The Number Sense

The Number Sense

A farmer has 10 cows. All but six wander off. How many cows remain? Tim has five marbles, which is two fewer than Jen. How many marbles does Jen have?

Do problems like these make you cringe? Do they remind you of word problems that brought you to tears when you were in school? We might have been pretty good with numbers, but throw some words into the mix and we were lost.

Remember struggling to memorize the multiplication tables? Oh, the twos, threes, fours and fives were all right, but the sixes, sevens, eights, and nines scrambled many a brain.

In his 1997 book, The Number Sense: How the Mind Creates Mathematics, Stanislas Dehaene writes that the reason so many children have trouble memorizing tables is because we do not have “digital” brains like a computer does. Our brains work by association. That is, we make sense of the world by associating new ideas to those we have already assimilated into our memory banks.

That doesn’t mean that children cannot learn math concepts. As Dehaene notes, four-day-old infants can “decompose sounds” into smaller units to actually count syllables. Researchers, using very clever tests, have tested babies and found that even newborns can perceive differences in color, shape, size and number. We come into the world as pretty smart cookies. So what happens?

One problem is adults. Kids have their own way of understanding mathematical concepts. Young children perceive the world differently than adults do. Their brains are wide-open and willing to try new things. Everything is a wonder – even math. Math is just another world puzzle to decipher. Kids jump into exploring math concepts just like splashing in puddles. They love getting their brains wet.

Then well-meaning adults begin to teach children the math system they have assimilated. Children who cannot easily understand these models become anxious. Children need to wander and we want them to stick to the path. Children also pick up non-verbal signals from the adults they love. If Mom or Dad is intimidated by or “hates” math, children will assume the same attitude to numbers.

Dehaene states that he is “convinced that children of equal initial abilities may become excellent or hopeless at mathematics depending on their love or hatred of the subject. Passion breeds talent – and parents and teachers therefore have a considerable responsibility in developing their children’s positive or negative attitudes toward mathematics.”

It’s up to us folks; can we be good models for our children? Can we learn to love math and encourage our little ones to love it too?

         

The farmer has six cows left (all but six wander off). Jen has seven books. Five is two fewer than seven. Children know that cows and books are wonders of the world. 

Math can be too.

      

         

Somebody Loves You!

Somebody Loves You!

Which group of people gets the most Valentines? I guessed grandparents, figuring that the multiplication factor would somehow work in -- you have two kids, they have two kids. Boy, was I surprised when I heard the answer. Give up? It’s teachers. I should have known. Teachers get all kinds of love, some in the form of superhero or princess Valentines.

Love is a major perk for teachers. We love the kids and they love us back. Our love comes in the form of lessons, tying shoes, sharing books, zipping jackets, patting heads, and “way-to-gos.” Kid’s love comes back in smiles, giggles and hugs, good work, and those once-a-year Valentines. 

We get lots of love. 

One of my favorite books is Somebody Loves You, Mr. Hatch, by Eileen Spinelli. Mr. Hatch leads a very dull life. He works in a factory, dresses in drab clothes, eats a turkey wing for dinner every night, and sweeps his porch every Saturday morning. The illustrations by Paul Yalowitz reflect the grayness of his life. One day, the postman, Mr. Goober, knocks on Mr. Hatch’s door with a package. Mr. Hatch opens it to find a huge heart-shaped box of candy. The note attached says, “Somebody loves you.”

     From that day on Mr. Hatch’s life changes. He wears a yellow polka-dot tie. He helps his neighbors. He bakes brownies and throws backyard picnics. He laughs and plays his harmonica. As his life brightens, so do the illustrations. Reds and yellows replace blues and grays.  

     Then Mr. Goober sheepishly returns to tell Mr. Hatch that he made a mistake. He had delivered the heart box to the wrong address. Mr. Hatch returns the box. How foolish he was to think that somebody loved him. He stops laughing. He puts his harmonica away. The grays return to his life.

Love made a huge difference to Mr. Hatch, even the love of some unknown admirer. Love makes a difference to us all. It changes our outlook. It changes our circumstances. It changes us.

Kids have so much love to give. The sad thing is that some children do not feel loved. Children who feel loved have the confidence to take risks and to try to learn. They say, “I can.” Unloved kids are afraid to try; they set themselves up to fail. They say, “I can’t.”

How can children tell if they are loved? How about spending? Do gifts and possessions make them feel loved? Children can have every material blessing and still not feel loved. How about spending time with them? Time is great, but it’s only time. How it’s spent is what’s important.

Children need to know that they are appreciated. They need to know that they are valued. They need to feel that you are doing what is best for them. They need to feel secure.

