The New Old Math

            Math and I are formidable foes and I have written about our rocky relationship before.  But there’s a new twist to the story of late-- one I think you’ll enjoy.  For those of you who’ve been following along, I’m in graduate school to get a masters degree in teaching elementary education.  I mention it because the class I took this semester was in how to teach young children math with Cognitively Guided Instruction or intuitively—in other words: letting the child solve the problem the way he or she instinctively wants to.  “Intuitively?!” you exclaim.  Yes, you heard right.  The entire gist of the class and the bedrock of the two textbooks we worked from was this: allow kids to arrive at the answer the way in which their brains naturally get them there.  “What!?!” I hear you blathering, “but that’s the opposite of how I learned math as a child!  I spent hours learning logarithms that made no sense and buckled under the weight of wrote memorization drills.  I remember fear, anxiety and being told I was doing it wrong as if it were only yesterday.”  I know, pal.  You and me both.  Calm, down, you’re sweating a little.  Are you okay?

            The idea is that children show up the first day of kindergarten with a robust brain full of informal or intuitive knowledge of mathematics—just ask any four year old what to do with one cookie when his sister is sitting next to him in the back seat of the car.  Break it in half.  That’s intuitive problem solving.  That’s math.  Over the years, addition, subtraction and multiplication become organic extensions of what little kids already know, and they know a lot.  Then, with any luck, your young child will get a teacher who has been taught that creating a positive attitude about math is not only important but germane to her bright future.  No more fear—a lot less shame.

            Imagine a teacher who is actually paying attention to how your child is thinking not just what he’s thinking.  Imagine a classroom where as much time is spent discussing wrong answers to fraction problems as correct answers.  Imagine a pedagogic ethos wherein children are not only taught to learn from their mistakes but actually come to understand mathematical concepts by exploring mistakes, locating the exact spot where her brain jogged left when it should have jogged right, then letting the child enjoy the excitement of an ‘aha!’ moment, where she notices what she did wrong herself.  That’s right, folks, in this math utopia, the teacher doesn’t publically tell her her answer is wrong, the student locates the problem-- perhaps in concert with a peer partner or group-- then fixes it.  Together.  I know.  It sounds crazy to me, too.  But it’s amazing.  And it works. 

            If children learn early math concepts they way that makes most sense to them—by counting on fingers, drawing pictures, talking out loud, or moving legos, pretzels or ‘manipulatives’ around in groups on a desk or rug, they’re more likely to get it.  And if they can help each other and arrive at the answer by reasonable group discourse, (the way adults do in many, many career fields) then maybe the harsh competitiveness of math will be removed long enough for your child to actually feel free to fail and therefore learn.  And don’t worry-- if you think they’ll be counting on their fingers forever, they won’t be.  It’ll take too much time and they’ll become impatient and eventually a classmate will show them how to skip-count by tens or multiply instead of add and they’ll happily jump on that bandwagon.  Who wouldn’t?  It’s our nature to embrace the shortcut-- to evolve and improve. 

            Once the basics are embedded, children are encouraged to see oncoming new math strategies as compatible layers to an involved and fascinating game-- the way they learn the rules for Pokemon trading card duels or professional baseball line-up strategies.  They’re much more likely to remember the algorithms—those slippery rules and strategies-- because they’ll make sense.  If children can approach an algebra problem the way they approach a video game, with curiosity, gumption and the resolve to keep going until they find the gold coins or the trap door or the answer for what x stands for—just imagine!  Imagine not feeling shame when you get the answer wrong, or not comparing yourself to the kid who always seems to know what’s going on when you don’t.  I know, easier said than done.  If only. 

            But it’s going to get better because more and more teachers are going to allow your child’s mind to follow its own path to the answers.  Math will become more like building a snow fort with your friends.  I’ll do it my way and you do it your way and we’ll all meet in the middle.  And if there’s a weak spot, we’ll find it together, and work through to improve it, with persistence and resolve-- as a team of learners.  As a mighty force for mathematics good. 

