I did some rearranging of old posts, so that the Homeschooling category now contains most of what I've written here about homeschooling. Some of the questions that followed my last post on homeschooling have come up before, like what about socialization, and (in that same post) what about subjects I can't teach, and what about unschooling. (I've been thinking more about unschooling lately, though, and roughing out another post on why it's not a good fit for me.)

Also: let me be clear that I am no paragon. As you imagine me going through the morning I described last time, imagine my hair getting wilder and wilder as I run my fingers through it. Imagine Os glued to my shoulder by means of Pete spit. Imagine me losing my temper a couple of days a week, and hitting my goals with decreasing frequency as the semester progresses. All right? Got it?

Today I wanted to write about how we tackle math. I left AmyinMotown with the mistaken impression that we just don't do math, and she's probably not alone. So let me hasten to clarify: we do math! We like math. We just don't use a particular math curriculum, and I don't own any math workbooks, and I would prefer fleas to flashcards. I am a relaxed math homeschooler. Sort of.

My husband has a PhD in a field that required years and years of math coursework, and his math skills pay our mortgage. His perspective is skewed, because his professors were forever saying things like, "You all learned topology in junior high school, right? Vector calculus in preschool?" We were driving home tonight and he was talking about the boys' math skills. "They're a little bit behind--" he began, and I immediately began to excoriate myself inwardly. Because Alex doesn't have his 6/7/8 times tables down perfectly, and Marty is wobbly on his addition, and even though they can both come up with the right answer eventually maybe eventually isn't good enough -- but then I noticed the sly grin on my husband's face as he finished his sentence: "--on differential equations. They're supposed to learn those in kindergarten, after all."

So maybe we have an anomalous definition of relaxed.

But I like numbers. They please me. When my oldest son was four he
begged me to play math games with him -- I would tell him a silly
story, about when the bedbugs played the roaches in baseball, and he
would have to keep score when the roach pitcher hit a surprise triple
with the bases loaded. (Early math skills *and* the evils of a designated hitter, all in one fun lesson.)

For years I thought I was bad at math, but really I was bored at math. Halfway through a homework assignment I would start thinking about other things because I GOT THE POINT already; I knew how to multiply two two-digit numbers. Yes, sustained attention is important, but I know with utter certainty that seven eights is 56. Any additional drill would be wasted time. I don't want to waste my children's time.

So here's what we do: Marty and I just play math games. For Alex I pick a topic each week. He works for fifteen minutes on a particular type of problem. Some weeks it's straight-up arithmetic -- times-table drill or similar. Other weeks it's something else entirely. This is how you find the slope of a line. This is the Pythagorean theorem. This is how you solve two equations in two variables.

I used to worry about this approach. Was it appropriate to play around with division when he didn't have his addition facts down pat? And then two years ago I read a fascinating article for my professional continuing ed requirement. Children, the article said, don't learn in pyramid fashion. You don't have to lay the first row of blocks down like so much granite, and then draaa-aag the second row of blocks up on top. Learning is more like a spiderweb, in which you make connections all over the place. You can learn more complex skills at the same time that you're perfecting simpler ones. (The authors were writing about a different domain, but I think the comparison holds.)

The arithmetic facts are coming along just fine. My third-grade son
can subtract 38 from 64 in his head without batting an eye. And!
Actually! That's a story in itself: I was trying to encourage him to
play with two-digit subtraction in kindergarten and he was reluctant.
"You know what 60 minus 30 is," I said. "And you know four minus eight
is negative four." A light bulb went on for both of us. He knew that
30 and -4 yielded 26. And I understood, suddenly, why we teach kids to
borrow. For 25 years I had done it by rote, but in that moment I
understood what I'd been doing all that time, and that it wasn't the
only way to get to the answer.

Recently I was talking to a homeschooling friend who says her boys do ninety minutes of math every day. I'm didn't say what I thought, which was AAUUUGGGHHH! NOOOOOO! I'm just not convinced that ninety minutes of math drill is a good idea for an average first-grader. "Drill and kill," Elizabeth Foss calls it.

My goal as a math teacher is to help them acquire solid skills, sure. But at the same time I want to impart three other lessons as well:

**Math is fun. ** My husband found a book for Alex called The Number Devil. He loves it -- he's read it six or eight times. Who knew you could laugh about prime numbers and the Fibonacci sequence?

**Math is interesting.** One day in ninth grade I noticed that
squares are separated by consecutive odd numbers. One night fourteen
years later, as I was lying in bed nursing a 9mo Alex to sleep, the
explanation dawned on me.* I love finding patterns and I hope my boys
will too. The order I see in the mathematical world reflects the
beauty of creation's order. It makes me happy.

**Math is useful.** If you are saving for a Lego set and there's a
15% sale coming up, how many weeks of allowance is that?

Math matters. Math is doable. That's what I want them to know.

*Some of you will find this obvious and some will find it a snore,
but here it is if you're interested: for consecutive numbers A and B, B^{2} always equals A^{2} + (A+B). A^{2}+A=AB, and AB+B=B^{2}. So: consecutive squares are always separated by consecutive odd numbers. And they say nursing a baby sucks up brain cells.

