Those Who Can't, Teach...

I am responsible for helping a class of second graders understand two digit subtraction. When I was a child, the process of transferring an amount from the tens column to the ones column was called borrowing. Now it's called regrouping and the initial lesson for visual learners begins with a paper divided in half on which wooden pieces of various lengths are laid. One half of the paper is labeled TENS, the other half, ONES. A single rod marked into ten squares is a ten rod. Small single squares are ones cubes.

"Show me the number 23," I instruct a small girl with owlish glasses who, after three days of general class instruction, still does not understand the concept. She peers at me, then reaches for the rods and cubes and organizes two ten rods and three ones cubes. So far, so good.

"Now," I say, "I want you to take away 18. Can you show me how?"

She peers at me again and reaches for a ten rod. I nod. She lays the rod aside. "How much is that?" I ask.

"Ten," she murmurs and lets her hands hover over the ones cubes. I wait, she hovers. Finally she says, "I can't do that."

Teaching moment. "What about the ten rod you have left?" I ask. "Can you make that into ten ones and borrow them?" She looks at me. A long time. Finally she sighs and says, "No."

"Because?" I prompt.

"Because," she says, obviously puzzled by my stupidity (I am the teacher, after all), "they're all glued together." She pauses. "And I can't put a whole stick on the side with cubes."

Ah, the literal mind. "How about if you trade the ten rod for ten cubes and put them on the ONES side?" I suggest.

She dutifully removes the remaining ten rod, picks up ten cubes, and deposits them on on the ONES side. She waits, staring alternately at them and at me. "Now, how many ones do you need to take away?" I ask her.

"I just put them on there," she says. I bite my tongue. I begin again.

"You started with 23. I wanted you to subtract 18. You took away one 10 rod and borrowed the other ten rod. Then you regrouped the ones. Now you need to take away how many ones?"

"Two?" she guesses.

"Why just two?" I ask. I can hear the echo of her puzzlement in my own voice.

"Because," she tells me with teacherly patience, "I took away two rods." She holds up her two index fingers. "One and one are two, see?"

*************

I must confess, numbers baffle me, too. They’re mysterious. They multiply and divide with impunity, they add up to something else or take themselves away. When they are called statistics, they lie. When they are angled, they get obtuse. And when they are money, they disappear. Put them on a form with words in fine print and they scare me to death.

I also have trouble making numbers do as I ask. For instance, I can write the number 56 but when I am not looking, the five and the six sometimes change places. That happens a lot in my checkbook. I have difficulty with zeroes, too. I was told in first grade that a zero represented nothing. Then I was asked to subtract 9 from 10. You can see my dilemma.

As a child, I was an embarrassment to my mother who could add whole columns of figures in her head and do long division without crying. I was the last one in sixth grade to earn a gold seal for learning the multiplication tables and the only one to continue using my fingers (and toes) for adding and subtracting long after calculators were introduced to the modern world.

In high school I dreaded math class. I had enough trouble with numbers I could see. When they became letters such as X and Y, I was lost. And when they got all mixed up in word problems – well, I ask you, if a train traveling at X miles an hour passes Chicago at 2:00 p.m. and a car traveling Y miles an hour leaves Des Moines two hours later, who cares where the conductor and the driver of the car meet for lunch?

As for fractions, they make me fractious. They are conveniently marked on the sides of a measuring cup; if I have to do other than cook with fractions, I leave the problem alone. Fortunately, for people like me, the ruler was invented. I am perfectly capable of counting the little lines between the big ones and the only numbers I have to deal with are the ones I am most familiar with (1-12).

*********

I reach over and remove eight ones cubes from my student's paper. She watches me with indifference. "How much is left on your paper?" I ask her. She counts the remaining cubes.

"Five," she sighs.

I write 18 + 5 = ____  on a piece of paper. "Can you add those numbers?" I ask. She takes a pencil, chews on the eraser for a moment, does some magic with her fingers and says, "Twenty-three."

"That's the number we started with," I gloat, trying to rouse some enthusiasm in the small, pained face before me. "Good job! Shall we try another problem?"

My pupil looks at me with a sigh of resignation. "I'd rather go to the nurse, please."

You Think?

I walked down by the river

 

through the covered bridge

past the newly fuzzy yellow willow tree

 

and the reddening osier withes.

The first of the returning red-winged blackbirds

 

sang amongst the budding branches.