(Author’s note: Download: “The Kindergarten Files” on iTunes for shining examples of this exciting revolution in learning or read Thomas P. Carpenter et al.’s “Children’s Mathematics: Cognitively Guided Instruction, 1999)

Winter's Last Quiet

It’s odd to be writing an essay about spring when it’s 33 degrees outside.  I feel like I do when I have a miserable hacking cough and I can’t recall ever not coughing.  I honestly get to the point in week five where I cannot remember a point in time when I didn’t cough my way through the day and wake myself up coughing at night.  I acclimate to my new reality as Lifetime Cougher and accept my fate.  I even embrace the shreds of tissues bulging my pockets and the skateboard ramp’s worth of pillows on my bed as part of my life forever.  And then, miraculously, my cough goes away.  I say ‘my cough’ because by this time it has become a part of me, and though I try not to let it define me, it does.  Then eventually, I reach a moment in time when I can’t remember coughing.

At this point in the year, I can’t remember not being cold.  And cranky, and sure, okay, maybe just a teensy bit depressed.  And yet, I am hopeful-- but cautiously hopeful.  Like when I’m waiting for the dream job offer to come through.  It’s almost as if I don’t really believe it could happen to me.  I mean, spring is for the lucky ones, isn’t it?  Like slender ankles and personal chefs-- it’s for people more fortunate than I.  Or maybe I don’t want to believe spring will come so that I won’t be disappointed if it doesn’t arrive this year.  I suppose it could happen.  We could be bypassed.  Winter practically bypassed us last year; maybe it’s spring’s turn.

All of this makes me slightly miffed at the flowers poking through their crusty earthen shell when I should be over the moon.  “Look at you, Snowdrops,” I sneer at them as I walk through the icy slush up my driveway.  “You ninnies,” I say.  I can still see my breath.  “And you, crocuses, don’t be so daft.  You are way too soon, my friends.”  It’s as if they’ve arrived too early for a party that was cancelled.  I feel bad for them but am also wondering why they didn’t double check the evite before heading out the door.  And yet, they know a thing or two about a thing or two.  The flowers and forsythia have intel we can only dream about.  They know, without an iota of doubt, that spring is coming.  They are hopelessly optimistic and so I have no choice but to respect them.  Deeply.  I take back my slanderous jibes.  I beg their petals’ forgiveness.  Then, I relax a little.  Spring is coming, like the mail and grey hair.  I can bank on it, so I do, and this frees me up to enjoy the last vestiges of winter for it’s most glorious attribute: quiet. 

Spring, with all its allusions to rebirth, will bring with it the screaming wails of leaf blowers.  The dulcet tones of distant planes and falling snow will be replaced with the near-constant whinny of bands of roving landscapers, hired by homeowners who are—for the most part—not home to receive this daily aural barrage to the senses.  Napping children, stay-at-home moms and work-from-home-ers will be assaulted by this relentless grating, wondering how they inadvertently landed in houses purchased on the center median of a thousand lap Nascar race.  Then, when you can’t remember a time when there weren’t leaf blowers boring into your soul daily, they will stop.  And be replaced by lawn mowers and air conditioners. 

The near-constant throbbing grind of air conditioning units will blanket the bird’s song and the wind’s caress like a local oil refinery might, and follow us like inescapable tinnitus throughout our October days, when even the cool 65 degree night breezes won’t give them pause.  This seemingly final crescendo of leaf blowers and air conditioners will follow us right up until the end of November, when quiet will re-emerge once again.  Late autumn yards with gorgeous Japanese maples and oaks will preside over the naked, leaf-less lawns of Texas, bereft of the vestiges of why some of us chose the North East and not the desert in the first place.  It’s then that I’ll finally take out the earplugs that I’ve been wearing for seven months during the day and through out the night.  I’ll open my windows for a week or two before doing so would be like throwing heating oil money out the window.  By then, of course, the cicadas will have headed to Miami along with the blue jays, and the leaves will no longer be around for rustling. 

I get why people use landscapers’ leaf-blowers instead of raking, I suppose, and I turn on my own air conditioner at times.  I’m being a cranky hypocrite because winter has lasted so darn long this year and I’m just so ready for it to be over.  But, I will force myself to cherish its last few days.  I will strive to live in the present and enjoy the budding roses, the slow shedding of down coats and the calming effects of tranquility.  Because soon, before I know it, I will have forgotten what it sounds like.  I will have forgotten the exquisite peace of quiet.

