. Who and reading Garfield.  We get bucketloads of that...So, sometimes my suggestions of things to do are a hit and sometimes they are a bit of a flop. I'm trying to come up with some ways to play with math that will appeal to Eliza - I'm looking for a hook, an in. She has a grasp of basic functions but does not enjoy math at all, finds it intimidating and horrible. One approach to this would be to just focus on the math that comes up, which is a lot of what we do: measuring, figuring out finances, etc.  Another approach would be to pile on the math, which doesn't really make sense to me. Hate math? We must not be doing enough of it!! 

My brother-in-law, who has a keen interest in how and what we are doing around here, being an avid learner himself, thinks the "in" might be geometry, appealing to the artist in her.  I mostly want it to be playful and interesting.  I do ask myself (an echo of my daughter), why is it important that she work on math? My answers vary.  One, I think it is good to challenge and stretch your brain and know a little about a lot of things.  Math is like gymnastics for your mind.  I think it can also deepen appreciation of art, architecture, science, and even history, understanding how people saw and thought about the world hundreds of years ago.  The reason that we keep plugging away at our math program (Teaching Textbooks - terrible name, fine program), to varying degrees of satisfaction, is that we are required, as registered homeschoolers, to provide evidence of progress and learning. Ugh. This does not feel like a real reason, but there it looms.  My solution just now is to do a little of the lessons - one or two a week - to keep a hold on the things that have been learned, and to find what else is out there to play with. 

This week it was a Vi Hart video about snowflakes, which lead to some snowflake cutting, of course. We also played a little Euclid The Game, but got stuck early on and it just didn't catch on. Another day, perhaps.  Ani wanted to make another times table and was really enjoying the patterns, especially in the nines, which she and I are rather enamored of right now.  I've also picked up a book called The Adventures of Penrose, The Mathematical Cat by Theoni Pappas that she and I are reading through.

Math came up while were reading the materials that came with Mapping the World with Art (Ellen McHenry's Basement). There is a brief chapter with each drawing activity, focusing on the history of mapping.  The first lesson talked about how people actually figured out that the earth was more or less spherical a very long time ago. The second lesson talked about Strabo, the ancient Greek geographer, and Eratosthenes, the mathematician and geographer who figured out the circumference of the earth.  Math!  Ani and I had come across Eratosthenes earlier, reading The Number Devil, and played with his "sieve" of prime numbers.  (Wow. That sounds pretty geeky. Math geeky. Me. HA!)

Ani's Nile

Mesopotamia by Ani

We started back with the homeschool coop this week - no it wasn't as bad as I was anticipating - and the girls seem excited about their classes.  Eliza is taking a fashion/sewing class and spent the next day and several hours since at her machine.  We've been moving things around in her room trying to take advantage of the light and clear things out a bit.  She is feeling so proud and happy about her space...

...and having a friend come down from Columbus for the weekend was good incentive to keep it looking good!  

That brings us to the weekend! It was gorgeous. Spring gorgeous. Dan and Ani and took a couple hours to walk down the bikepath and around across the river.  Bluebirds, Pileated woodpeckers, blue skies...so beautiful.

mathing this fall

playing with triangle numbers

I've written about how we "do maths" before, but it's been a while, and though the core of it hasn't changed a lot, there are some new resources about that we're having fun with.

Part of what has changed about math is that Eliza follows a curriculum several days a week. What drives this is a couple of things.  Ohio requires a summary of what we have accomplished over the year, either by standardized test or portfolio review. If that were not the case, I would be letting math unfold for her in a different way.  There is also the possibility that she is going to want to try school at some point, and I don't want her lack of math to be a huge obstacle.  Since I have a harder time just slipping math into whatever we are doing, and she and I are so similar in a way that creates a mini-storm when we attempt to do a few things together (math and piano), taking me out of the equation for the most part has been very helpful.

I heard a mom complaining about long division the other day and wondering how else she could explain it to her child who hates it, and I asked if they were using a curriculum at all and she said "Oh! Yeah! I guess I could farm that one out!" I think it's helpful to know when you need to employ other means of getting something across in order to protect your relationship with your child!! If we're arguing or frustrated, there's no learning happening anyway, so why persist in that direction?

So, she works on Teaching Textbooks, usually alone, and sometimes she grouses about it but I'll tell you what, she never gets more than a couple wrong, if even that. She shakes her head in bewilderment sometimes, and then a grin spreads. How did I do that??