Is it spring, do you think?

An overnight snowstorm thwarted travel plans.

 

By 11 a.m. the sky showed signs of clearing.

 

An hour later the clouds boiled up over the hill

and down came the snow!

The birds, however, are not fooled. Today I saw a flock of fat, orange-breasted robins, their feathers fluffed against the cold. The winter birds - the juncos and nuthatches and chickadees - chirped from the feeders but the robins picked frantically at a bit of exposed ground, looking for something more substantial than seeds. Not finding anything, they lifted and flew awkwardly into the wind.

I thought of them often during the day, wondering what drove them to come back before the snows of March had melted, before the ground released sleepy worms, before bugs swarmed and grubs hatched. What drives any of us to go forward before conditions are favorable? Partly it’s genetic inheritance, and in the case of birds, factors such as food supply and a safe place to nest. Come to think of it, that applies to humans, too. We can’t always explain our own journeyings. We respond to some inner urging that makes us flee safety and head into the perilous unknown.

We all come to times in our lives when we have to make some small obeisance to bravery. We face a loss or a challenge and off we go into the unknown with our thimbleful of faith, trusting that whatever we believe in will sustain us along the way.

I cannot know what those robins were thinking as they hurried north into unexpected snow and ice, or what survival plans they made as they shivered together at the edge of the meadow. I hope they find sustenance in some sheltered part of the woods, that food and a place to sleep are close at hand. For my part, I will look for them again tomorrow. I have cleared a space beneath a large pine, a place where the snow was already beginning to melt. Perhaps they will find food there among the rotted leaves and the twining roots. Perhaps, unwittingly, I am a contributor to their thimbleful of faith.

Spring Break

Snowflakes and raindrops and

no school, oh my!

 

We're getting a dose of winter. The roads are treacherous, the wet, heavy snow is threatening to down tree limbs and power lines, and the school where I work is closed for the day.  My neighbor's house, though only a few hundred feet away, is nearly obscured by a curtain of wafting flakes. The storm is beautiful and inconvenient, dangerous and flamboyant, and will be followed by yet another that is swirling into position off the Atlantic coastline. By Saturday, though, the weather will have settled, the snow will again start its slow withdrawal, and we will be a few days closer to spring.

Addendum

I succumbed to the lure of the outdoors and took a long walk. A mile from home the snow turned to rain and I turned reluctantly. It isn't cold - the temperature is hovering right around 35 degrees - and I could have happily stayed outside for hours. I made a little snow companion in the seat of my outdoor swing. He looks a little more wistful than his brother of a few months ago, pictured below Little Snow Dude II.

Wistful Little Snow Dude II

 

Happy Little Snow Dude I

 

 Dawn and the promise of sunshine

 

that splashes on the floor through a window prism.

I soaked my bare toes in color

for luck...

and as luck would have it

one of these, a red shouldered hawk,

balanced precariously on the fence post

just outside my window.

I could not reach my camera but found this image

(see below). 

Often small birds - juncoes, sparrows, chickadees - 

will spend a moment preening on the post. 

Once or twice a squirrel has made it

a lookout point.

The hawk was a surprise - I can still feel

my jaw dropping.

The sun and wind were irresistible. I bundled up

and went out looking for signs of spring. The wind is

cold but not bitter, the pond's edges are beginning to melt,

skunk cabbage whorls are visible in the snow,

and I startled a flock of robins into windy flight.

In a mere month spring will be declared, rain will wash away 

the last of the grimy snow,

and I won't have to go looking for signs.

I will be surrounded by the season.

And so the great wheel keeps turning.

*hawk photo from: birdsasart.com

At The Cobble On Sunday

 

The sun dances on the river

under hand-holding trees

 

while tumbled rocks pull snow quilts

over their shoulders and sleep

Out of the mouths...

I made Valentines for my two grandchildren early in the week and sent them off in the mail. I was on the phone with my son when the cards arrived. "Here," he told the two of them as they hovered near the phone. "Memere sent you cards."

I heard a rip, an exclamation, silence. Then the small voice of my six year old grandson. "This says I stole Memere's heart! I don't have her heart! I didn't steal it!" Then, with growing consternation, "Did I?"

He's big into policemen ("I'm a COP!" he announces as he approaches with plastic handcuffs. "You're under arrest!"). He loves the thrill of the chase and there's usually jail time involved in their big leather armchair. I thought he'd get a kick out of thinking he stole my heart. Apparently not.

