Making Thinking Visible

Making Thinking Visible
Making Thinking Visible

Arts Integration

Arts Integration
Arts Integration

Tug-of-War in the Math Classroom

At the beginning of every new school year, I go through a mourning period. It usually hits me at the end of the first week of school. This year is no different. I asked my fifth graders, "What do you think?" And I looked out at a sea of blank stares. Crickets. I even tried applying the old-uncomfortable-silence-during-wait-time trick. I stood silently and waited for someone to say something. Usually, it works because people become so annoyed by the silence that they'll say something just to break it. Again, crickets. 

Outwardly, I smiled brightly, the picture of virtuous patience, but on the inside, my brain moaned and groaned, "I miss my kids from last year who couldn't wait to think and talk." It was time to break out my thinker's tool box. I needed my visible thinking routines. They had become so automatic in previous years, but the summer was long, and I was as rusty as my students. The next day, we began again.

The Problem

We had been working with the concept of area. The focus of our lesson was that the area of a rectangle could be represented by square inches and square feet.  Students were working with grid models of area using mixed and whole numbers.  They were struggling to understand that the area of the picture in front of them could be measured in two different ways. 

Allison and Justin were laying tile in their bathroom floor. Allison said they needed 5 square feet in tile. Justin disagreed and said they needed 20 square feet. Who is correct?

We zoomed in on the Allison and Justin problem together. After reading it over, one student volunteered to give the answer. He stated that Justin was correct. To my delight, controversy exploded! Many students agreed that Justin was correct. Others argued that Allison had the right idea. The debate became heated, so it was the perfect time for the visible thinking routine Tug-of-War. I gave each student a sticky note and asked them to write their stance and thinking on it. After doing so, students placed their sticky note on the side of the tug-of-war line I had taped to the board. 

The next day, we returned to our tug-of-war line and the controversy. I arranged my kids into "councils of thought." This was a fancy-pantsy way of putting them into discussion teams. The Justin team met together to formulate a common solution. The Allison team did the same. Both were trying to use pictures and words that would prove their stances and convince those on the other side of the tug-of-war line to move their sticky notes, to change their minds. 

After the councils had met, the debate continued. Each side presented their evidence. The Justin team, with the erroneous thinking, shared their evidence, and the Allison team challenged their thinking! The Justin team then gave a rebuttal. Then it was the Allison team's chance to present their evidence. 
They presented passionately. At the end of the debate, most students moved their sticky notes to the Allison side of the tug-of-war line. Here's what was cool about this: 
1. There was no crying or sense of failure because the Justin team could explain their error in thinking, and the Allison team could completely understand how that happened.
2. Students practiced the secondary goal of the math lesson: To practice mathematical discourse. It was remarkable to hear "I disagree...because..." and "Can you tell me more about that?"
3. Every single student was engaged. I'm serious. I had one of those tingly teacher moments when I watched them debate. No one was idle. Not one student.
4. When we were done, I asked students how their understanding had changed. Every one of them was able to identify how they had changed. It was a fabulous day for exit tickets!

Sometimes, teachers need their students' blank stares, because they are reminders to bring their very best strategies and instructional tricks to their lessons. I guess students aren't the only ones who get rusty during the summer months!
If you're interested in reading more about visible thinking routines, you can read more HERE and HERE

You might also like to check out these resources! Simply click the pictures to visit.

When Your Readers Are Squirrels

Have you ever sat on a park bench in the fall and watched the squirrels? They are fascinating. They chatter, and chastise each other. They romp and play. They cram their mouths with acorns and then try to run, somewhat off balance, back to their hidey holes. Their tails twitch with excitement or irritation, and their bright shoe-button eyes will follow your every move, even while they're engrossed in their never-ending hunt for food. They are adorable and charming, even when they're robbing your bird feeder. 

They remind me of my fifth grade students. 

