Visible Thinking in Math

Yesterday, I looked at visible thinking in general but today its time to look at its practical applications in math.  I read about a gallery walk that could be applied in Math.

Students hang their completed problems on the wall.  This presentation would include information on the steps taken to solve the problem.  Each paper is numbered so students names do not appear.  Every student is expected to check out each piece of work and write two things on sticky notes they attach to the paper.  The first is a question about the work and the second consists of a positive observation.  At the end, the author reads all the questions and comments.  This provides immediate feedback.

A good way to introduce a new unit in math is through the see - think - wonder strategy.  The teacher asks students "As you preview the unit, what do you think you'll be studying? What do you think you'll be learning? What do you wonder about this unit?"  When using questions like this, students need to be given a lot of scaffolding to learn to do it.

When starting students on a problem, use the think - puzzle - explore strategy.  Ask the students "What do you think will happen? What are you puzzled about? What do you want to explore to confirm or counter your thinking?"

For vocabulary, place the words on papers which are spread out around the room.  Have students go through with markers and write down what they believe the definition is or make a comment about the word.  This is done silently because the marker does the talking.  This technique can also be used to have students reflect on their learning.  Post a few questions around the room and have students write their understandings, examples or questions down.

For deeper understanding, ask students what made them say that.  It provides clarification of their thinking.   They can also explain what they used to think and what they think now to show how their thinking has changed.

The idea behind having teachers model visible thinking is because many of us are unable to explain why we do this or that.  We've always done it that way because it was the way we were taught.  By taking time to teach students how to make their thinking visible in math, we will increase our understanding and our ability to express our thoughts. 

Let me know what you think.  I'd love to hear.  Have a great weekend.