"I'll let you go," I told my son. "And I'll let you explain." I hung up hastily.

I haven't spoken to them since Wednesday. I hope I don't have to do jail time on my next visit.

One Bright Spot

Years ago when I was homesteading in the Northeast Kingdom of Vermont with my then husband and our four children, I met a man who introduced himself, saying, “I’m Bill. I author for a living.” He was standing in the cellar hole of our unfinished log cabin, admiring the way we were making ourselves snug there for the coming winter. “I’m just up the road,” he said. “If you need anything, don’t hesitate to ask.”

As it turned out, I had occasion to ask often. Our hand dug well went dry before Christmas. He helped us haul water. When he bought himself a new refrigerator, he gave us his old one and though we had no electricity, we used it as an ice box, filling the top shelf with jugs of frozen water and storing our food on the shelves below.

When, one after another the children came down with chicken pox, he took pity on me. For two months I’d nursed the older three. Now the fourth and youngest was ill. One cold day in March he drove down the hill to fetch us, made a bed for my daughter in front of his fireplace, drew a steaming hot bath, filled it with scented soap bubbles, and left us to enjoy his house for the day.

He constantly issued invitations to come watch the ballet or the Olympics or the news on his television. He would call and say, “Come. I need you to read this.” I’d hike the mile to his house to find one of his manuscripts on a table, a red pen beside it. He’d have poured coffee, set out a bowl of nuts and disappeared into another part of the house. I’d sit for an hour in the sunny room, reading and making comments in the margins. He’d amble in after awhile and we’d talk. He called me the Queen of East Hill and loved to tell stories about his adventures in the Navy or his latest writing project. I never left without a hug and a borrowed book or two under my arm from the hundreds and hundreds he owned.

On the day my divorce was final, he wrapped his arms around me and let me sob until I had no tears left. Then he bundled me into his car and drove me to a cemetery where we parked overlooking the rising hills that jostled each other on their way to Canada. We wandered among the gravestones. “These people all had problems,” he told me, “and someday you’ll be here, too. Try not to waste too much of your living time in regret and sorrow.”

My memories of the years that immediately followed my divorce are shadowed, though as in all hard times, there were bright spots. Bill was one of them. He gave my sons jobs around his house so they could earn pocket money. He paid me to clean, to iron his shirts, to edit his writing. He dropped off melons and strawberries out of season, let me spend a weekend in his summerhouse when my kids were with their dad, loaned me his car when mine was in the shop.

Once the three oldest kids were off to college, I sold the log cabin and made my way back to my old home in Massachusetts. Bill and I kept in touch for a while but like many long distance relationships, ours was reduced to a card at Christmas and then to no correspondence at all. Last week I learned he died this past December. Now there’s a hole in my heart where he dwelt but in my memory he is still a beautiful, bright spot.

His obituary is here. http://www.nytimes.com/2010/01/14/arts/14lederer.html

Counting Blessings

desk where I do my bookwork

Checking my bank balance after writing the monthly bills, I've ruefully decided I will never be rich. As I was mentally reviewing my financial woes before going to sleep last night, it occurred to me that though I may not have millions or even hundreds in the bank, I am rich beyond measure in the things that really count.

I have my health. All my faculties work. Some better than others, it’s true. I can see a sunrise bathe the morning in gold or watch dusk cloak the landscape in royal purple. And with my glasses on I can see clear across the room. I can hear birdsong and laughter and music, and if they don’t mumble, I can hear other people when they talk to me. I can smell freshly baked loaves of bread and the soup bubbling on the back of the stove. I can also smell snow in the air (and danger there, too when I wax poetic about snow to the wrong people). I revel in the cuddly touch of polar fleece and the puffy softness of my down quilt. I like the satin smoothness of bread dough under my kneading fingers and the stickiness of cookie dough that must be licked from the spoon.

I have a place to come home to, a beautiful little cottage with lots of windows to let in the light. There’s room (if I rearrange all the furniture) to toss a mattress on the floor for whatever wandering guest, child, or welcomed grandchild is here for a sleepover. Not everyone is as lucky as I.