It is the second or third week of school, and I've been teaching reader's workshop expectations and routines. We've read about 10 books together already. My kiddos are always in awe of my classroom library. When Richard Allington said that a classroom library should be filled with 1,000-2,000 books, I took him seriously. Actually, his advice was just an excuse to continue my hoarding...but that's another blog post. 

They mill around the library with their book boxes in hand. Some of them try to fill their boxes with at least ten books. Those readers are like the squirrels who over stuff their mouths and then can barely run back to safety. Other kids wipe out an entire bin of The Babysitters' Club books. They're like those squirrels who hog the bird feeder so nobody else gets a taste. But it's when we settle down for independent reading that I can't help but make the comparison.
Their bodies flop. Some switch books every five minutes, never fully diving into the texts they selected for themselves. Others sit with their books open, their bright shoe button eyes glitter as they track my movements around the classroom. When I look their way, they suddenly feign interest in their books. It never changes. It's always the second or third week of school that I have to teach this particular lesson: What To Do When You're Feeling Squirrely.

This past week, I taught the lesson, right on schedule. I began by showing them a youtube video about funny squirrels. I wrote this question on the board: As a reader, how are you like the squirrels in this video? This is the video I used:

They roared with laughter, and it was a great way to hook them. Afterward, they were able to make the connections I wanted. 

"I'm like that squirrel that was laying on the pavement. I get tired!" 

"I'm like that squirrel spiraling on the bird feeder. Sometimes I end up reading the same sentence over and over and over again." 

"Those two squirrels fighting were like Justin and me fighting over The Lightning Thief." 

I listed their comparisons on chart paper, leaving space between each one. It was fun and fascinating to hear them talk about themselves as readers. Then we began discussing and adding solutions to our reading focus problems. 

"I get tired, and so I lose focus." 
Check to see that your book is the right level. That can tire you out if its not. 
"I keep losing my place."
Use a bookmark to help you track through the text as you read.

"Chapter books feel too long sometimes."
Keep some shorter texts like comics, picture books, or nonfiction books about topics you love in your book box. Switch books when you need a break.

"I can never find what I want to read when it's time to read."
Keep a wish list of what to read next in your reading folder or reader's notebook. That way you'll remember when the book is available again.

"Sometimes I get bored."
Are you choosing books that are genres or topics that you love?  If not, conference with a friend about what he or she is reading. They might have some great recommendations!

By the end of our mini-lesson, we had some great solutions for what to do when you find yourself reading like a squirrel. Every one of the behaviors my students mentioned had a solution for them to try. They copied the chart in the back of their reader's notebook and then skittered back to their desks for independent reading. Our workshop session ended with students reporting the different strategies they tried to maintain their focus during their independent reading session. 

Since this lesson, we check in with ourselves periodically and ask, "Am I reading like a squirrel or a fifth grader?" My students are becoming more self-aware of their reading habits as a result. That's the beauty of a great reader's workshop lesson-it reveals the hidden things that successful readers do. The mystery is solved, for everyone. 

If you're interested in reading more about reader's workshop, you  try reading HERE or HERE.

These resources, some free, support my reader's workshop classroom practice. You might find them useful. Click the pictures below to view them. 

Once Upon a Time...Slaying Dragons & Story Problems

Fairy tales are more than true; not because they tell us that dragons exist, but because they tell us that dragons can be beaten.
                                                                           -Neil Gaiman, Coraline

I fought dragons nightly. At our kitchen table. I mentally donned my chain mail armor, strapped my trusty sword and scabbard to my side and prepared to do battle with the math textbook. There were different kinds of dragons on those long nights. There was the fraction dragon and the long division dragon, but the most terrifying of all was the story problem dragon. Despite my mental armor and weaponry, I was usually reduced to damsel-in-distress status because I dissolved into tears within ten minutes. 

Story problems still cause anxiety to ripple through me. I think most teachers feel that way. I know many students do, too. And if the problems are multi-step, I'd rather give up the fight and toast marshmallows in the dragon's fiery breath. With chocolate and graham crackers.

