Teachers can gain valuable insight into students’ mathematical thinking by asking just a few carefully chosen questions about their multiple-choice problems. In Beyond the Bubble, Grades 2-3 (and the forthcoming companion book for grades 4-5), Maryann Wickett and Eunice Hendrix-Martin explore students’ thinking through 30 sample problems that span five strands: number, measurement, algebra, geometry, and probability.
From actual conversations with hundreds of students about their answer choices, the authors found that both correct and incorrect responses often painted an inaccurate or incomplete picture of students’ understanding. But probing with a few additional questions enables teachers to get “beyond the bubble” and make more effective decisions about future instruction.
For each of the 30 sample multiple-choice problems, you’ll find:
• a brief overview of the problem’s objective;
• typical student strategies used to solve the problem;
• conversation starters;
• several actual student work samples;
• student-teacher conversations and teacher insights;
• suggestions for instructional strategies;
• reassessment questions.
A Reader Confesses By Kathi Appelt
I could tell you how much I loved
Black Beauty, and how I longed
to touch his silky skin, to pat his
neck when he was nothing more
than a street horse, “Oh Beauty,”
I would say, and stroke his
soft nose, his velvet ears,
and how it was that I wept for
his old stablemate Ginger.
I could tell you how horses
thundered through my dreams,
ran straight out of the page
of Marguerite Henry and Will James
and Anna Sewell. I could say that
Misty and Smokey and Fury
were my best friends, and maybe
in some small sweet corner,
some dusty, yearning place
they still paw the ground,
swish their tales.
I could tell you all this,
but I’d rather say what books
are to me today, now that
those dreams of stallions and
mares and newborn foals
have passed to some other girl,
some other dreamer. Now that
my breasts sag and my
heart beats harder to coffee
than to Appaloosas and grays.
They didn’t stop, the books.
They rest beside my bed,
the next to last thing I touch
before I mosey off to
sleep, my husband being
the last. They ride in my
purse on airplanes and ferries.
They come with me to
foreign countries and accompany
me to the dentist’s office.
I share them with my closest
friends, feel connected through
our conversations of what we
loved, what we didn’t, what
moved us, where we went.
They bind us, don’t they,
these pages, these wandering
words, these stories that call
us to meet on a common street.
I could tell you about Black Beauty
and that girl who loved him.
But she wouldn’t know to say
that it was the book that mattered,
not the horse.
Peter Lourie is not only a traveler, adventure writer, and author, but he is also a college professor. He is teaching an adventure writing and digital storytelling course at Middlebury College in Vermont. His course takes students out of the classroom to embark on an adventure of their choosing and then the students work together to produce digital stories.
“I believe that the young writer’s artwork and the way he or she showcases a piece of writing for an audience is as much a part of the writing process as the writing itself,” writes Ann Marie Corgill in her recent book, Of Primary Importance: What’s Essential in Teaching Young Writers. Ann Marie says that she makes sure that parents and teachers not only see the final, polished product, but also the messy beginning and middle that show how long and hard her students worked on their artwork and writing. In this week’s Quick Tip, she describes the process of creating self-portrait collages with her students.
Self-Portrait Collages At the beginning of the year, during our Establishing the Writing Community study, the children and I do lots of talking about what it means to be a writer and the kinds of work writers do in preparation for publishing a piece. Oral storytelling is a big part of our work as writers in the first few weeks, and getting the children to talk about their stories and lives is the first step in helping them become writers. The self-portrait collage is a great way to get this talk out into the room while also publishing a piece of artwork that becomes the springboard for more talk and writing.
Typically during the first week of school, before the children create their self-portrait collage, I send a letter home to families asking for help in collecting items for the collage. These self-portrait collages hang at the top of a long wall or bulletin board that’s out of reach for regular use in the room for the entire year.
I like to say to the children after the self-portrait collages are hung that our room is “wrapped in writers.” That’s the way a writing classroom should be—one that’s wrapped in the work, the ideas, the thinking, and the lives of the children that inhabit the space.