My happiness knows no bounds. If I started to count the things that made me happy I’d be up all night. I have four children that have grown into marvelous adults and they still love me. I have two grandchildren and a daughter-in-law that have caused my heart to grow at least three sizes. I have friends with whom to share my greatest joys and my deepest sorrows (and all the paltry stuff in between). I have food in the pantry and clothes in the closet and a cat that prefers my lap to all others.

My bankbook may be a lot thinner than my waistline but it is by no means the measure of my wealth. That's a good thing to know.

A Day In The Life Of...

 

The setting moon

 

the rising sun

 

the frozen pond

 

the day begun

 

a snow filled nest

 

some wings of white

 

the sinking sun

 

and so, goodnight.

Crossroads

 Influenced by Steven's marvelous post, I've planned my day:

 

here the road of hurry and rush

here the street of noise

here the way of helter-skelter thought

here the path of forest and tree

here the hush of clouds

here the way I chose today to walk

It Won't Be Me

Over and over I thank my lucky stars that I am not responsible for inventing new things. If I was in charge, we'd still be back in ancient times, hanging out in trees and eating fruit with worms. There'd be no fire, no wheel, no sewing needles, no sickles or hoes or threshing machines, no cotton gins or paper or railroads, no TV or packaged food or rocket boosters or cell phones. Think how far we've come just in the past twenty years. Then watch this and be amazed at all you didn't know!

Did You Know 4.0

www.youtube.com


photo courtesy of: abc.net.au

Monuments to Imagination

My refrigerator has always been a repository for fine literature and great works of art. Stick figures drawn by tiny hands, mosaics made in art class from bits of colored paper, cartoons cut from newspapers, scrap paper quotes, their ends curling against magnets, a few photographs, a poem, a recipe or two—whatever catches my eye or piques my interest is apt to spend some time stuck to the door or the side of the fridge where I can see it often.

Since magnetic poetry was invented, my refrigerator has also become a poet’s corner. My kids gave me the artist’s version for Christmas. Words like sculpt, create, and masterpiece abound and short poems, one-liners, and clever quips are blossoming like forced paperwhites all over the door.

For example, “Live wild, weld nude.” (The thought gives one pause, doesn’t it?) How about, “dazzle with metaphor,” or “chisel her beauty in concrete.” One of my favorites, “stop inside and water the moon,” is right next to, “she is more like an angel than I imagined.”

I’m especially taken with a short poem that appeared behind a departing guest. “Come see the glorious green water, like harmony and rhythm painted on a shimmery canvas.” You can tell a lot about people by the poetry they leave behind.

Now and then, I take all the phrases apart, scramble the words and lean against the counter, letting my eyes scan the offerings until some new combination appears. The words seem to associate on their own. The next thing you know, “black ink looms as a monument to imagination.”

To Look, To See

Ancient wisdom suggests we look at each day not as if it was our last, but with new eyes, as if every day was our first. Finding that thought compelling, I step out into the sunrise and am struck by the beauty and the mystery of everything around me. I leave my yard to walk along the edge of the pond in the growing light and watch the sun coat the ripples with silver. Last year’s dried oak leaves dance toward me in a sudden gust of wind. I look up and my eye is caught by the movement of small birds high over the pond, swallows perhaps. They are too far up for me to tell, but their joy is clear as they swoop and rise and sail out over the water and back, diving and skimming and soaring again and again. The sun touches the undersides of their wings so that they seem to float on feathers of pure light.

The wind swoops through the tops of the pines, rushing from one to the next, whispering green secrets. The boughs rise and fall as though breathing and I am caught up in the sound and the rhythmic dance of dark needles against blue sky. Then the wind is at my feet, whirling the loose snow into miniature cyclones before blowing off across the open fields, losing itself in the woods at meadow’s edge.

Later in the afternoon and into the evening as the light wanes and the day’s colors melt into darkness, I will walk again beside the pond, watching the water, different water now, new water, make its way to the falls. I will understand again that nothing lasts, though nothing appears to change, and tomorrow and tomorrow I will see again with new eyes the same ordinary things.

Here and Now

Life

is good

in my little corner

of the

world.

Good News

A natural upper: There will be an increase of three minutes of daylight over yesterday...

WInter Day

My days are filled with birds.




