math

I love homeschooling.  Every year I love it more.  I've mentioned before how incredible it is to tinker with curricula.  You get to do whatever you want.  If you don't like how schools do things, then try something else.  If you or your kids don't like how things are going, then try something else.

Being an experienced homeschooler (I think this is our 15th year), I get to really up my game.  I remember watching a video of this crazy father who drove around in a van with his family for years and never taught them any math whatsoever.  I thought that was the nuttiest thing I ever heard of.  But boy was it intriguing.  All the things I thought education "needed" might not be true.  All of my assumptions might be false.  I might be locked into all sorts of premises that are preventing true learning.

I read Lockhart's Lament in 2008.  I think it's been simmering in my brain for the last few years.  He talks about presenting mathematics in a way that it engages the part of our minds that enjoys questions.
He talks about how music and art, although to be done professionally and "properly" need a lot of knowledge and skill, are played with by preschoolers and children.  Why are we not playing with numbers and mathematical principles?

He says, "If I had to design a mechanism for the express purpose of destroying a child's natural curiosity and love of pattern-making, I couldn't possibly do as good a job as is currently being done--I simply wouldn't have the kind of imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education."

"They [the students] say, "math class is stupid and boring," and they are right."

" 'So you would remove mathematics from the school curriculum?' 'The mathematics has already been removed!  The only question is what to do with the hollow, vapid shell that remains.'"

"To help your students memorize formulas.. you might invent this whole story about "Mr. C" who drives around "Mrs. A" and tells her how nice his "two pies are" (C=2πr).. or some such nonsense.  But what about the real story?  The one about mankind's struggle with the problem of measuring curves; about Eudoxus and Archimedes and the method of exhaustion; about the transcendence of pi? Which is more interesting--measuring the rough dimensions of a circular piece of graph paper,using a formula that someone handed you without explanation (and made you memorize and practice over and over) or hearing the story of one of the most beautiful, fascinating problems, and one of the most brilliant and powerful ideas in human history?  We're killing people's interest in circles for god's sake!"

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So since Chana is thinking about going to High School, we have been doing the sort of basic mathematics that is a prerequisite for algebra.  Fractions, decimals, integers, etc.  I wrote a list of all the things I could think of.  And most nights, at around 9pm, we sit down and I try to think of what would be kind of fun, and we sit down and do it.  I've been enjoying the opportunity to tinker with the mathematics curriculum and just try to get it to be interesting and fun.

Chana's been enjoying math again.  When we talked about adding, subtracting, multiplying and dividing negative and positive integers, Chana framed it as negative is like owing someone money.  So if you owe someone 5 dollars (-5) three times, then you are going to owe someone 15 dollars.  In other words, it made sense to her that if you are multiplying a negative and a positive, that the answer will be negative.  I'm so happy she's thinking about math again and integrating into her worldview in a real and experiential way.

On Friday, she asked me about 5.9 minutes.  (We've been working on adding, subtracting, multiplying and dividing decimals all week.)  So she was wondering about decimals in terms of minutes.  It's a piece of a minute--but how much of a piece?  How would you convert it?  I'm so delighted that she's wondering that.  We started talking about 0.5 being a half and what that means in terms of minutes.  We were just casually chatting.  What about 0.9?  What about 0.05?  or 0.50?  She was thinking about it and trying to figure it out, and I was answering direct questions.  Then she said, "Hey, maybe after Shabbos you can teach me that."  So that's our next math topic.

As I mentioned about unschooling, math was one of the last subjects to be unschooled.  It's been really freeing to let go of the way that mathematics is usually taught in schools and just give Chana some space and then the opportunity to play with math a little.  I want her to be proficient in math.  But I want her to realize that math is a way of thinking about life, and that math is an art, and that math has beauty, and that the mind naturally thinks mathematically.  Homeschooling has not only given me the chance to pay close attention and teach on Chana's level when she was conceptually ready, and teach her in a way where she could understand it and not fall "behind" (though she technically was "behind" the school curriculum for 4 years, she didn't feel behind because she wasn't failing), it also provided the opportunity to really approach math in a completely different way.