The Savings Time

I love the arbitrariness of Daylight Savings Time.  Like national events that don’t really fall on certain presidents’ or civil rights activists’ actual birthdays, Daylight Savings Time has an almost legendary air.  It’s a fluid concept historically, one that ebbs and flows depending on the whims of those in power at any given moment—not unlike Turkmenistan’s first President for Life, who renamed all the months just because he could.  He renamed April after his sainted mother, Gurbansoltan.  He also re-named the days of the week.  My personal fave is Hosgun or Favorable Day, which used to be Wednesday.  Good luck booking a flight to Turkmenistan. 

I’m thinking of writing a thank-you note to 2005’s US Congress who passed the Energy Policy Act, which moved DST three weeks earlier beginning in 2007, from Gurbansoltan to Nowruz—formerly March-- and one week later to Sanjar—formerly November.  The theory was that we as a nation would use less energy to light and heat our homes if it were not so dark so early in the evening.  But, like the nation of rogues that we are, Hawaii, American Samoa, Guam, Puerto Rico, the Virgin Islands and Arizona, don’t pay it no mind. “Feh, to Daylight Savings Time,” I can hear them collectively saying.  Although how one gets the top elected officials of Arizona and Samoa in a room together I’ll never know but I’d like to be a fly on the wall at that brunch.

I, for one, believe that Daylight Savings Time is misnamed.  Do we really feel like we’re ‘saving’ anything—really?  It’s like some parent has dressed up broccoli by calling them ‘tiny trees from Little Land’ in order to get us to eat our vegetables.  I don’t know about you but I’m asleep at 2am most nights.  But I am a saver by nature.  Why, just the other Favorable Day, I offered my girlfriend these super fancy Italian cookies to have with our tea when she stopped by.  Actually, I didn’t offer them, she discovered the large tin of Lazzaroni Amaretti Di Saronno cookies in the back of my uppermost shelf of my dry food cupboard.

She said, “What are these?  Oh, my goodness, I love these.  Can we eat these?”  She’s taller than me and doesn’t stand on ceremony.

“Sure, get them down,”  I said and opened the tin.  It was still half full.

“Are you saving these for some occasion?”

“No,” I said.

“Are you saving them for someone more worthy than me?”

“Clearly.  But since you were able to reach them, you are now worthy.”

My girlfriend reached in and chose one of the beautifully wrapped duets of cookies in the delicate pastel inscribed paper that sounds like rustling taffeta.  She unwrapped one and smelled it. 

“These are bad.”

“What?!” I said.  I loved these cookies.  They practically melted in my mouth—so subtle, so perfectly sweet with that touch of almond.  I was heartsick.

“We have to throw them out.”  She was right.  She added, “What were you waiting for?  You save too much.  Your life is passing you buy and meanwhile fancy Italian cookies are going bad right under your nose.  This is a crime.  You could literally be jailed for this in Italy.”

I was speechless.  All I could do was stare at all those tumbling little bundles as she shook them into the garbage.  Probably fifteen or so of them gone.  My girlfriend continued to lecture me like only a good friend can, “You’ve got to burn the fancy candles, eat the good cookies and spend the gift certificates.  This is your life.  Stop waiting for the right occasion or the right person to drop by.  You’re the right person and right now is the right occasion.”

“Okay, okay,” I said.  “I’ve got some champagne I’ve had chilling for about a year in the basement fridge, you want to pop it open?”

“It’s ten in the morning.”

“Right.  Good point,” I said, “I promise to eat the good cookies from now on.  And stop saving so much.” 

She was right, of course.  Maybe we should rename Daylight Savings Time.  Maybe we should call it Sleeptime Wasting Night.  Or Extra Christine Time, after my mother, the famous martyr.  Either way, it’s time that should be well spent-- like having an impromptu cup of tea with an old friend.

I sipped the warming tea then remembered something else I was saving.  I leaned down toward the floor and reached deep into the pots and pans cabinet and pulled out a bag of special treats.  Turning the clear zip-lock over for display, I said, “Please choose whatever you like.  There is no one more worthy than you, my dear friend.”  She rolled her eyes and shook her head then reached into the bag for a piece of my son’s Halloween candy.