Good teachers provide this for their students. We praise their efforts. We welcome them to the classroom each day. We have a schedule. We have rules. We are consistent. We are where they expect to find us, and we act as they expect us to act. We share our pleasures with them, reading and writing, math, music, art, languages, history, science, and much more. And books! Teachers love books only a little less than they love children.  

Parents give love by showing pleasure in their children, by sharing themselves and their interests, by disciplining themselves, and by consistently guiding their children in loving ways. Parents model the values they want their children to have; if one of these values is love, children feel loved. They know somebody loves them.

Mr. Hatch shrinks back into his narrow world, but luckily for him, his neighbors remember the loving Mr. Hatch, the Mr. Hatch who helped them, who shared and laughed with them. Together, they show Mr. Hatch that he is loved, and the colors spring back into his life. 

Loving parents pour colors into their children’s lives. Loving teachers brighten the colors for their students. And beloved children?  They make rainbows.  

(Somebody Loves You, Mr. Hatch by Eileen Spinelli, Ill. By Paul Yalowitz, Aladdin Paperbacks 1996)

Just Like Abraham Lincoln

Just Like Abraham Lincoln

Every February, I read a great picture book, Just Like Abraham Lincoln by Bernard Waber, to my second graders. In the story a young boy notices that his neighbor bears a remarkable physical resemblance to Abraham Lincoln. Like Lincoln, his friend is a lawyer who helps people. Like Lincoln, he likes to read and discuss ideas. He also teaches the boy and his classmates about the real Lincoln.

As a boy Abe liked to read and learn. You may know stories about his reading by firelight and walking many miles to borrow and return books. Although he lacked a formal education, he valued learning and read everything he could get his hands on. He also liked to have fun and played many practical jokes on his family, including putting his footprints on his mother’s freshly white-washed ceiling.

Abe was a hard worker. There were many chores to do on his father’s farm and Abe was needed at a young age to help. He often plowed a field with a book propped in front of him. This didn’t help keep the rows very straight. As a young man he held many jobs, including splitting rails, and he always worked hard and responsibly.

Abe was honest. As a young man he was partner in a general store. He was not a very good businessman, but he built a reputation for honest dealings. His honesty is highlighted by the story about his walking miles to return two cents a widow who had overpaid him. He traded groceries for a barrel of books in which he found Blackstone’s Commentaries, a legal compendium, which became the basis for his law career. 

Abe knew the laws and he kept them. Abe was an militia captain during the Indian wars. Once, his men captured an Indian messenger. The rules of war stated that all messengers were to be given safe passage. Abe’s men wanted to kill him anyway. Abe would not allow it, even though his decision made him very unpopular with his men.

Abe was kind. He found time to help children, animals and people in trouble. Once he helped free a pig stuck under a fence, getting himself very muddy in the process. In his law practice he often defended the underdog -- free of charge.

Abe liked people. He sat for hours swapping tales with travelers and friends. He loved a good joke. A judge once fined him $5.00 for telling a joke that disrupted the court. Later, the judge asked Abe what he had been whispering. After hearing the joke, the judge repealed the fine.

Abe loved his family. Even after he was president he took time to play with his children. His boys often played around the feet of Abe’s Cabinet members.

Abe hated war. During the Civil War, he was grief stricken about the tragic loss of lives. He wrote many condolence letters to families who had lost sons, fathers and brothers. Even his face displayed his agonizing, aging visibly as the war dragged on.

When my students read about the life of Lincoln, they learned about a good man who knew what was important in life and who lived by his principles. 

They also learned that by helping others and living by our principles, we too can be “just like Abraham Lincoln.”

Mittens!

Dear Family,

  Yesterday, as I exited my place of employment, I walked
out into a winter wonderland. Snow covered all. My car was smothered
in the white stuff and the temperatures hovered in the low twenties.

While others shivered and reached for their snow scrapers, I boldly
strode up to my car and swept the white stuff off, scattering snow to
the east and west with my hands.

Was I cold? Did my hands get frozen and wet? 

NO! 

Fear not!  I had my .... MITTENS!

Yes, the very same mittens that my sainted little brother had
given me oh so long ago (30 years!). That same brother who diligently
saved the pennies from his allowance, shoveled snow, raked leaves and
stood on the corner selling matches in order to buy his ungrateful
siblings mittens for Christmas. 

Yes that little boy, Tiny Mikey we called him, worked his fingers to the bone

so that his brothers and sisters would not have to suffer frozen digits. 

And did we appreciate it?  Did we thank him?  NO! 

Well I for one, yea though it be thirty years late, repent. 

Thank you, Mikey! Your gift is much appreciated. Long may my fingers 

(so effortlessly typing this message) be warm -- thanks to YOU!
 

Your loving and many-fingered sister,
 

Lisa (2005)

PS  Did I mention he did all this by the time he was five?