This week I had the pleasure of meeting with a graduate class of ESOL teachers from Prince Georges County and Montgomery County, and two classes of undergraduates in the elementary education program to explore facilitating math discussions. I want to thank University of Maryland Math Education School Professors Rodrigo Gutierrez, Lisa Bote and Maggie Peterson for inviting me to visit their classes.

Both the undergraduates and the practicing teachers had lots of ideas about what makes it challenging to facilitate classroom math discussions. Some ideas they discussed that stick with me are:

• Students may lack self confidence about their ideas, so be unwilling to share
• Students may not be used to explaining their thinking about math, and feel they don’t know how to express their ideas.
• Students may not be comfortable with math vocabulary.
• Students may have trouble listening to each other.
• Once students start talking, they may have difficulty staying on topic.
• Teachers may worry that they will not understand the ideas of all students and not know how to respond.
• Some students may dominate the discussion.
• Teachers may be in a school where other classes are not encouraging students to learn how to participate in math discussions.

Then we read Hatching Butterflies, where two students gradually learn to share their ideas as partners, and then share those ideas with the class. They go from not understanding each others’ ideas at all, to working together to compare their strategies. We talked about the subtle ways the teacher in the book, Ms. Green, teaches the students how to discuss math and clarifies her expectations about students working together to learn.

Then we talked a great deal about the importance of developing a classroom culture where all students feel comfortable discussing their thinking and taking risks that help them build their self confidence as math learners.

Teachers described how they would like to use Hatching Butterflies with their students to help them reflect on their own use of the Common Core Standards for Mathematical Practice. It was great to hear teachers collaborating on ways to enhance students’ participation in discussions, including thoughts from a 4^th grade teacher who would like to use the books in the beginning of the year to help her develop a positive classroom culture.

Some teachers purchased the Use Your Math Power books not only for themselves but also for their colleagues, as a tool to help them work together to set goals and try new practices. These teachers know the power of working with your colleagues to enhance their practice!  My only regret was that I was so busy listening and sharing that I forgot to take pictures to post!

Educators have asked me a variety of questions about using the Use Your Math Power books.  I put together this set of ideas.  I’d love input from any of you, especially based on experiences with the books.  I’d like to make these ideas more accessible to users.  Here is what I have so far:

Suggestions for using the books with students:

• To model student discourse and perseverance in solving cognitively demanding problems.
• To model students using the Standards for Math Practice as they learn together.
• To discuss how the characters in the books share their thinking about unfamiliar problems.
• To reflect on use of the Standards for Math Practice in your classroom.

These books focus on the practices by showing students discussing a math problem. This table can help you coordinate each book with a time of year when students have had relevant experiences with the math content.

First Reading:

Pre-read:

• Have students think about a time when they worked on an unfamiliar math problem.
  • What was that like?
  • What helped you?
• Optional: Do or think about the math problem in the book*

Read the story and discuss:

• What was the story about? Any surprises?
• What did the characters do? What were they feeling? Why?

Subsequent Readings

Discuss how the characters engage in math class. Draw connections to your own class. Suggested questions:

• What does Ms. Green mean when she tells her students to use their math power?
• How do Ms. Green’s students use their math power?
• Think about our class. How do we use our math power? How can we use our math power even more?

Support your students in discussing:

• How the characters discuss what they notice and wonder about unfamiliar problems
• How the characters use retelling, acting out, and visualizing to make sense of problems and find entry points for solving them
• How the characters develop problem solving strategies using a variety of tools and modeling

Also reread portions of a book to focus on issues coming up in your class. For example:

• What if your students are shy about explaining their ideas?
  • Monkeys for the Zoo focuses on Mia who works up her courage to share her ideas. In all of the books, we see the characters figuring out how to share their thinking.
• What if your students are reticent to ask questions?
  • Hatching Butterflies focuses on Carlos and Hannah who figure out how to ask each other questions to help them work together. The characters model asking questions in the other books too.
• What about students who have trouble working together?
  • Hatching Butterflies shows how Carlos and Hannah learn to share their thinking in ways that helps both of them learn. Penguins on Parade shows how Zoe helps Trevor see that they can work together to figure out how to do a problem.
• What if your students have trouble persevering to figure out how to work with a problem?
  • Penguins on Parade shows how Trevor learns that he can figure out strategies to solve problems without a teacher showing him a strategy.

This chart shows the  practices appearing in each book.  It may help you focus on particular practices.  Pages 30 and 31 in each book give more details.

I had a lovely visit in a Boston Public School 1st grade today.  Several weeks ago the teacher read Monkeys for the Zoo to the class, and they discussed the story.  Today I reread most of the book to them, and we discussed how students can use their power in math!

