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## September

I love September for many reasons, but one very important one is I love the part of the year that is focused on the establishing of community, friendships, and exploring how we will learn together. After being a math coach at my school for several years, I returned to a classroom position this year as a kindergarten teacher. I have missed the creating of community and routines, and just three days into the school year I am in love with my class and remembering how powerful it is to build a new community from scratch with kids.

My kindergarteners begin and end their day with Explore (which I also wrote about here and here).  Even in our math workshop has many of elements of Explore during this part of the year. We focus on working together, communicating with one another, and figuring out how we can investigate our questions.

Today I got the chance to have an impromptu math exchange with a few of my new friends as they played with some interlocking elephant toys.

“Look at all those elephants you have lined up!” I said as I sat down on the floor with my kids.

“It’s like a hundred of them!” yelled Sebastian.

“Is it?” I asked. “How could we check?” Just introducing this kind of “Really? How do you know?” question can push children in their thinking in a low-risk kind of way. I’m not insisting they do something, not assigning a project. I’m just being curious and encouraging them to be curious as well.

Luna, who was working alongside Sebastian, started counting the elephants right away. Her one to one correspondence wasn’t perfect so I encouraged her to slow down and point to each elephant, counting with her and guiding her fingers at time. Sebastian counted along with us, watching our pointing. After about twenty they no longer knew the names of the numbers, but I supported them in their counting. The task was beyond their counting ability, but when I helped them they joined in some with the sing-songyness of the counting. And more importantly, they understood the concept that we were approaching a large number.

“70! We have 70 elephants! And that’s not even a hundred!” they declared.

“Should we make a sign telling people that?” I asked. They were beyond thrilled as we got a sticky note and I helped them find seventy on a number grid in order to record it.

I know they’ll be back to those elephants tomorrow. They have important projects of their own to investigate. Questions to investigate (How many elephants will fit on the tape we use to line up on?) Planned math exchanges are very important, but in September, my focus is on building a community of mathematicians and creating strong routines. Nevertheless, I’m still having math exchanges everyday, all day. I’m finding ways to push their thinking as we learn to work and learn together.

How are you introducing informal math exchanges into your beginning of the year routine?

## Publishing Student Work

Publishing, sharing and celebrating student work is an integral part of reading and writing workshops. Students share books they have written, they blog about the books they are reading, we host author’s teas and poetry slams to which we invite families and friends to celebrate our hard work. We acknowledge having an audience and a community as something that is critically important in literacy.

A few years ago, as I was thinking more about communities of mathematicians and writing Math Exchanges ,I decided to think more about publishing, sharing and celebrating students as mathematicians. One thing I worked on a lot was having a way of sharing and celebrating our work within our classroom community of mathematicians. We created a Multiplication and Division Museum and brought in all sorts of items that encouraged mathematizing. Students spent time in the morning and during the math workshop writing story problems about these items and publishing them for their fellow mathematicians to think about.

In the picture above Felisa, Blanca and Sandy wrote about some sticky notes that someone had left on the table. In Spanish (this was a Spanish immersion classroom) they wrote, “Each package of sticky notes costs \$1.50. How much is 10 packets?” Below Max responded with his strategy to the girls’ problem.

The students loved this interaction. I remember how excited Felisa, Blanca, and Sandy were when they saw that they had a response to their work from a fellow mathematician. They raced to the Multiplication and Division Museum to read what Max had written for them.

Later we took some of this sharing and publication of our work to the internet, using Voicethread to publish our mathematical ideas and reach (and receive feedback from) a wider community of mathematicians. “Hey, Antonio!” yelled a thrilled third grader, “your mom posted a comment on my story problem!!”

This year I’m hoping to continue learning about the process of sharing, publishing and building communities of mathematicians inside and beyond the classroom walls. How are you doing this 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?