Ani and I do something mathy every day.  Her current bedtime request, before she gets to her own reading, is for a chapter of The Number Devil by Enzensberger.  Oh my gosh, I love this book and I wish he'd written enough for us to read several chapters a week and still not be done.  I don't get all of it, but I love puzzling over the patterns and tricks, and obviously she does too.  I think we'll go through it again in six months or so with a notebook instead of a pillow and play a little more directly with the ideas.

doubling a muffin recipe, on the window

Sometimes her math looks like a card game of war, or a game out of Family Math.  It can also be a bunch of problems I write up on the window for her (at her request) or a sudoku puzzle.  Lately we've all been working on the multiplication tables. Let me tell you, I think what drove us all to learn them when I was a kid was competition!! There is just no drive to learn them! I remember memorizing them, but it's been slow here - until I remembered Schoolhouse Rock and found their videos for 0 through twelve.  YAhoooooo!!! Ani thinks they're the bee's knees and I found her skating in her footies around the living room with her multiplication table in hand, filling in the eights as she sang the song over and over and over...(It's ok if  you're rolling your eyes - it isn't always like that around here, and no, she doesn't beg for spinach over chocolate.)

Why are they learning them if there is no drive? Well, the mistakes Eliza makes in her math aren't generally because she doesn't understand the process but because she doesn't know her times tables and it really slows her down.  Since she doesn't love math, that is a bad thing!  I also love how since it's something we are all doing, we are able to play with numbers all the time...

Which leads me to the dorky games I come up with to practice.  Exhibit A, Eliza, on a freezing cold day, finding a game I'd drawn out and then abandoned because it was so cold.  She actually loved it.  (It's just simple: stand on the heart while I call out a multiplication problem, then jump to the answer. Back to the heart. Repeat.)

I ransacked our 5 decks of cards and merged them into the perfect Multiplication War game: each player has a stack of cards with only the numbers we are working on (2, 4, 8, 3) and a stack with everything else (including 2 of each of those numbers).  For each turn you turn over a card from each pile, and do the problem, and the person with the highest product wins.

Colorku - like Sudoku with colored marbles

We've also been using The I Hate Mathematics Book and Math for Smartypants a little for ideas.  Definitely more to mine there.

math + pajamas = most mornings

My brother-in-law is a whiz and enjoys puzzling numbers over, so he is often eager to check in on what we're doing and how we're feeling about math.  During a long drive home from the coast this summer, he talked to me about what he calls "fuzzy math".  The math that is huge and abstract.  The math that is not just about numbers, or is about numbers but only in one facet. The math that is music, art, architecture, shapes and beauty. Fuzzy math.  So we've been trying to make sure at least some of our math every week is fuzzy.  Eliza calls them "math art days".

Thanks to a couple of new books at the library, we've played with Cool String Art and made tesselations with Cool Paper Folding (all right, so I picked them up even with the lousy titles).  

Which of course led us outside to fix up our dusty and loose geoboards for more math art...

pretty picture of rubberbands. i couldn't resist the colors.

Of course there is Fibonacci, every six months or so, because who doesn't love spirals?

And when the weather throws you a sunny, if blustery, curveball and you have to get outside, there is always the number line, skip, skip, skip...

mathematician clearly rocking out

Writing a post a day for November...

fibonacci

 It's just fun to say: Fibonacci. Never mind that it's all about a fun sequence of numbers to figure out:  0+1=1, 1+1=2, 1+2=3, 2+3=5....0,1,1,2,3,5,8,13,21,34,55, and on and on - it's also all about spirals, making spirals, finding spirals, seeing these numbers repeated everywhere in nature...it's a brilliant way for someone like me to get completely geeked out about math.  How come I didn't know about it until I was in my thirties?? I suppose it could have been that I wasn't really paying attention, but you'd think I'd remember something like that.

We've played with Fibonacci before (there is a funny book about him from the library, called Blockhead) and looked for the numbers in nature, but this week we looked at Vi Hart's video on spirals. We are loving Vi Hart right now. So of course we had to play some more*...

 

*keeping it real: While Ani loved the idea of looking for spirals all over the house, she quickly grew SUPER frustrated trying to trace them out on a pine cone (a la Vi Hart) - which I found a little challenging too - and didn't even WANT to try to draw one.  She yelled about it a whole bunch.  We let it go.  Eliza drew a cool spiral, after figuring out the numbers on graph paper, and days later I managed to coax Ani, with a piece of cheese and a few games of Nim, into figuring out some of the sequence and talking me through drawing it out on graph paper, and then she wandered off to do something with the rest of the beans while I totally entertained myself by lining up the different colored beans in their boxes: 1,1,2,3,5,8...well, that's as far as I got, 'cause that's already a lot of beans!