Before rereading the book, I asked them to think about what Ms. Green means when she says, “Use Your Math Power”.  After listening to the story, the students shared ideas about:

• What it means to”Use Your Math Power”
• How the characters in the book use their math power
• How each of them use their math power, especially when something is new

These first graders talked a lot about the importance of thinking and learning from each others’ thinking.  They discussed the importance of listening and sharing ideas with classmates.     Many talked about how they can use their math power to try different ways, an important component in Monkeys for the Zoo.  Then they each got to write about how they can use their math power.

Here are some of their reflections.

We talked a lot about how nervous Mia was when she took a risk and shared her answer.  The class said Mia worried that she might be wrong.  We all acknowledged having similar experiences.  We talked about how Ms. Green helped her feel okay about taking a risk.

It was lovely hearing the students thinking about how they can engage in math.  I think conversations like this stimulate students to engage more productively in math class.

Many teachers ask how they can engage their students more effectively in math class. In the past decades we have learned a lot about how we can build classroom communities where students are thinking and learning  The Common Core Math Practices provide very helpful guidelines.  http://www.corestandards.org/Math/Practice/

Many of you may be using strategies to help build these communities. Perhaps you give students non routine problems or situations to puzzle over and provide them with tools, time, and discussions that support problem solving. We can also provide students with models of what a math community looks like, and help students reflect on how they  can engage more effectively as a class.

My Use Your Math Power books show children in Ms. Green’s primary classroom  learning to use their math power to solve unfamiliar  problems. As they listen to one of these stories, students can reflect on the level of engagement and use of math practices in Ms. Green’s class. Students can relate to times when they work on unfamiliar problems.

After an initial reading of one of the books, students can share their reactions and discuss some basic questions, such as:

• What does Ms. Green mean when she tells her students to use their math power?
• How do the students in Ms. Green’s class use their math power? What are they doing?
• Now let’s think about our class. How do we use our math power? How can we use our math power even more?

Here are some things students have said about the way Ms. Green’s students use their math power:

             “They tried to figure out a way to solve the problem.”

             “They’re planning with their partners.”

              “asking the teacher…but that’s not a strategy”

              “They put everything they knew together to figure it out.”

              “[The] adding part is the easy part but explaining is hard.”

I would love to hear how your students reflect on how they take part in group math work!

Subsequent readings of the Use Your Math Power books might focus on particular behaviors or practice standards. Here are some ideas from other educators. Click here for more:

“This series is the perfect way to introduce students to solving problems in a variety of ways as well as learning how to participate in a math congress. After reading these books, my 2nd graders can relate to the characters and how they often think and feel during math lessons. ”   Edra Wigder, 2^nd Grade Teacher, Angier Elementary School

 “…as kids learn to stick with hard problems, work together, articulate their thinking and make sense of the reasoning of others.”                       Nicole Feret, math consultant

“Readers can follow Ms. Green’s students as they work their way through challenging math problems, and explore different ways to solve them. Teachers will recognize the real struggles that students face in math, from not understanding a problem to having difficulty working with a certain partner. Students will also see themselves in these characters, and may find themselves saying ‘Hey, that happened to me, too!”                        Laurie Ciardi, First Grade Teacher, Curley K-8 School, Boston, MA

“We just read Monkeys for the Zoo and had a great discussion about problem solving. I will continue to use it as a Math Mentor Text for math thinking.”                                                                                                                     Michele Lever, Lewiston Public Schools

I look forward to hearing about the discussions in your classrooms!

I look forward to sharing this space with dedicated math educators as we work to empower all math students.  I’d like to say a bit about my “Use Your Math Power” picture books published in June 2015.

Welcome to Ms. Green’s classroom where students are learning to become powerful mathematicians. This classroom is my creation, based on my years teaching and coaching in elementary math classrooms. A first grade teacher I worked with planted the seed for this classroom when she asked for a picture book that would show her students a class engaged in math conversation. “What a great idea!” I thought. But I couldn’t find the book. Finally I decided to write a picture book myself, inspired by the teachers and students I’d worked during my career.

I wanted to show a math classroom where students are expected to work and solve problems together, where students are learning to respect and listen to each other’s ideas, and where they are reflecting on whether different ideas make sense. I thought about the different ways teachers set expectations that foster a community of mathematical thinking. And I thought about the many things that teachers do to help their students develop confidence in their power as mathematicians. I based Ms. Green and her classroom on these memories of successful math lessons.

Ms. Green recognizes that in her class there are students who are bursting with things to say, and students who are uncertain about sharing their ideas. There are students who leap to conclusions and students who take more time to process ideas. There are students who tend to speak quietly and students who have trouble listening. There are students who are not used to taking risks and students who have are just learning to cooperate with others. Ms. Green works to give all of these students the opportunities and challenges they need to grow.