Just this week I went back to Keith Devlin’s fascinating book, The Math Instinct. Devlin’s book takes a look at some studies with very young babies that illustrate the fact that we humans are born mathematical creatures. In one study designed by psychologist Prentice Starkey, babies were shown images of one dot and two dots on projectors. At the same time one or two drum beats would be played. When one drum beat was played, the babies would spend a significantly longer time staring at the projector that showed one dot. When two beats were played, the babies would stare at the projector with two dots (Devlin, 12-13). Many other studies have also shown that babies have some understanding of numerosity and number sense.

Babies are mathematicians too! So you can imagine that I’ve been watching my own little mathematician for signs of number sense. I’m pretty sure she’s counting already

Now that I’m getting used to being a mom and getting a little more sleep I plan on getting back to the blog more frequently. Looking forward to catching up with math friends here! What mathematical adventures have you all been up to?

September and May are my favorite teaching months. September because everything and everyone is fresh and full  of hope for the school year ahead. May because it is a month full of moments in which you marvel at how much your students have learned, at the amazing people they are.

There have been many of these May moments in our math workshop lately. We have done a lot of work around the idea that math is storytelling, that you need to be able to tell and interact with the context and story when problem solving in order to figure out a problem.

We use these mathematician statements to encourage this kind of thinking and set a purpose:

• “Mathematicians listen to the story and tell it again to figure out the problem.”
• “Mathematicians think about what is happening in the story. This helps them solve the problem.”
• “Mathematicians look for their own problems to talk about and solve. They are creative.”

We’ve been using some of the story mats from Kathy Richardson’s Developing Number Concepts, Book 1: Counting Comparing and Pattern to help generate some stories. (Thanks, Katie for reminding me of these!) We talked about different kinds of stories we could create, the questions we were asking of the solvers of our problems, whether the result would be more or less than our starting point based on the action in the problem.

Here is Bryan telling an ocean story.

We’re also always engaged in counting collections. This week we counted a giant collection of gum drops for a spring fairy (long, involved imaginative story created by class behind this fairy!). I loved watching as children organize, count, and talk about the collection. In the beginning of the year counting collections focused on maintaining 1:1 and the number word sequence. Now we spend time focusing on finding efficient ways to group and count.

Here is Madeline organizing a collection of gum drops into groups of five.

We’re savoring the May moments in our classroom. What end-of-year moments are amazing you in your classroom?

My kindergartners are investigating one of the big ideas of numeracy–decomposing numbers.

We have been using Cathy Fosnot’s Contexts for Learning unit, “Bunk Beds and Apple Boxes,” which is based around a story that comes from the accompanying big book, “The Sleepover.” The math investigation is based on the story of eight girls at a sleepover jumping back and forth between the top bunk and the bottom bunk in an effort to trick Aunt Kate who is hosting the sleepover.

We acted out the story in small groups with our bodies, moving children between two blankets we dubbed “the top bunk” and  ”the bottom bunk,” looking for all the ways to make 8. Then we worked with partners to model and represent ideas on paper with partners before reflecting as a group and charting our ideas.

Understanding how numbers are composed and decomposed is an idea we keep returning to throughout the year, and one I know my students will continue thinking about long after they’ve left our kindergarten classroom.

I believe that teachers should search out quality resources that support responsive teaching. These Contexts for Learning units are both contextually meaningful and mathematically significant, the litmus test of all curriculum for me!

Here’s a peak ahead to what I’ll be presenting at NCTM:

“Guided Math in Kindergarten” with Lorna Cordero, Lauren Nye, and Tricia Tyskowski

Thursday, April 26, 2012, 12:30pm-1:30pm, Marriott Downtown, Franklin Hall 2

We’ll share 3 Elements of our shared philosophy in practice

Many of the problem solving situations that I recognize in the world and in my classroom with my kindergartners are numerical.

We wonder how many steps it takes to get to P.E. (A lot! We’re just about as far as possible from the gym in a very large school!)

We wonder how to figure out how much birdseed the birds are eating from our window feeder.

We figure out how many more days until our chick eggs hatch.

We measure our pea plants in the garden with Unifix cubes and figure out how much they have grown. We wonder how tall they will be when summer comes. “Will they still be there when we are first graders?” someone asks.

And while numerical problem solving is the center-piece of our mathematical lives and math workshop, we do a lot of problem-solving that is not entirely numerically focused as well.

Recently we’ve been exploring water and why some things floats and others sink in water. After investigating various materials that sink and float, we challenged children to construct boats that would float and carry a load of plastic frog manipulatives. This is more of an engineering challenge, and yet it involves many of the same problem solving skills we use when focusing on numeracy.

We plan and think through our ideas. “This bowl will float upside down. The frogs will go in the cup on top to stay dry.”

“The aluminum foil will keep the boat from getting soggy and sinking.”

We revise our thinking. Alejandro thinks that if one if using one aluminum foil/paper bowl construction makes a pretty good boat (as measured by floating and carrying a good number of frogs), then his three bowl masterpiece will carry even more frogs.

We collaborate and debate with other thinkers.

Problem-solving extends beyond the numerical. All kinds of problem-solving creates flexible, creative, constructive thinkers.

How are you problem solving through the day?

Triangle Reflection:

“Three sides and vertices.”

“Can be skinny.”

“Can have one long line.”

“Two can make a square.”

“Two can make a special star.”

“Kandinsky loved triangles and me too.”

Shape Composers and Decomposers.

