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Math Is Storytelling

Just returning from the NAEYC annual conference in Orlando,  my head is swimming with ideas–ideas that both extend and challenge my previous beliefs. I love that hopeful and refreshed feeling of returning to my classroom after an amazing conference feeling ready to take on the world!

I want to share an abbreviated version of my presentation, “Mathematics is Storytelling: Bringing Play and a Sense of Narrative to Problem Solving” with you all. And while the slides only tell part of the story, I hope they give you a sense of all that is possible when you build a culture of problem solving and live a rich mathematical life alongside your students.

So, how are you bringing play and a sense of narrative to problem solving in your classroom?

Boxes and Marbles

From the Marina Pics Photostream on Flickr

Sometimes the best teaching, learning and play happens at unexpected moments, in unplanned ways. I’ve developed the habit of collecting interesting odds and ends (or, as my husband refers to it, junk!) that I think might be interesting for my students to use or play with. Last year I began to collect all sorts of small boxes with tops. Jewelry boxes. Chocolate boxes. Party favor boxes. Any kind of smallish box. One day during Explore Time I put these boxes out with very little introduction. “I’ve been collecting all of these little boxes. Some are smaller, some are bigger. Some are long. Some are tall. I wonder what you could do with these boxes.”

I thought, perhaps, that the kids might sort them, stack them, line them up from largest to smallest, switch around the tops to see if they would fit on other boxes–all worthwhile and independent tasks. And for a few days this is exactly what they did. I walked around and asked some questions–”How do you build a strong stack of boxes so they don’t fall over?” “How did you know which box was ‘bigger’ when you lined them up–the long skinny one, or the shorter deep one?” We talked in groups, we debriefed as a group, more children became interested in the boxes.

And then, a couple of days into the box play, one girl decided to bring over a large jar of marbles to the box play area (the kind of marbles with flat bottoms that you can buy in bulk at craft stores like Michael’s) and started to pretend that she was a queen filling her boxes with jewels and passing out these “presents” to her faithful followers (other children she had roped into this game!). I listened as the children played.

“I love presents. Please, Queen, fill this big box with jewels.”

“Oooh! Look how many jewels fit in that box!”

“I am an evil witch. So I only get one very small box full of bad jewels.”

“Ha! Only five jewels in that bad witch box.”

I watched. I listened some more. “Ah ha!” I thought to myself. “This is exactly that magical moment I’ve been waiting for.” I could have stopped here. The children’s independent play was mathematical and imaginative. However, this was the perfect opportunity to go deeper. During our debrief session, I helped the group of kids playing with boxes and marbles explain to the other children what and how they were playing. I asked questions like:

“How did you know which present box would fit the most jewels?”

“Are there some boxes that are the same size? How could you tell if they were really the same?”

“Which jewel boxes were good for giving to the evil witch?”

In our next Explore Time sessions (the “replay” sessions) I helped the children to explore volume and capacity with the marbles and boxes, and think about how we could estimate, count, measure and record our results.  This exploration lasted many days and resulted in some great play and child-made charts detailing which boxes were “present boxes” and which were “witch” boxes, listing the marble capacity of each box.

I started this post by writing about what a happy surprise this investigation was. Those “junk boxes” I collected provided a lot more mathematical investigation that I ever imagined. But it’s not all “luck.” There are some important elements we can put into place in our classroom to encourage this kind of play. These are some I’ve come up with. What would you add or change?

Creating a Culture of Mathematical Play:

• Collect interesting materials that you think may spur mathematical play. Include traditional math manipulatives, but also go beyond them. Introduce materials that seem to beg certain investigations (collections to be counted, different size vases to be filled with water) Change the materials available on a regular basis.
• Give it time. In order for deep play and learning to occur, kids need time to engage however they want with the materials before they get into deeper investigations.
• Ask questions. Say, “Let’s try that out.”
• When one or two kids start a particularly “mathy” investigation, help them to get others involved. “Laura is thinking about how to make a poster for the witch boxes. What should she put on the poster? Maybe you all want to work together on this project. Let’s get you some chart paper and markers.”

