Monday, February 22, 2010

Building Bridges

In the fall, the fine young gents chose to do a bridge-building study. Third-grade gent has ambitions to be an engineer who builds bridges "and other stuff." Well, sort of. He's either going to be an engineer who cooks and plays music for fun, or a musician who cooks and builds bridges, or a famous chef who designs bridges and kitchens and plays several instruments. And why not? We started our bridge study with this amazing book:

Bridges: Amazing Structures to Design, Build & Test (Kaleidoscope Kids), by Carol A. Johman.

The book is a wonderful blend of information and hands-on practice. We had a grand time making human structures to demonstrate the principles of tension and compression. The fine young gents learned about different occupations involved in bridge building and drew and labeled their favorite of the three basic types of bridges.

And the fine young gents started building:
Third-grade gent started with a single sheet of paper across two books. Will it hold a car? He took notes on his failures and successes. He ended up with an accordion-fold sandwiched between two flat pieces to give his Hot Wheels a sturdy smooth bridge.

We've only gotten halfway through the Bridges! book. We keep getting sidetracked by other fantastic building resources, like Bill Nye the Science Guy's video, Structures. Check out these egg structures!

We also got the idea for this bridge of straws and pins from a Bll Nye video:
The gents wanted to explore and discover construction using household materials, too. They made a maze for the Minotaur, a ziggurat, pyramids, and refrigerator box forts. They built bridges using stacking cups, dominoes, marbles mazes, pick-up sticks and (of course) wooden blocks.
I stepped around and over block bridges, mazes and houses for weeks.

The holidays afforded construction opportunities with a new set of materials. What can you make with graham crackers and leftover icing?
Or gumdrops and toothpicks?
Or gingerbread and candy?
And we've been doing challenges from one of our favorite blogs, Think! No pictures, so no posts, but we've kept ourselves busy. Eventually we'll finish our Bridges! book, but not (I think) our bridges study.

Next up, the book the eldest of the fine young gents spotted the day after Christmas and went, "Oooooooooooooo."
I didn't see him for nearly an hour.

Monday, February 15, 2010

ReRun: A Mathematician's Lament

Originally posted 3/08

"A musician wakes from a terrible nightmare....
Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the 'language of music.' It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having thorough grounding in music notation and theory. Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school."

From the introductory paragraphs of this article:
"A Mathematician's Lament," by Paul Lockhart.

If you love mathematics, read this article. If you have hated mathematics since you stepped foot in your kindergarten classroom, read it. If you were dumbfounded by division, befuddled by algebra and confused by geometry, read it. If you're teaching a young person (or people) mathematics, or if you have a child who is or will be learning mathematics, read it.

Actually, if you're teaching a young person anything, read this article because it's got a lot to say about teaching. And about math. And about learning.

Read it right now. Really.

Go ahead. I'll wait for you.

Who knew that I could be blown away by an article about teaching, about learning mathematics? For real. I'm not exaggerating for effect. I nodded my head. I laughed. I scribbled all over the paper. I said "Yes!" and "Exactly" right out loud a couple times. I read the article during a fine young gent's gymnastics class, and I'm sure the people nearby were a little leery of the crazy lady muttering to herself as she read.

I was inspired to be a better teacher. By a math article. Go figure.

I was always a bit of a math-o-phobe myself. Until I got to college and stopped attending my math classes. Instead I read the textbook, muddled through on my own....and loved it. Statistics, trigonometry, the other math classes I took that I can't remember the names of. Suddenly I got it, I understood math, all by myself. I turned in all of my homework, but I only attended class when I didn't understand the assigned lesson. It usually took ten minutes to figure out what I'd missed, then I'd work on my English papers until the end of class because I thought it would be rude to get up and leave while all of the other students sat and listened politely and quietly. (A side note: Handing back a midterm test my trigonometry instructor pointedly remarked that three people scored above 90%, and he was happy to report that the two people who scored above 95% actually came to class regularly. He looked right at me while he said it, to where I was hiding away behind the tall guy in the back of the classroom. I got a 93.) My point is that I found math classes excruciating. But I found out that I kind of liked doing math.

Back to the article, the analogy with which Lockhart begins. Can you imagine teaching music this way? Not allowing children to sing or play music, an activity that comes to most of us as naturally as breathing or speaking, without learning the theory and notations first?

Or painting? (Another analogy used by Lockhart.) Having to learn color theory and perspective before you pick up a paintbrush?

Science? Memorizing the scientific method and the periodic table before you can look through a microscope or mix baking soda and vinegar?

Yet we rarely explore mathematics playfully with our children as an art, as an experience, as a way to play with the ways the world works. Mathematics is a part of our daily lives: Cooking, drawing, jumping, building. Children naturally count things, measure things, create meaningful patterns in their play. And we don't take advantage of it because we don't know to recognize and point out the mathematics in our daily world, because the way we were taught didn't give us a grounding in playful mathematics and exploring math ideas. (The way I was taught, at least...and though I can't speak for the general "we," I suspect that many of you had similar educational experiences.)

Lockhart points out that mathematics is a discipline, as much of an art as music or painting, and in our culture we've reduced the teaching of math to math facts and how-to without addressing the theory, the why, the art behind the drills and the formulas. He writes:

"There is no question that if the world had to be divided into the 'poetic dreamers' and the 'rational thinkers' most people would place mathematicians into the latter category.
Nevertheless, the fact is that there is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics (mathematicians conceived of black holes long before astronomers found any), and allows more freedom of expression then poetry, art, or music (which depend heavily on the properties of the physical universe)." (p. 3)

And later ("Exactly!" I said as I scribbled notes on the paper, drew a big red star in the margin, repeat as I re-read it today):

"By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the "truth" but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity--to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, to cobble together their own explanations and proofs-- you deny them mathematics itself." (p. 5)

Lockhart is passionate about mathematics, and he's passionate about teaching mathematics. He's not just sounding an alarm, a call for change. He's not blaming teachers or students or parents. He's asking us all to look at mathematics differently, to see its beauty and complexity, and to find ways to help our children experience math without killing their natural passion for learning. He writes about how to teach mathematics as an art...and how not to. How to engage students. How to help them make sense of it all for themselves and how to inspire a meaningful relationship with mathematics. How to create a sense of discovery.