Carniverse

I saw the most extraordinary thing in the parking lot at Whole Foods.  When I came out it was right next to my car.  It was an ordinary car on the outside, an older model two door Honda Civic of some kind, maybe dark green.  The extraordinary part was its interior.  “Wow,” I said out loud.  I couldn’t help myself.

The car’s owner had decorated the entire dashboard, console, steering wheel, door panel and ceiling with miniature trinkets.  There were myriad little figurines with smiling faces-- most of them plastic-- all standing up right and packed in tight like a crowd scene in a big-budget action movie.  There was a delicate wire tree with a watch face hanging at the end of each of its branches.  There were beads and goddesses, planets and birds, crystals, stars and flowers—all of them co-mingling, as if at a sunny, crowded day at the fair.  The ceiling alone was impressive on it’s own merit.  Hanging from every available inch of real estate were earrings and key chains, more planets and pearls-- a dangling canopy of its own constellation.  All the stars hung within reach, just above the driver’s head, just grazing his or her thoughts.  I imagined the enchanting sound they made every time the car lurched to go or came to a stop.

A love of tchotchkes and an exacting way with a glue gun had figured prominently into this fanciful auto escapade but so had something else—permission.  The owner of this car had given him or herself permission to turn his car into a canvas.  She had given herself license to buck social convention in order to create a fantasy universe of whack-a-doo whimsy right inside her car.  This was one brave artist whose passion had a total disregard for social criticism or external judgment.  How freeing that must be.

I stood outside the car, peering in.  I longed to sit in the driver’s seat of this mobile museum, to sweep my fingers gently overhead, a tinkling of tin and plastic in my fingers’ wake.  A few folks passed by with their groceries in hand.  I invited them to stare with me.  “Check this out,” I said, “Have you ever seen anything so wild?”  Apparently they had because they didn’t take the time to look.  Fools! I thought.  If this car were in an art gallery you’d look.  If some big museum anointed this car with the label of American Folk Art, you’d pay admission to look.  Don’t wait to be told!  I thought, see art everywhere!  Find it for yourself!  This is your chance.  But they didn’t take it.

I stood for a while longer then went back inside to eat my soup at the window counter.  Surely the owner would be easy to spot.  A woman, maybe, in her sixties, with a multi-colored boiled-wool cape and big red glasses frames with chunky jewelry.  I expected lime green leather shoes and dread locks.  Maybe a turban, if I was lucky.

I watched people approach their cars and drive away—none of them fit my profile.  Then a woman walked by my window.  She looked to be in her late thirties with mousy brown hair pulled into a low ponytail.  Her glasses frames were no-nonsense, as were her clothes: dark winter solids with clean, simple  lines.  I would have ruled her out immediately, but something told me to hold my gaze.  Incredibly, she weaved closer and closer to my car and then—voila—her key went into the ignition of That Car!

Was this the mad, passionate artist?  The glue-gun maestro?  I wanted to talk to her, but I was too slow.  I wanted to ask her how it began and have her point to the piece that started the whole thing.  I was curious about the progression, how long did all of this take?  I wanted to ask her what else in her life she’d rendered dazzled and what was her house like.  But mostly I wanted to find out what else she’d given herself permission to do.  Had she ever been a stowaway?  Had she taught herself how to snake charm or mastered the hula dance?  In what other segments of her life did she throw caution to the wind—convention be damned?  Because once you’ve created the entire universe inside your car, the sky’s the limit.

All the Teds in the World

(sung in the style of an Irish pub drinking song)

There once was a boy, a little lost boy

This bo-oy grew into a man

He harbored the aching, then buried the quaking

Fell deeper inside of his mind.  He was clearly that kind.

He busied himse-elf, books lining the shelves

Doing work of the angels he simmered

In silence he lear-rned, while his body churned

Padding the depths of his room.  His bed a soft tomb.

(Chorus)

Alllllllllllllllll the Teds in the wooorrrrrrrld

The Johns, Joeys and Earls

Who can barely contain

Allllllllll_ the-Steves, Bills, Bobs and Daves

Who succeed in behave-ing

Hide their sweetness in pain, though their hearts they disdain,

They never complain

There once was a girl, a lost little girl

This girl never did learn compassion

She toyed with the boy, gave him glimpses of joy

Then left him to question his mind.  She was clearly unkind.