This year we added an extra touch to the self-portraits, with each child painting his or her name in bubble letters, outlined in thick black rope or yarn. I got this idea from my friend Kendall Fousak, a fabulous art teacher at Bronxville Elementary School in New York. Using the thick black yarn is an amazing way to highlight the children’s names, rather than just having them outline their work in black marker. It gives each child’s name texture and depth and really says, “Hey, look at me!” from the walls in our classroom.
✐ Photographs of the child, child’s family, special moments, and so forth
✐ Magazine or newspaper cutouts of pictures or words that describe the child, represent an interest or a hobby, or connect to their lives in some way
✐ Cray-Pas, oil pastels, watercolor, tempera paint, crayons (whichever medium you or the child chooses for the portrait will depend on your access to supplies and the depth of your patience for the day!)
✐ Cups or plates and brushes if paint is used
✐ Newsprint to cover tables
✐ Paper towels and spray cleaner for cleanup
✐ White butcher paper/bulletin-board paper
✐ Black fadeless paper
✐ Glue sticks
✐ Fabric glue
✐ Fabric or yarn
✐ Black cording or thick black yarn
✐ Skin-colored paints, markers, or crayons
✐ Photograph of the child’s face and upper body
Tips and Techniques
I first demonstrate how I would draw my self-portrait, giving the students a sense of how to begin, how big to make the portrait, and what details to add. I ask the children to first sketch their face and upper body using whisper writing—a term I learned from my friend Joan Backer at Manhattan New School—which involves writing lightly with a pencil and makes erasing easier and less messy. We work lots on drawing big so that filling in the pictures with color is much easier and more attractive. I also show the students examples of what not to do if they want people to see the portrait and for it to show up on the walls in our classroom.
After the children sketch their self-portrait, it’s time to decorate using color. The media you choose is up to you. One year, my students used Cray-Pas and oil pastels for their faces and tempera paint for their T-shirts. Th is year, my students first outlined their face, hair, features, and T-shirt with black permanent marker and then colored over it with crayon. (It’s important when using crayons and permanent markers to use the marker first, since they don’t work well over waxy crayon.)
Hair—The children then either paint their hair color with washable tempera or acrylic paint or use yarn and glue the hair around the face with fabric glue.
Young children have an easier time making the details of their faces with skinny permanent markers. Once the face is painted or colored with the appropriate skin color and is dry, then the students add the details. Once the entire portrait is dry, the children then paste pictures, words, cutouts, and so forth on the T-shirt part of the body.
This year, we added an extra step to the project, painting our names in bubble letters and then outlining the names with fabric glue and thick black yarn. I used acrylic paint this year. It’s much brighter and doesn’t fade as much as regular tempera paint or watercolors. But make sure your kids wear painting T-shirts or smocks. Acrylic paint is stubborn and can ruin clothes!
After fi nishing the collages, the next two weeks of writing share is devoted to two or three children talking each day about their self-portraits and the meanings and stories behind the pictures and words on the collage. This share time is the perfect support for helping us begin to talk and write about our experiences and for us all
to learn about the members of our classroom community. It also gives me a talking point when I have those first writing conferences of the year and still need to remind the children of their experiences and how those experiences can become ideas for writing.
We all agree that kids need lots of in-school time to read, enjoy books, and share their books and ideas with others. Besides the guided reading time, how else can we make that happen in classrooms where teachers are pushed to do test preparation and worry about their overflowing curriculum demands?
While guided reading is one time in your day to have your students reading, there are many more opportunities we, as teachers, can create. If our goal is making sure we have kids who not only can read, but choose to read, then we must provide lots of opportunities within the school day to help all readers develop a reading process system and practice using it with meaningful, authentic texts. Having choice in what they read helps these readers see how reading can become a part of their lives. Our daily read aloud time, independent reading time and the teacher’s modeling can support not only the readers who struggle, but also every other reader in your classroom.
