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I’ve been thinking a lot about math communities, mindset, and how children define mathematics. I got the chance to write about some of these thoughts, and share some stories from a great 5th grade classroom in my blog post, “On Being a Mathematician,” over at Stenhouse’s Summer Blogstitute page.

While you’re there, check out all of the summer Blogstitute posts, especially, “Teaching Through and For Discussion,” written by Elham Kazemi (@ekazemi) and Allison Hintz (@AllisonHintz124). They’re the authors of one of my favorite new math books, Intentional Talk. If you haven’t checked it out yet, you should!



Since Math Exchanges was published, many teachers have asked if there are any videos of math exchanges in action that they could check out. Readers wanted to see and hear more from teachers and students as they met in small groups. I’m so excited that I will now be able to tell teachers “YES!”

“How Did You Solve That?” takes a glimpse into math exchanges in my kindergarten classroom and the 2nd grade classroom of my wonderful colleague, Rachel. The part of making this DVD that I am most proud of is how real it is–it was filmed over a couple of days last fall and really captures what it looks like, sounds like and feels like for teachers and students when they are immersed in the work of math exchanges. Teachers will get to see how Rachel and I plan for, teach, and reflect upon math exchanges. You’ll see us wondering about our teaching language and discussing student strategies. You’ll see that not every moment in our classrooms is perfect (I believe a slamming bathroom door makes an appearance in the middle of one of my math exchanges!), but that we, like you, are constantly reflecting on our teaching and revising our next steps for our young mathematicians.

I’m happy to share this part of my teaching life with you all, and hope you will find it a useful tool. 

Back to Blogging!

I have taken a very long break from blogging! I’ve still been here teaching and learning about math, life has just gotten in the way of blogging. And a wonderful part of that life has been the birth of my daughter, Louisa, this February!


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!

A Peak Ahead to NCTM

This week some of my wonderful kindergarten colleagues and I head to Philadelphia for the NCTM conference! I can’t wait to hear some great presentations and do some thinking.

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 be talking about how our kindergarten team builds a culture of math workshop with a shared philosophy, but different teaching styles.

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

  • Math is storytelling.
  • Kindergartners are powerful mathematicians.
  • Teaching is responsive to student learning.
 “From Counting to Place Value: Making Meaning through Guided Math”
Saturday, April 28, 2012, 8:00am-9:00am (Come, on early birds!), Convention Center, 115C
I’ll be talking about why base ten understanding is the gateway to numeracy, and the ways in which we can create math workshops and make time and space for math exchanges that promote a deep understanding of our number system.
I’ll also be debuting a new video clip of a math exchange in action with some thoughtful young mathematicians at work!
So, if you’ll be at NCTM in Philly this year, I hope you’ll stop by one of our talks.
What other great presentations are you headed to? Leave a comment with your suggestions.

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?