Poem #1 (Light on math, heavy on spring reflection)

The spring season of  teaching defies all measures of time.

Outside our window, past the bird feeder, we 23 watch the pear tree.

(Pear trees are wretched creatures, so I’ve learned.

Dusty rose-colored petals stain the sidewalks.

And short-lived trees, hardly worth the bother, really?)

But I did not know that then.

To me, to all of us on our walk, they were magical.

Weeks ago, nothing. “Bone branches,” said the five year old.

And now?

Petals drifting,

carpeting the underneath. An uncountable collection.

I resist the urge to shove my pockets full of them

in a desperate moment to preserve the short moment of smeared petal perfection.

And now?

Each petal swept away.

replaced by green buds.

The poem that is most beautiful to me is, unsurprisingly, a mathematical poem.  It can be found in the first pages of my book, before I start my own words.  I’ve been experimenting with some of my own mathematical poetry recently (standing on the shoulders of Mary Cornish and her poem!). Every once in a while I may include one here. Watch for one coming soon!

Numbers

I like the generosity of numbers.

The way, for example,

they are willing to count

anything or anyone:

two pickles, one door to the room,

eight dancers dressed as swans.

I like the domesticity of addition—

add two cups of milk and stir—

the sense of plenty: six plums

on the ground, three more

falling from the tree.

And multiplication’s school

of fish times fish,

whose silver bodies breed

beneath the shadow of a boat.

Even subtraction is never a loss,

just addition somewhere else;

five sparrows take away two,

the two in someone else’s garden now

There’s an amplitude to long division,

as  it opens Chinese take-out

box by paper box,

inside every folded cookie

a new fortune.

And never fail to be surprised

by the gift of the odd remainder,

footloose at the end:

forty-seven divided by eleven equals four,

with three remaining.

Three boys beyond their mother’s call,

two Italians off to sea,

one sock that isn’t anywhere you look.

–Mary Cornish, Poetry magazine, Volume CLXXVI, Number 2, June 2010

During Morning Explore (45 minutes of open play/projects/creativity/joy) two friends explore Thinkfun’s Sudoku , a problem solving and reasoning game. We’ve been talking a lot about how mathematicians work together to problem solve and look for challenging problems. They found some of that in this game for sure.

Cute.

Activity.

These are two words that I hear a lot as a kindergarten teacher, and they make me cringe.

Language is powerful, and as someone who is deeply interested in how teacher language affects the way children form identities as mathematicians and define for themselves what it means to “do math,” I spend a lot of time thinking about words.

Now, if you’re a user of “cute” and “activity” you may have stopped reading already, but I hope not. Because recently, I’ve been wondering if I’ve created a dichotomy between cute and purposeful where perhaps there shouldn’t be. So maybe you can offer me some new thoughts.

I have always defined cute as the antithesis of purposeful and meaningful. When a visitor comes into my classroom, looks at what my children are doing and responds, “They’re so cute.” “What a cute activity! You are so creative!,” I usually give them a piece of my mind.

I sometimes have to restrain myself from stepping up on my soap box and saying, “All of the work I plan and the invitations to mathematical play I extend come from serious consideration of what message I am sending about math.  I think, “When I ask my students to work on this problem, what message are they walking away with about what math is?” When I question their thinking and ask them to explain their thoughts or listen to the thoughts of others, I think, “What am I showing them about what it means to be a mathematician?”

Cute is not the message I’m looking to send. Activity, to me, means purposeless work with no real meaning behind it. Now I’m sure I’ve lost a few readers. But if you’re still here, keep reading on, even if you disagree.

This week my mathematicians and I have been talking about different ways to measure. During our Explore time, our kitchen has been converted into a vet clinic as part of our study of heroes and power. During one investigation (I much prefer this word over activity) we measured the length of the stuffed animals from our vet clinic using Unifix cubes. As I planned this investigation, I thought to myself, “What message do I want to send about measurement as a form of mathematizing? I want to show them the usefulness of measurement.”

Our stuffed animal measurement became a “Make a Bed” investigation. ”Some of these animals in the vet clinic may need to spend the night in the clinic. They’ll need beds, but in order to make a bed you’ll have to figure out how to make one that fits the animal.”  So, away they went. Measuring, recording, and taking their recordings and Unifix cubes over to the Lego table to construct beds for the animals that would accommodate the length of the animal.”

The kindergarten mathematicians were beside themselves with this investigation. They made the animals talk as they measured them beds. “Don’t give me a small bed,” said an alligator through her puppeteer.

To a kangaroo one boy at the Lego table said, “Let’s see. Your bed is now eleven cubes long. As now I’m going to add some flowers to it, because all kangaroos like flowers.”

As I watched the measuring and constructing of beds, I felt a word bubbling up. A word I detest. Cute. Don’t worry, I didn’t say it aloud. Banish the thought! Is it possible for mathematicians or their work to be simultaneously purposeful and cute? Is cute always a way to belittle the importance of someone’s thoughts or work? Or is it simply a nod to the importance of aesthetic and play in our work? The talking alligator? The kangaroo’s flower bed?

I’m not sure yet, so I haven’t yet said the word aloud. Instead I said, “You really thought about how that alligator would feel in a bed that was the right length for him.” “You’re thinking the kangaroo wants a bed that is the right size and looks nice.”

So, you tell me, is there a dichotomy between cute and purposeful? I’m still figuring it out. And for now, that’s an ok place to be.