But then, I had an epiphany.  I was teaching fraction story problems when the reading teacher inside my head said, "You haven't taught the text structure."  I went home that night and began to plan for the next day.

When reading teachers teach about different types of text, they use mentor texts. Mentor texts are books, essays, poems, etc. in which the author has used structures, features, and traits that support the the teacher's lesson focus. In short, a mentor text is any text that models the reading or writing strategy that is being taught. I began to think about story problems as mentor texts. My students needed to learn how to read the text structures of story problems, and then they needed to learn how to write that same text structure. I believed that doing so would also improve their ability to tackle any story problem.

I wrote a collection of mentor texts for story problems. I currently work with fifth graders, so the problems I used are focused on fifth grade standards. I divided my students into small discussion groups of 3 or 4 and gave each group 3 mentor texts (story problems). While they read the texts, I asked them to use a thinking routine called See-Think-Wonder.  We had used this in other subjects before this lesson, so it was a well-known learning routine. 

My students began to read the story problems, and they jotted down their noticings. This is the "see" part of the routine. Here are some of their responses: 

  • I see numbers.
  • I notice that there are characters (people) in the problem.
  • I notice it says "altogether."
  • I notice it says "more."
  • I notice it uses clue words.
  • I see fractions. 
  • I see a beginning, middle and end.
  • I see that every one ends with a question mark. 
Then, they read them again and discussed what they thought about what they observed. 
I think we have to add in this one.
I think that the ending of a problem always asks a question.
I think that the first sentence is like a lead.
I notice that all 3 problems have three sentences.
 One of the things I began to notice in my students' responses is that some were focused on the mathematical thinking: "I think we have to add in this one." and "I see fractions."  Others were noticing how the texts were written. The distinction between the two types of thinking are important, because I believe they indicate differences in understanding. 

The last part of thinking routine is "wonder." What do your observations and thoughts make you wonder? I saw a big range of understanding in my students' questions, too. 
I wonder what the answer is.
I wonder if all story problems have 3 sentences.
I wonder if story problems are like mini stories.
After my kids had the opportunity to examine the mentor texts within their groups, they reported out to the whole group, and I charted their responses. Then I explained that while all of their observations were important, I wanted to focus on some specific ones. I highlighted all of their responses that had to do with how the story problems were constructed.

Out of their observations, we decided that story problems are a lot like stories. They have 3 parts: A beginning, a middle, and an end. Each one of those parts has a specific purpose for the reader/mathematician. My kids noticed that the beginning is written to introduce the mathematical situation. For example: Ayesha and Ben each started a dog walking business. 

The middle part of the story problem presents the mathematical information and tells even more about the situation. For example: Ayesha charged $5.00 per customer per day and was able to walk 6 dogs every day for one week, while Ben charged $6 per customer per day and walked 4 dogs every day for one week. 

They also noticed that the mathematical question was almost always asked at the end of the story problem. For example: Who made more money by the end of the week? 

After looking closely at how story problems are organized, we used what we discovered about them to discuss other problems that have different structure. Knowing the structure of a basic story problem helped us tackle harder ones. My students worked with a partner to write their own story problems. We analyzed these together. Finally, I returned their fraction story problems, and they tried again. Let's just say that dragons were slayed!

It's important for students to read and write like mathematicians. Recently, there have been many articles and books written about using reader's workshop structures in the math class. That's all well and good. However, it's not just about the workshop's about the type of thinking that a student does while reading and writing. Guess what? They need to do that type of thinking when they read and write in math! There should be a skill transfer, and if there isn't, then teachers need to facilitate those lessons. 

If you like what you read here, you might want to take a look at the materials I used for those lessons. You can find them by clicking on the picture.

In addition, I'm a featured author on Rachel Lynette's Minds in Bloom blog this week! There's more reading and writing like a mathematician goodness over there. Click HERE to read about ways to help your students write better math responses. 

I've teamed up with other teacher authors for Teacher Talk, a monthly blog link up filled with teaching ideas and goodies. Consider visiting them below!