Dawn brings the seed-eaters to my doorstep. The two feeders that hang from the bare branches of the lilac bush are always filled with millet and sunflower seeds for the small songsters that winter over. By first light the chickadees, the little white-breasted snowbirds, and a pair of cardinals are breakfasting just outside my window. They come unannounced and speak quietly among themselves. Only the jays make noise. They perch and sway on the bendy branches at the very the top of the lilac and screech. I stand at the door and watch them, the steam from my teacup curling up and fogging the window. When I rub it with my sleeve, the motion frightens them and the jays take off like buckshot.

Most times when I open the door the chickadees merely flutter and hop to the far side of the bush. They are not as timid as the snowbirds or the tiny finches that dart off at the slightest movement. If it is not too cold, and it is near their feeding time, I can stand still with my hand outstretched and a chickadee or two will light on my fingers and eat the seed from my palm.

Where summer birds herald the sunrise, winter birds don’t sing at all – they talk. They twitter to one another. They might chirp a warning or tootle a couple of notes but they don’t sing melodies the way songbirds do. They’re too cold, I suspect, and too busy eating. Their limited tonal offerings only accentuate the great silence, that deep hush that descends with the cold and underlies all sound.

Car Games

It used to be the custom for children to be seen and not heard. When I was a child, it was our duty to be heard, especially in the back seat of the car on a long journey. (Any car trip that took more than seven and a half minutes was considered long.) To keep us occupied—and reasonably amused—my parents relied on a number of car games. Now that kids have their own mini-TVs and video games installed by auto manufacturers, these games will probably go the way of the Model-T.

Our favorite was the license plate game simply because it had the most variables. We began by seeing who could collect the most out-of-state-nameplates. Shouts of, “I’ve got six New Yorks,” and “Yeah, well that Vermont one is mine!” made my father’s knuckles go white on the wheel after a few miles.

Next, we’d make the numbers on the passing plates add up to a hundred. When we tired of that, we spelled words with the letters. I’ve never told, but often before the hour-long trip to Holyoke to visit our grandparents, I would look up words in the dictionary, hoping to stump my little sisters. “Spell acrimony,” I’d suggest. They’d just look at me. “No,” Jackie would reply. “I’m going to spell monster.”

We often expanded the list of available numbers or letters to billboards and the numbers tacked to signposts. Or, instead of spelling words or adding numbers, we found all the letters of the alphabet, or the numbers 1-100 in succession.

Our efforts at amusing ourselves weren’t limited to math and language arts. We sang songs, favoring the unending rounds that eventually made my father threaten to leave us by the side of the road if that %$#@ bear went over the mountain one more time. My mother would look at him and say, “Jay,” very quietly. He knew she meant he ought not to be increasing our vocabulary. In retaliation, he taught us Army songs. We’d bowl along the highway, yelling in unison, “And those caissons went rolling along,” until he was sorry we knew that song, too.

One of my uncles let slip that if we did not hold our breath going past a cemetery, the ghosts of the dead would enter our noses or mouths, a thought so horrible that when we knew we were approaching a cemetery, we would hold our breath ahead of time, just in case. My mother disapproved of such nonsense. My father welcomed the respite.

As we grew older, the games became less sophisticated and more physical. The boys favored punch-buggy. Anytime we spotted a Volkswagon Bug, the first to see it cried out, “punch-buggy!” and whatever color the car happened to be. A solid punch to the upper arm was delivered at the same time. My arms were perpetually “punch-buggy blue.”

Padiddle was the girls’ favorite. It required a kiss at the appearance of a car with one headlight. My eye was keener at night, apparently. It was an especially exciting game if there happened to be two fellows and one girl riding in the back seat. It’s a shame, really, about those in-car TV and video games.

Resolutions

Big things insist on our consideration. They are in our faces, demanding action. It’s the little things, the quiet moments, the often unnoticed inflection of voice or questioning of eye, the small tootle of a morning bird, the singularity of a snowflake, that need our awareness.

So, we begin to listen to the unspoken, to see beyond the obvious, to open the eyes and ears of the heart. We begin to pay attention and in the very act of noticing, we acquire what we need most – perception, insight, patience.

In the silence, we get to hear ourselves – and that just may be all the incentive we need to make a change.

Clean Slate

January snow
a crisp, white page
a new year.

Nature sketches
last years grasses
to remind us of next June’s.

Hardwoods show their bones
redbirds paint
the hemlocks.

In the cold pewter sky
a crow featherstitches
the clouds.

White flakes drift like
windblown curtains -
January snow.



Photo curtesy of Russell
http://iowagrasslands.blogspot.com/