ARITHMETIC IS WHERE NUMBERS FLY LIKE PIGEONS IN AND OUT OF YOUR HEAD ~Carl Sandburg

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Beremiz Samir, Education, giveaway contest, Malba Tahan, Math, mathematics, The Man Who Counted

 I don’t know about you but I’m not sure this math teacher’s qualifications measure up.

I’m pulling the honesty card here.  For me, math is humbling.  Numbers appear to be dazzlingly simple.  They are not.   Ask my live-in tutor/guru/scholar, a mathematician who knows my every calculation is beset with error.  He’d rather teach a giraffe to sing.

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Unfortunately, life requires math.

If it’s zero degrees outside today

and it’s supposed to be twice as cold tomorrow,

how cold is it going to be?

I love the Weather Channel, don’t you?  

‘

Storm Nemo ignited an urge to purge my bookshelves. My library’s book sale will benefit and I’ll have lots more room for cookbooks.

I came across plenty of books I forgot I had.  Like The Man Who Counted ~ A Collection of Mathematical Adventures by Malba Tahan.  It’s about the adventures of a 13th-century Persian mathematician named Beremiz Samir who travels the world in search of math, and along the way, settles disputes, gives wise advice, and overcomes danger. Think: A Thousand and One Nights-meets-math on an exotic cultural journey.

Beremiz is a natural math whiz.  As a young shepard in Persia, he learns to count flocks of sheep at a glance.  Soon he can count flocks of birds and swarms of bees and clusters of fruit.

Beremiz enters a shop in Baghdad called Four Fours where an elegant bright blue turban catches his eye.  Everything inside, including the turban, costs four dinars, a mad extravagance for a poor shepard.

Four Fours, Beremiz announces ~ such a coincidence, the name of this business and the wonders of calculus. (I’m thinking perfume! caftan! bracelet!) So he begins to think of all the ways to use the number four.  Using four fours, he says, you can get to any number whatsoever.

How does he do it?

Here’s how Beremiz used four fours to make zero.

44-44 = 0

And here’s how he made the number 8:

4 + 4 + 4 – 4

The merchant is quite impressed and gives Beremiz the turban as a gift.  Although Beremiz is over the moon about it, he notices that it does have one small defect ~ it’s form is not strictly geometric ~ and that’s the seamless segue into his next story about the multiple beauties of geometry.  And so it goes.

Ah, Math.  We have the eyes to see it, the intelligence to understand it, and the spirit to wonder at it. Yet it doesn’t hold my interest the way words do. But Beremiz, being Beremiz, doesn’t stop with zero or eight.  He isn’t wired that way.  Are you like that, bursting with arithmetical curiosity? Do you know/wonder how he used four fours to make the numbers 2, 3, 4, 5, 6, 7, 9, 10?

I challenge you, Readers, to make any of the numbers above using only four fours. The prize for the first correct answer? Your very own copy of The Man Who Counted.

Mathematics is the art of giving the same name to different things.   — J. H. Poincare

Toni 2/9/13

A High-Poverty/High-Achieving Classroom Teacher Knows to Find the ZPD: Another Story from Vogel-Wetmore’s Fifth Grade, One I Begin with a Speck of Memoir.

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E. B. White, Education, High-achieving Fifth Grade at Vogel-Wetmore, observing at Vogel-Wetmore School, teachers need to know about ZPD, teaching moves that maintain high expectations, what does a high performing high poverty classroom look like, zone of proximal development

Today Miss Fournier taught me something I didn’t already know. Rob pours himself an after-school bowl of Frosted Mini Wheats, pauses before the first bite and adds, First time.

Rob was in 10^th grade.

So how come it took 10 years of school for one of Rob’s teachers to teach him something new?

The answer’s simple really.  His teachers didn’t know what he knew. When teachers either teach kids things they already know or try to teach a kid something he isn’t at all ready to learn, they haven’t figured out his Zone of Proximal Development.

ZPD is the edge between what the student can do without help (Zone of Actual Development) and what he can do with help. Successful teaching requires knowledge of a student’s ZPD.

It’s a basic.

Here’s how using ZPD looks in Mrs. P’s writing workshop during conferring:

First I hear Mrs. P listen carefully to what the students say about their writing. Then she asks questions to clarify and deepen her understanding. She gets the students to verbalize what they know and then assists them to tackle what they don’t yet know or do, but are ready to learn.