She grew very pretty, moved to the big city

Swept the lost boy’s love aside

Eschewed his amends, then collected boy friends

Delved into their bodies and looks.  She stopped reading books.

(Bridge)

Some Ricks, Sams and Dougs may speak volumes with shrugs

But their lips they rarely do pa-a-art

The Vincents and Simons whose insides are dyin’

Are cryin’ their eyes out with shame

With no one___ but themselves___ to blaaa_a-aaa_a-aame. 

One day she was older, the nights had grown colder

Her boyfriends had lost all their luster

Craving a bright mind, someone witty and kind,

She exhumed the lost boy from her past, knowing his love would last.

He answered his phone, to her he was still prone

She’d papered his thou-ghts for years

When he heard her voice, he knew his only choice

(Was to gi-ive her a second chance.  Then he hung up and danced.)

OR (Was to hang up and finally be done.  He smiled knowing he’d won.)

(Repeat Chorus)

Defending America

I always had a job.  When I was fourteen I got a position as a candy concessions girl at our local movie theater, but really I’d babysat long before that and would waitress for many years thereafter.  Because I loved to travel more than anything I lived in a perpetual state of earning money for my next trip.  During my twenties, instead of eating in swank restaurants, buying designer shoes or having a nice one-bedroom apartment to myself, I ate at diners, wore second-hand shoes I bought off the street, and lived in inhumanely small apartments with strange roommates in lousy neighborhoods.  I spent the money I earned on plane tickets—chiefly to Europe—patiently watching the airlines for fare wars then pouncing when prices fell.  Any time a friend of mine or a friend-of-a-friend ended up anywhere in Europe on a student visa, a work visa or—in the case of my Philippina girlfriend, long story, stuck in Paris and unable to return to the states for five years-- I visited.  If I met you on the F train, or at a roof party or waited on your table, and you lived outside of America, then I’d come visit you.  It didn’t matter where.  I just wanted to be not here.

The more countries I visited and the further afield I traveled the more often I found myself in the peculiar position of Defender of All Things American: Including but Not Limited to All the People, their Customs, their Many Foibles, the Government and its Stunning Catalogue of Incompetency, the Ineptitude of the Educational System, All Crass Major Motion Pictures, Delinquent Rock Stars, a 20 Year Span of Bad Television Re-runs and Fast Food.  The onslaught could be overwhelming.  What might start out as a modest get-together of gracious locals looking forward to practicing their English with an American visitor often ended up with me getting the third degree.  “You Americans all think you’re so…” or “You don’t even bother to learn…” or “Your president is so…” pelted me through my smile.  Sometimes I would try to defend Whatever it Was they were so irked by and sometimes I let them vent.  But, I wasn’t there to get lambasted and I had no interest in proselytizing.  I was there to flirt with cute guys, look at cool clothes, check out architecture and eat cheese.  But they were going to make me work for that cheese.  I would have to earn that hazelnut chocolate, the Belgian beer, the kugel and fresh figs.   

I had not majored in political science and was a naturally feeble debater.  I knew I should have an eloquent show-stopping speech ready where I would wax about our constitution and the genius of it’s forethought, its exquisite malleability via the amendment process, and our peaceful transition of power every four or eight years.  What a marvel is America!  Why do you trash-talk it so?  But to be honest, I sometimes agreed with what they were saying.  They occasionally had a point.  So, I suffered through these awkward diatribes until my next run in and eventually became inured. 

What was curious to me, though, was the reaction I seemed to have, time and again, upon my return home.  Sometimes it came to me as early as my wait at the luggage carousel at JFK.  Some old broad with a voice like gravel, resplendent in leopard would say something absurd to a cabbie in a thick Brooklyn accent and my heart would sing.  Or some wry graffiti would catch my eye my on first day back and make me laugh out loud in a public restroom.  Or I would bite into a slice of local pizza and swoon.  Each of these moments caused me to relish another singularly American phenomenon.  I was home again, at long last, and with each return, I fell more deeply in love with America. 

