"A Little Bit Behind"

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, B² always equals A² + (A+B).  A²+A=AB, and AB+B=B².  So:  consecutive squares are always separated by consecutive odd numbers.  And they say nursing a baby sucks up brain cells.