Note: In my last two posts, Explore and Play-Debrief-Replay, I wrote about the importance of mathematical play throughout the primary grades (and beyond!) and how we, as teachers, can help focus and deepen children’s play.

Play-Debrief-Replay

My kindergarten colleague, Lauren, brought up an important issue in her comment on my last post, Explore:

“In the first few weeks of school we use a lot of explore time in kindergarten with Unifix cubes, pattern blocks, and other manipulatives. What kinds of questions can we ask during discussion to create meaningful reflection and what supporting materials should we provide in order to make the play time more focused?”

Lauren brings up the point that the role of the teacher in Explore Time is very important. The teacher, through her carefully crafted questions and facilitation of group reflection, can help children take their play to a deeper level.

Selma Wassermann writes about exactly this issue in, Serious Players in the Primary Classroom: Empowering Children Through Active Learning Experiences. In this book Wassermann explains her “play-debrief-replay” structure in which a question, materials, or idea is introduced and children freely explore and play with it. The teacher’s role during the initial exploration is questioning and observation. After the initial play session the  teacher facilitates a debrief session in which she helps children identify problems to be solved and ideas to be further explored. She helps plant the seeds of thought that can be explored further and more deeply in the next  play session, the “replay,” which immediately follows the debrief.

Although this book is a little older, is has great ideas for open-ended math and science inquiries you can set up and how you can lead children through the “Play-Debrief-Replay” structure. In an upcoming post, I’ll walk you through one such session in my classroom and delve deeper into the teacher language used for facilitation. In the meantime, find yourself a copy of Serious Players for some ideas on how to deepen and empower children’s play in your classroom!

Explore!

Time for mathematical play and exploration is critical to the development of problem-solving skills, creativity, and persistence. And yet, play is something that is increasingly getting set aside as outside pressures in the education world distract from real learning.  When I was having trouble finding time for mathematical play (or any play at all, really) as a third grade teacher I decided to set aside time for Explore Time several times per week. An idea I borrowed from Katie Keier over at Catching Readers Before They Fall, Explore Time allowed children to invent projects and follow their own interests in just about any direction. Many times I would introduce materials and questions that lent themselves to mathematical and problem-solving types of explorations and many students would eagerly take on the challenge.

When I first began Explore Time as a third grade teacher, I have to admit that I felt a twinge of guilt. I was newish to my school at the time, and I kept thinking, “What if someone comes in here and sees that I’m letting them ‘just play’?” and “No other third grade class is doing this. Is that ok?” After some time I realized that amazing, complex, and thought-changing moments happened during Explore Time. Some of our deepest conversations came from the reflection time we had after each Explore Time. And most importantly I learned that there is no such thing as “just play.”

In the picture at the beginning of this post three of my wonderful third graders are using some blocks to record how many different ways they could combine shapes to make triangles. They were exploring the big idea of composing and decomposing shape more deeply than they had previously done even when I, the teacher, gave assignments! And this was all by their own choosing. As they worked, Melanie grabbed a clipboard and some paper and began to record the all of their ideas. “We can keep this list going so we know which ways we’ve made and which ways we’ve haven’t.” This exploration extended over several Explore Time sessions. Over that time I’d check in with them to ask questions about what they were thinking, how they recorded, and what patterns they noticed in their work.

I know that the time we dedicated to Explore Time was worth it. The thinking and collaboration exhibited in Explore Time transferred into all parts of our day, especially mathematics. The beginning of the year is a great time to begin Explore Time, and puzzles and blocks are great materials with which to begin.

So, how do you find time for mathematical play? Explore Time is one of my favorite topics—I’m sure I’ll be writing more about it. What else would you like to read about when it comes to this topic?