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Making Thinking Visible

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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...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.



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