Read Alouds. I read aloud as much as possible in the classroom. There is no substitution for a teacher passionately sharing a book he/she loves. Bringing in new books that I find and sharing them with my students helps them see reading as something we do for enjoyment as well as a way to learn new things. I use picture books in every classroom I work in, from kindergarten through sixth grade. I share books from favorite authors, new books I discover that I know kids will love, and books connected to content area topics. What better way to introduce or sustain a topic in science or social studies than by sharing an engaging book? I also use interactive read alouds to teach reading strategies and to help children see a reading process system at work. Our writer’s workshop often starts with a read aloud, as students learn to read like writers through these mentor texts. I don’t see read aloud as a separate time that I may or may not squeeze in, but rather as a key piece of my instruction.
The books I read aloud to kids are the ones that don’t stay on our class bookshelves or in the library for long. Kids want to take these books home and reread them independently or with friends and family. It’s important to make sure your readers who struggle are not pulled out for intervention during read aloud time. This is not “just reading aloud”, but rather a critical time where they can hear fluent, expressive reading modeled, laugh or cry in response to a great book, share ideas and feelings with classmates, and hear a teacher think aloud. Read aloud time also exposes struggling readers to books at a higher level than they can read independently. They need these opportunities to comprehend and participate in discussions. Feeling part of the classroom reading community is important. Protect your read aloud time. All kids need to be there for it.
Independent Reading Time. Kids need lots of time, every day, to read books independently. It’s really the only way we can improve at anything – by practicing. Sadly, independent reading time often gets pushed aside in favor of test preparation workbooks, lengthy organizers for kids to record what they are reading (instead of reading), and other activities that take away from reading. Without sustained periods of independent reading time, our students will not be able to have the endurance necessary for the standardized reading tests they are required to take, nor will they learn to enjoy and love reading – our ultimate goal. Independent reading time is a necessary piece of every school day.
In the classrooms where I work, children have boxes or bags of books that are “just right” for them. Often these are books they have read with a teacher in guided reading groups, or a teacher has helped them choose based on a reading level. I agree that kids need to be reading these books every day. Books that are just right for them support their developing reading process system. The more they practice reading strategically in appropriate level texts the stronger their system becomes.
However, I also feel that kids need time to read books they have chosen, maybe for no other reason than that the topic or the picture on the cover interests them. A fellow teacher once gave me the idea of having kids keep their “just right” books in a large Ziploc bag. They could also have 4-6 free choice books outside the bag, in their individual book box or desk. It didn’t matter what kind of books these were. The agreement during independent reading time is that they have to read from their bags first, then they can read their free choice books. This has worked quite well at keeping a balance of “just-right” books with free choice books. And it’s amazing how often those free choice books end up moving into the bags as the kids become stronger readers!
Modeling what readers do. When I tell my students that I read on Twitter that Chris Van Allsburg has a nonfiction book coming out in April, they are as excited as I am. I share author blogs with my students and videos on YouTube of authors reading their books. I bring new books into the classroom frequently, and share my excitement with my students. I love books and reading and love sharing that with my students. I try to be a constant model of what a lifelong reader does. I talk to my students about trying to navigate my way through the complicated owner’s manual on my new camera as well as how I read Pete the Cat to my dog because I was so excited to get it in the mail (and it’s one of those books that begs to be read aloud!)
I feel that bringing excitement and enthusiasm about books into your classroom will get a lot of your readers who struggle to rethink what reading means to them. When you create this culture in your classroom, even your most reluctant readers will be motivated to find a book they enjoy. The more you read aloud great books, provide time daily for students to read in class, engage your class in conversations about books, take note of your student’s interests and find books that appeal to them, and support them in creating a reading process system, the more likely you are to have readers who not only can read, but choose to read.
“Writing is hard work,” says Mark Overmeyer in his book When Writing Workshop Isn’t Working. To make teaching writing easier, Mark answers the tough questions about writing workshop: How can I help students who don’t know what to write about? How can I help my students organize their writing? How do I manage writing conferences? And how do I plan for writing instruction. For this week’s Quick Tip, we pulled a section from Mark’s book where he talks about planning writing instruction for a school year.