We are a grand experiment still—a great collaboration between the educated and the instinctual, an unlikely amalgam of the exquisite and the crass.  We are doing the best we can, except for when we could be doing so much more, which is nearly always.  But we know that about ourselves and we’re working on it.  We are a national work in progress, yes, but one teaming with such creativity and humor—and passion.  Our freedom of expression informs us in some way, everyday, in so many tiny little ways that we can’t help but take it for granted.  So when our President is inaugurated and my son asks me about our government and constitution, I want to yank him off the couch and put him on a plane.  I want to take him somewhere where he will see how people eat fresh food in small portions and live at a reasonable pace among the carefully carved stone facades of beautiful, majestic buildings, then I will return him home, to where it’s complicated and messy, sometimes ugly and often uneven.  And so implausibly great to be American.

Singing Our Hearts Out

My father’s mother, Alice, was a divorcee in the early forties back when there weren’t many around.  Her shoes and bag always matched her hat and she wore a size 10, even though she was a size 14.  If Alice was lunching at Lord and Taylor she would pull a little bottle of vodka from her purse and add it to her beverage because she maintained, “It’s uncivilized to not have a drink with lunch.”  She went to Elizabeth Arden once a week where she got her hair done along with all the gossip about movie stars in town.  She never went out in the sun and as she aged semi-gracefully, passersby mistook her for the Queen Mum. 

Alice was a concert pianist who never played the piano.  She enjoyed the single life in Manhattan and had many friends, most of whom were gay.  At the parties she went to there was always a fair amount of singing.  Alice loved to sing and most everyone in those days had a piano, even if it had to be lifted into your 9^th floor apartment by a crane.  Not wanting to be caught unprepared, she kept a list in her purse of all the songs that she knew all the words to, just in case.  If no one asked her to sing, she would sidle up to the piano player and offer her list.  Knowing Alice, if he didn’t choose a song, she probably chose one for him.

When I first heard this story in college, I too, set about creating a list of songs I knew all the words to so that I would always be ready.  Besides twenty or so standards, there were also the titles of various eighties tunes like Roxanne, Heartbreaker and 867-5309.  I kept this list in my purse and waited to be called upon to sing.  My shoes did not match my hat, but I was ready. 

I was never called upon to sing.  Most apartment pianos were long gone and the days when folks stood around a piano and sang at parties were gone, too.  But sometimes if the lights were low enough and the stereo was loud and Billy Joel or Prince came on, we all sang, in unison, at the top of our lungs.  We sang and danced and jumped on furniture and sweated so much that the mousse we’d scrunched into our hair ran down our faces alongside our mascara.  We had a ball singing our hearts out—shouting the lyrics we knew so well.  It was admittedly uncivilized, but it was crazy-fun.  And thankfully, I’m happy to report, if the lights are low enough at parties and the music is loud, it still happens—this crazy-fun singing and dancing. 

The business of singing around the piano, however, is taking more effort to resurrect.  But, it can be done.  It helps if the guests know what will be expected of them, and it helps if you live in a community where two out of three people either sings or dances or plays a musical instrument—or is married to someone who does.  Then, after dinner’s been cleared and the lights have been lowered, folks with pianos sit down to play.  Or if they don’t play they ferret out the guests who do.  And those guests, rather than pretending with false modesty that they don’t want to play or no longer play say, “Why, yes!  What the heck, I’ll play!”  Then the magic happens. 

This past holiday season I witnessed it all come together beautifully.  The piano player began with a few recognizable favorites and one or two ringers were tapped to mosey over to the piano and sing.  People came out of the woodwork, edging closer like moths to flame.  Before we knew it, there was a robust group singing round the piano and many more joining in from the sidelines. 

The words on the sheet music for some of the more obscure songs were printed in tiny font, which drew us closer together, huddled over the pianist like a squinting scrum.  He persevered under our elbows as a table lamp was moved closer to the music stand and folks found their glasses.  Then a standing lamp was plugged in and a cell phone flashlight was aimed.  We chuckled at our poor eyesight and laughed when the piano player commanded us to sing the last verse, “Now, in Latin!”  But we sang our hearts out and it was marvelous.  My list is long since gone and my shoes still don’t match my purse, but Alice would have been proud.