Jamie, you rock. And you hurt my head, at the same time. You KNOW I'm not friends with Math. I don't like it and can't do it.

Hats off to you, my friend.

Posted by: Carmen | January 09, 2006 at 02:12 AM

Math. I have a similar husband to yours, with the extensive math knowledge. His students gave him the "King of math tricks" award a few years ago at the department end-of-year get-together. I am no math slouch myself, but I have a hard time with the subtraction in my head. I like to pretend that it is because the calculus shoved out the simple arithmetic.

I may be a dork, but I love that thing about the consecutive numbers squared. I have never seen that before.

Also -- Fibonacci numbers. WHAT GOOD ARE THEY? I mean, they are nifty and appeal to my orderly little brain, but is there a use for them? Do you know? I remember doing computer programming in high school and one of the things we did was to make the computer spit out Fibonacci sequences, but WHY? WHY WHY WHY??

Posted by: mary | January 09, 2006 at 04:30 AM

I love math, and having gone to college with a bunch of kids who had been homeschooled, I have a secret rage for parents who homeschool and fail to school their kids properly in math and science. It sounds like you're doing a great job; I've got no rage for you, only admiration. Keep it up!

Posted by: Arwen | January 09, 2006 at 05:34 AM

I love math, too, but hated it in school. The orderliness and wonder is completely lost after all the drills. I feel extremely sorry for those kids who do 90 minutes a day. Sounds like a huge waste of time to me, since the estimations are that a motivated kid could learn everything from addition up to calculus in 50 hours. The key is letting the kid get interested in it.

This morning in the whoer I was trying to do the multiplication in my head of the number of different sudoku puzzles possible. (9! x 9!) My mind if definitely not as nimble as it used to be, because I had problems multiplying the 9! out. I suppose if I worked with factorials more often I'd have it memorized anyway.

Posted by: Moxie | January 09, 2006 at 05:43 AM

I'm a bit hopeless with numbers. I have this strange problem...I bet its some kind of LD...but I can't hold numbers in my head very well, unless I can sing them, if I try to picture them they turn into letters, and occasionally I will write numbers as letters, and they are consistent substitutions, 4=H, 3=C, 5=B (see, I just wrote B=B and had to go back and erase). Consequently, I was an advanced student in Geometry and symbolic logic, pretty good at algebra, and a complete numbskull at trig.

Fortunately, I could take logic for my math requirement in college and I was saved.

This is what scares me about the prospect of homeschooling...my kids might learn to count 1, 2 C, H, B, 6 7...

Echoing...hats off...you amaze me...

Posted by: Jennifer | January 09, 2006 at 07:59 AM

I just went back and read your "why we homeschool" post and it is, as always, brilliant. My guess on the Socialization Question would have been something along the lines of your family size in terms of the positive aspects of time with other kids (they are learning to share and take turns and so forth by being part of a somewhat larger family), and that they can be shielded from many of the more negative aspects by homeschooling.

And finally--will you teach ME math? I have a similar LD to Jennifer, I cannot get my head around the language of numbers in much the same way someone with a language learning disability can't unlock words and grammar. Grammar and spelling and what words mean have always come almost instinctively, however. In college, I placed into honors English and remedial math.

Thanks for the post, Jamie. I am fascinated by your approach to homeschooling and excited to read more about your adventures in education. (oh, and thanks for the link. I just revived my blog and wonder if anyone is reading it--but it helps me get my head around things).

Posted by: AmyinMotown | January 09, 2006 at 10:11 AM

Great post!

Posted by: liz | January 09, 2006 at 12:56 PM

I really enjoyed this and it helped me with my own homeschooling second-guessing question of the day. (Hmmm, Rabbit seemed to get this math concept by the third problem. THere are 3 days worth of excercises in the math book. Need we do them all? NO)

Also, if you have not already, I highly recommend getting Math Curse by John Scieszka. Very fun math read.

Posted by: Elizabeth | January 09, 2006 at 05:12 PM

I loved math until I got into High School, when it wasn't fun anymore. Part of what I loved about it was being in multi-grade classes and listening to the stuff that the older kids were learning - and part of it was what was then called "new Math". It wasn't just rote drill and memorization but it was also the reasons behind it. I remember learning about number lines and about different bases (base 10 being the one we most use but in the old British money system we used base 12 and base 20 as well). And the idea that you could write an equation that would make a picture was incredible.

Jamie - you might want to pick up a good translation of Euclid and leave that around. I remember when I looked in our copy (Part of the Great Books of the Western World, which I would have used had I homeschooled!) and learning how to use a compass and straightedge to bisect a line. It was downright fun.

When I got into high school, though, the focus changed and I got stuck with standard math textbooks that were, frankly, boring. Not at all like the School Mathematics Study Group (the yalies who developed 'new math') books that I'd been using. And so I tuned out and started to fail in a subject at which I had once been a pro.

BTW - I can teach almost anything, but I have not been able to teach my kids math. Their dad does that.

Posted by: alicia | January 12, 2006 at 09:40 AM