Go forth and multiply

“Six times eight?”  I asked.

I looked at Molly expectantly.  She didn’t look back at me – but that didn’t mean she wasn’t paying attention.  Her eyes roamed upward, then wandered left -- vast, blue, and unfocused as a summer sky.   Two seconds went by.  Five seconds.  Eight.  I could practically hear my kid’s synapses overheating. 

“Forty-eight!”

“Excellent!” I beamed at Molly with all the positive reinforcement that my bored, fidgety parent-self could muster.  But at the same time, I wondered – did my eight-year-old simply have a pathetically slow time-release on her powers of recall, or had she spent ten seconds actually calculating the answer?

On a math test, of course, it would only matter that ten seconds per answer is at least six seconds too long. Both my third-grade twins are required, by the end of the school year, to be able to answer (legibly and correctly!) fifty-six multiplication problems in under four minutes.  From the point of view of the unforgiving Speed Test clock, how they obtain the answers is immaterial.  From my point of view, however, the details of that invisible mental mystery make all the difference in the world.

(To the friend who has previously groaned, “Nancy, you’re mathing again” – yes.  Yes, I am.  My apologies.  Stop here, while you’re still safe.)

“So, Molly,” I asked casually.  “How did you know that six times eight is forty-eight?  Do you have that memorized?”

“No.”  She sighed.  Molly hates memorization.  Like, really, really hates it.  I try to push her on the things that matter – yes, you really do need to know your own address and how to spell “enough”– but when it comes to stuff like state capitals my heart isn’t in it.  I, too, suck at rote memorization.  Yeah, I’ll tell you where you can put all your state capitals.  You might think you want me on your Trivial Pursuit team, but, truly, you do not.  I will embarrass you.  I will embarrass myself.  I will not only fail to know anything about pro sports teams and soap operas (knowledge that I might snobbishly decry as plebeian), I will also fail to know anything about the Vietnam War, the Great Lakes, and any Vice President, ever.

“So, how did you figure it out?”

Molly’s answer was as rapid-fire as it was matter-of-fact. “Well, eight plus eight is sixteen.  Then I added another eight to make twenty four.  If three times eight is twenty-four, then six times eight is twice that much.  Twenty-four plus twenty-four is forty-eight.”

Yes.  Of course.  Because multiplication is not only commutative and transitive, but also distributive.  We all know that, right?  Right?

Molly’s line of reasoning seemed pretty good to me, as a ten-second effort by an eight-year-old – especially given the fact that math has been politely described by Molly’s teacher as “maybe not her best subject”.  Thus, I was moderately impressed.  But I was even more impressed with the math curriculum that got her there. 

I should pause here to admit that I know squat about curriculum development. I’m only a “teacher” in the way that many college professors are “teachers”: we earn a PhD in some esoteric subject such as “Species-Specific Effects on the Oxygen Isotope Ratio of Tree-Ring Cellulose,” and are then plopped down in front of a roomful of sleep-deprived teenagers and told to teach them Biology 101.  We have zero clue as to how to create the complex environment of excitement, engagement, and challenge necessary for learning.  We haven’t the faintest idea how to teach to different leaning styles, different skill levels, different majors, different genders, different socio-economic backgrounds, different shades of nail polish, whatever.  We’re also huge dorks, and the whole class knows it.  But I digress. 

In thinking about curricula, I can really only compare the way I was taught and the way my kids are being taught.  When I was in third grade, Mrs. Ricco tried to perk things up with cheerful bulletin-board displays depicting multiplication-airplanes flying across a colorful map.  None of us, however, were provided with any strategies for learning beyond rote memorization.  Purely as an avoidance strategy, I figured out ways to “cheat.” The nines and the fives were easy; I could multiply by ten and then either subtract, or divide the answer in half.  The twos and threes could be mastered via simple adding.  The fours were the twos doubled, and the ones and zeroes were obviously just silly.  The only facts I truly memorized were 6x6, 6x7, 6x8, 7x7, 7x8, and 8x8.  That I found it difficult to learn these six paltry problems shows just how dysfunctional I really am.  Nonetheless, I managed to be the first kid in the class to “fly my airplane across the map”.  I felt guilty about that achievement – because, secretly, I was cheating. 

A few months ago, Lizzy’s teacher sent an email to all us parents.  “Thanks for your concerns,” the message said. She explained that the school has a new math curriculum this year – EnVision Math, by Pearson Realize. “Yes, the bar has been raised. Kids' math grades are a direct reflection to the rigor asked for. They are learning....they surely are. It's just that we are so used to higher grades. . .”

“Okay, Lizzy, your turn.  Seven times nine?”

“Sixty-three.”  Two seconds.  “I did ten sevens minus one seven,” she offered.  Lizzy is a better memorizer than Molly, but it seemed that she, too, was using other strategies.

I answered that email.  I wanted that hard-working, dedicated teacher to know that I didn’t give a rat’s ass what my kid’s grade was, so long as her brain was being stretched.  (I didn’t use those precise words.  I’m, like, a PTA member and whatnot.)  As far as I was concerned, the new math curriculum – despite some laughably awkward problems pertaining to Grover Cleveland and/or the booking of conference rooms -- looked a hell of a lot less lame-o than the previous one. 