Tell me how you revised this. Read me the sentences that tell more. Good effort. You used the model. Here’s another way to vary your sentence beginnings.

You love lists. So does E. B. White. Here’s a copy of “Charlotte’s Web.” I bookmarked the page with his list of what was in the barn. It’s a good model.

This is not acceptable. You can do better. Tell me what you need to do when you edit for punctuation. Do it. I’ll be back in five minutes.

Real improvement over last week: you’re using commas in a series just right. Let’s look at semi-colons. “Curious George” has good model sentences.

You’re using what you know about engines here. Try an engine metaphor. Use the Gary Paulson model.

This isn’t enough writing, not for you.  I’m going to put an X here, and you need to write down to this point. I’ll be back and then we’ll talk.

This is clear, but I can’t hear you in it. I want you to read your writing aloud to your family every night this week. Begin with Max here, over in the corner.

Come to the Opportunity Room today. Put your name in the square.

The touch-each-sentence tactic works for you ordinarily; did you use it this time? You need to get in the habit of using the strategies that work for you on your own before we go over your writing.  I’ll be back.

These Vogel-Wetmore teachers I’m watching know their kids. They know what they’re bringing to school with them besides their backpacks. They have different words for different kids.

ZPD lights a teacher’s mind and teaching decisions like a bright neon sign, every day, every minute. When it isn’t on, classrooms fail. When it is, they thrive.

Rob’s teachers needed a bulb for their ZPD sign.

Patty 9/26/12

Vogel-Wetmore School Closes the Achievement Gap with WordsWordsWords. Another Story from These High-Achieving/High-Poverty Classrooms I’m Watching.

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Classroom, close the gap, CONN-CAN award-winning school: Vogel-Wetmore, Education, high-poverty and high-achieving classrooms: their stories, Literacy, observing at Vogel-Wetmore School, pump them full of words to close the gap, reading, vocabulary, Vogel-Wetmore

Words for How to Close the Gap: Or How to Talk to the Elephant

FACT:  Within the first four years of life, children from welfare families hear 13 million words; children from working-class families hear 26 million words; children from professional families hear 45 million words.

FACT: Words are the soil for growing knowledge; well-composted soil is going to work way better than thin soil.

FACT: The elephant in our high-poverty classrooms is the WORD GAP.

Since language is the basis of reading and writing, words have star billing in Vogel-Wetmore’s high-achieving, high-poverty classrooms.

I don’t see commercial kits with names like Build a Strong Vocabulary. I don’t see flash cards. I don’t see word lists to memorize.

I do see classrooms where students build concrete vocabulary by interacting with a complex learning environment. I see a wide, rich use of words.

Choral reads, Chants, and Readers Theater: We need to hear a word multiple times to get it into our functioning memory. Rich literature that tickles the tongue and pleases the palate provides enough repetition for the heard words to become reading sight words.

Accountable Talk: I overhear both teachers and students seriously responding to and further developing what others in the group have said. How do you know that? Can you give me some examples? Where did you find that information?  Can you show us which part of the text tells you that info? What do you mean? I know that because it says here…Can you explain that more? Say more about that. Here’s what I heard you say. Is that what you meant?

Labeled Rooms: I see signs on objects. This is the faucet; please keep it turned off to conserve. This is the pencil sharpener; use it judiciously.

I hear teachers read aloud. A lot.

I see teachers write in front of the class and then say, In your writing today, do what I just did to tell more in other words. Some of our students come into reading through the writing door.

Small reading groups meet several times a week. And it’s all about reading and discussing the words.

Students attend to words. Throughout writing and reading, math, and the content areas,I hear kids compare, combine, and contrast words; use more specific words; identify or change a word’s part of speech or tense; use the root or affix; visualize or act out a word.

Classrooms have access to several paperback book rooms.

A new study confirms what these teachers know: Understanding basic words may come from a flash of initial insight more than repetition. But the flashes of insight need the whetstone of a fertile environment. Or retention is nil.

I walk by the book rooms–the doors stay wide open and welcoming; sunlight pours in the tall windows of this ancient building; and I think, This is what it’s all about, creating readers who read, and listen, and talk–and, along the way learn tons of words.

And close that gap.

Patty 9/22/12