And that's what teaching is all about. No matter what the subject.
Books to Inspire Playful Mathematics

Buy them for your children. Check them out from the library. Leave them laying around without saying a word. Read them yourselves. Pick a day or two to do math puzzles instead of workbooks. Play the games. Tell the jokes. Work out the riddles.

It's fun. I promise.

Math for Smarty Pants (Brown Paper School Book) by Marilyn Burns.

I Hate Mathematics! (Brown Paper School Books) by Linda Allison, Marilyn Burns, and David Weitzman.

The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger, Rotraut Susanne Berner, and Michael Henry Heim.

Family Math for Young Children: Comparing (Equals Series) by Grace Coates, Jean Kerr Stenmark, and Brian Gothberg

Family Math (Equals Series) by Jean Kerr Stanmark, Virginia Thompson, and Ruth Cossey

Family Math : The Middle School Years, Algebraic Reasoning and Number Sense by Karen Mayfield-Ingram and Virginia Thompson.

Math By All Means series (Various authors).

Math Wizardry for Kids by Margaret Kenda, Phyllis S. Williams, and Tim Robinson

Janice VanCleave's Geometry for Every Kid: Easy Activities that Make Learning Geometry Fun by Janice VanCleave

Janice VanCleave's Math for Every Kid: Easy Activities that Make Learning Math Fun by Janice VanCleave
More Fun Math (and links and book recommendations) at Poohsticks here: Math

Go figure! The Fascinating World of Mathematics: "Links to math games, activity ideas, puzzles, articles, learning and teaching aids, freebies, math in daily life, 'unschooling math,' overcoming math anxiety, and much more..."

Wednesday, February 10, 2010

Copywork: A Cheerful Mom

Is a picture still worth a thousand words if it's a picture of words?

This is first grade gent's copywork. Last month we had one of those days. Weeks? Enough, anyway, that I did a Google search for quotes on cheerfulness and good attitudes for this gent to copy into his composition notebook. Today's quote: "A cheerful friend is like a sunny day, which sheds its brightness on all around." (John Lubbock)

This fine middle gent is clever and mischievous, a bit of an imp. Halfway through copying the quote, he put down his pencil, erased the word "friend," and wrote "mom" in its place. Gave me that cheesy little grin and a kiss. After I took this picture and he'd finished copying, he drew hearts all over the board.

I've noticed that the opposite holds true as well, at least in our home. A grumpy mom is like a stormcloud. Why is it, I wonder, that anyone else in the family can have a bad day and the others just keep on going, but when I have a bad day, when I'm feeling grouchy, glum, grumpy it infects the entire family? Mom sets the tone for the whole day.

My fine young gent has inspired me to remember that I've never regretted kindness and that gentle words and a smile help set young feet on the right path. I'm going to print this picture and put it on my fridge to remind myself that I want to shed brightness on our days.

Sunday, February 07, 2010

Friday, February 05, 2010

How to Get a Kid to Eat Squash: Squash Scones

Yesterday we had squash scones for breakfast. I had leftover butternut squash and happened across my pumpkin scone recipe. Squash, whole wheat flour and not a lot of sugar make this a delicious tasty way to begin the day. A caution: If you've got, er, discerning children like mine, make sure to call these Pumpkin Scones, as the word "squash" suggests defilement to my particular eaters. The fine young gents devoured these scones.

Delicious "Pumpkin" Whole-Wheat Scones

Preheat oven to 400 degrees.

Mix in a large bowl:
1-1/4 cups all-purpose flour
1 cup whole wheat flour
1/4 cup packed brown sugar
2 tsp. baking powder
1/2 tsp. salt
3/4 tsp. cinnamon
1/4 tsp. all-spice
A pinch of fresh nutmeg

Using a pastry blender, cut in:
1/2 cup (1 stick) chilled butter
Cut in butter pieces until the mixture resembles coarse crumbs.

Optional: Toss into the flour-butter mixture a small handful of dried cherries or cranberries.

In another bowl whisk together:
1 large egg
1/2 to 1-1/2 cup mashed butternut squash, pumpkin or sweet potato
Approximately 1/3 to 1/2 cup buttermilk (or more)

Note: The buttermilk is approximate because it depends on the amount and consistency of your vegetable. Fresh pumpkin has a very different consistency than canned pumpkin, squash has a lot less moisture than pumpkin, and sweet potatoes have a different texture, and so on.

Add wet ingredients to flour mixture and stir until flour mixture is just moist and can be patted into a ball. If your dough is too dry to make a ball, add a splash more buttermilk until the flour is just moistened and can be molded into a ball.

Turn out your dough onto a floured surface and knead gently until mostly smooth. Pat into a circle about 1 inch thick. Cut into 8 wedges and place wedges on an ungreased baking sheet. If desired, brush scone tops with milk and sprinkle each scone lightly with a pinch of sugar. Bake for 15 minutes or until golden-brown.

Mmmmmmmmmmmmmmmm. Squashy yummy golden goodness.

Thursday, February 04, 2010

2009: The Year in Review