What impressed me about it?  Well, I liked the fact that the kids were offered a host of different strategies for rounding numbers and estimating answers.  Not calculating – estimating.  In other words, they were being taught the kind of math that you might do as you toss items into your grocery cart, if you’re on a tight budget and don’t want to humiliate yourself at the register.  “What is a reasonable answer?”   Holy shit.  My brain exploded.  Because, teaching at the college level, I’ve faced students who chugged through all manner of complex calculations, and then gave me answers like “-8.4335” when the units in question were “fish”.

Second, I noticed that the twins’ worksheets used a lot of story-problems.  Yes, yes, yes!  In the real world, when you need to decide whether you have enough time to drop off the library books between the end of swim practice and the start of your dental appointment, the relevant numbers don’t appear printed on your dashboard, complete with +, -, and = signs. To me, it seems obvious that a kid needs to really, really understand what multiplication is – and some of the many situations in which it might be useful – before settling down to practice and memorize.  But when curiosity drove me to look up online discussions and comments about various math curricula, use of story problems popped up as a common criticism.  “EnVision Math doesn’t make sure kids know the basics before moving on to word problems!”  The basics?  Real life IS basic.   

“All right, Molly.  How about seven times three?”

“Twenty-one.”  The delay was too long.  She was adding.  But, heck, at least she knew enough to add seven three times, rather than adding three seven times.  “It’s an array.  Of course it’s the same either way.  You could just turn it around.” 

Third, the new curriculum demanded that kids write answers in words.  I don’t just mean answers like, “Tommy has six blocks.”  I mean answers like, “Tommy is wrong when he says that he will have ten blocks left after Susie takes two of his eight blocks.  He added instead of subtracting.”  Dubbed “Writing to Explain,” this is pretty much on par with rocket science, to an eight-year-old.  It is not a particularly popular activity at homework-time at our house -- but I love it.  Because… logic.  Because, kiddo, for the rest of your life, people will try to fool you with math, with graphs, with statistics, with numbers.  But you WILL NOT BE FOOLED!

How desperately do we need these skills?  Well, a New York Times article, succinctly titled, “Why Do Americans Stink at Math?” http://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html?_r=0 gets into all the grim details of our comparative international patheticness.  At the core of the problem is the difference between doing math problems and understanding math. 

It wasn’t until I was in high school -- and a proud T-shirt-wearing member of the Metropolitan New York All-Stars Math Team -- that I started to have an inkling that maybe I’d been doing it exactly right, all along.  These ideas gelled when I was called upon to step up to my first paid teaching job.  I was sixteen.  My long-time neighborhood buddy – who far outshone me in social skills, creativity, knowledge of pop culture, and ability to get the damned basketball through the hoop – had bombed the math section on the practice SAT.  Her parents, pragmatically, decided to hire the cheapest tutor available:  the Insanely Nerdy Friend.  Sitting at my neighbor’s kitchen table, I soon realized that my smart and vibrant friend could do any problem she was asked to do – but only if she was told precisely what kind of problem it was.  This was how she’d been taught.  It was utterly useless.

Newsflash:  in the real world, figuring out how to set up the problem is not just important, it’s everything.   Want to bake only 2/3 of this gingerbread recipe?  Want to know whether you can afford monthly payments on the house, the car, AND that sweet new snowmachine?  Need to understand the relative risk of vaccinating your child versus letting them get polio, for chrissake?  We have computers for any really serious numerical grunt-work -- but if you don’t understand the question you’re asking, you have NO HOPE of understanding the answer.

It’s not like I’m the only person who knows this.  As noted in that NY Times article, Americans have so poor a grasp on what fractions actually are that when A&W released a 1/3-pound hamburger to out-compete the McDonald’s Quarter Pounder, people didn’t buy it.  They thought it was a bad deal – because it was, like, smaller.  “Focusing only on procedures… turns school math into a sort of arbitrary process wholly divorced from the real world of numbers. ..  Instead of trying to convey, say, the essence of what it means to subtract fractions, teachers tell students to draw butterflies and multiply along the diagonal wings, add the antennas and finally reduce and simplify as needed.” 

I cringe.  I mean, consuming more cheap ground beef is probably not the solution to America’s problems, but… death to the butterflies. 

I highly doubt that the new math curriculum at University Park Elementary School is perfect.  (Seriously, what was with the problem about Grover Cleveland?)  The teachers are struggling with it.  Some of the kids are struggling with it.  Clearly, many of the parents are also struggling.  I’m sure we could all fault it.  But if I do pick holes in it, it certainly won’t be for its valiant efforts to teach kids to understand, to think, to look at everything in more than one way, and to relate everything back to the real world.

Last week, when the twins bounced off the school bus in the afternoon, Lizzy immediately chirped, “Guess what?”  That’s how kids set up dramatic tension in a conversation.  “Guess what, Mom?  I passed the Speed Test!”

I congratulated her with genuine enthusiasm.  She’d memorized a bunch of math-facts to get there, and those facts are useful enough to be well worth the effort.  We do, indeed, all need to be capable of answering 56 multiplication problems in under four minutes. 

“Good job!  Nicely done!”

Then I looked over at Molly, who appeared to be examining her boots.  She can answer 56 multiplication  problems, too – but not in four minutes.  Maybe in eight. 

“Don’t worry, you’ll get there too.  You just need a little more practice.  Let’s see, what’s eight times nine?”

[Boot-crunch on packed snow.  Rumble of a distant truck.  Rustle of snowpants.]

 “Seventy-two.”

Think on, America.  Think on.