Planning for a year If certain units of study are going to be followed through the course of a year based on state, district, or school guidelines, setting deadlines for these units of study can be helpful when planning instruction.
For example, for many years when I taught fifth and sixth graders, my teammates and I ended the year with a unit that required students to create their own magazine. This project required students to use all of the writing strategies they had been working on all year, and the open-ended assignment allowed for maximum choice while still providing a tool for determining how much students had grown in the year. The magazine became a sort of community celebration as it continued over the years, and families looked forward to seeing what their students would create during this project. Since the magazine took approximately five weeks to complete, and it was one form of summative assessment, we placed it at the end of the school year. We worked backward from there, fitting in units that included research, narrative, memoir, and technical writing.
As we planned for the year, we noticed when we could fit writing in across the curriculum. For example, we could do a research unit closely connected to social studies topics. Students had a choice of what they wanted to research, but we connected it to our American history standards. Technical writing in the form of lab reports could happen in science class.Writing did not have to exist just in the domain of language arts, so if there were days when we would have to shorten our language arts block, we could plan accordingly and make sure to have writing happen in science or social studies.Writing in other content areas is not only a good idea in terms of planning and scheduling, but I think it is also good for students. Many of my reluctant writers in the past have loved science, and they were more than willing to write in the context of their favorite subject. They may have reluctantly completed a memoir, but then enthusiastically explained their thinking in science class.
Planning for a year is an excellent way to think backwards: once my teammates and I decided which type of writing would occur in each month, we could begin gathering our resources and planning for instruction.We knew what types of writing we would need to cover in order for students to be successful in each unit.
Though we knew we would have to adapt our ideas according to student need, having the plan created a strong scope and sequence that covered the requirements of our district curriculum. Organizing for the year ensured that we would give students ample opportunity to demonstrate their growth in writing.
David Somoza, an elementary school teacher, and Peter Lourie, adventure travel book writer, have teamed up to write the new book Writing to Explore: Discovering Adventure in the Research Paper, 3-8. In their book, David and Peter show teachers how to guide students to write interesting, adventurous, well-researched papers that are rooted in real places, supported by facts, and developed with detailed descriptions of images from real locations.
In that spirit, we challenge you to send us your students’ best writing about a state or a place they have lived in, visited, or daydreamed about. When we say “writing,” we mean that any “old” or “new” form of storytelling is acceptable: photo stories, video clips, interviews, poetry, essays, research papers, or even cartoon strips. The important thing is that as we read your students’ work we’ll feel like we’ve been transported to the place they are writing about.
The essays will be judged by David and Peter and the top five submissions will be featured on the Stenhouse Blog.
One winner will receive a library of Stenhouse books of your choice (a $150 value), and the following books by Peter Lourie to start your classroom adventure library (a $180 value): Amazon, Arctic Thaw, First Dive to Shark Dive, Hidden World of the Aztec, Hudson River, The Lost Treasure of Captain Kidd, Lost Treasure of the Inca, Lost World of the Anasazi, On Texas Trail of Cabeza de Vaca, On the Trail of Lewis & Clark, On the Trail of Sacagawea, Rio Grande, Tierra Del Fuego, Yukon River.
Deadline: May 1, 2011
Send your stories to email@example.com. If you would like to send us a larger file, you can mail a CD or thumb drive to Stenhouse Publishers, Attn: Zsofia McMullin, P.O. Box 11020, Portland, ME 04101-7020.
Valentine’s Day is not until Monday, but here is something to get you started for a little romance. I found it on my usual weekly search for a Poetry Friday poem and I thought it was a perfect mix of education and love. Enjoy!
Lunchbox Love Note Kenn Nesbitt
Inside my lunch
to my surprise
a perfect heart-shaped
love note lies.
The outside says,
“Will you be mine?”
and, “Will you be