Making Your Thinking Visible

It is important to help students learn to make their thinking visible in math because it helps students become aware of their own understanding and thought processes and those of others.

When students share their thinking, it means ideas are formulated, refined, and adjusted through sharing.  We see visible thinking all the time when people brainstorm, collaboration, and discussions.  It is an important skill to have in today's world.

In the mathematical classroom, visible thinking is the key for students to learn math and be successful.  We can observe visible thinking in the math classroom during discussions, drawing, writing, and any way that conveys ideas.  We see it when teachers share their thinking with students, when students explain their thinking, when they listen to others explain their thinking, when they discuss their ideas, when they read for understanding, when they write down their thoughts, and when they are able to demonstrate their thinking through the use of technology, manipulatives, or drawings.

There are some things we can do as teachers to help students learn to make their thinking visible. Unfortunately, by the time I get them in high school, most of my students prefer just answering questions without making their thinking visible so I have to work on this.

At the beginning of a unit, have students do the "See, Think, and Wonder" exercise where they preview the unit and answer the questions - "What do you see?", "What do you think you'll be learning?", and "What do you wonder about this Unit?"  This allows students to begin thinking about the unit.  This can be done as a warm-up either verbally or via technology.  If you use technology, you can get answers from others.

When introducing a problem, ask students questions like "How do you think you might solve this?", or "What are you confused about?", or "How can you confirm or counter what you are thinking?", questions to help them think about the problems, rather than just learn by rote.  Further more add a vocabulary activity such as Chalk talk where the teacher writes vocabulary words on paper and hangs them around the room.  Give each student a marker where they can write down a definition, or comment about the term without talking to each other.  If you prefer, set up a google form that allows them to do this.  A second use for the Chalk talk activity is to use it for student reflection.  Write questions on individual sheets of paper so students can go around and write down their understandings, examples, or clarifying questions.

As you work through the unit, ask students "What makes you say that?" during discussions to help them clarify their own thinking. It can be used after the student makes a prediction, or a claim, or even a statement.  Students have to explain their reasoning to show how they arrived at the prediction, claim, or statement.  Unfortunately, too many books write problems in such a way as to follow the particular process being taught in the section, rather than providing more open ended problems.

For instance, if the section is looking at proportions, a student might see a problem that tells them that  Jimmy walks 1mile in 10 minutes while Jane walks 1 mile  in 12 minutes.  If Jimmy lives 1.5 miles from school and Jane lives one mile from school, who arrives home first?  What if you wrote the information that Jimmy walks 1 mile in 10 minutes while Jane walks 1 mile in 12 minutes down and the two children live between one and five miles away from school, then asked questions such as if Jane arrives home first, how far might the houses be apart?  If Jimmy arrives how first, what might be the distance between the two houses? If Jimmy and Jane arrive home at the same time, what is the shortest distance the houses might be apart?  What is the farthest distance apart?  In the second problem, the questions require more thought to answer.

One final activity to wrap up the section is the "I used to think........ but now I think......." because it offers students the opportunity to acknowledge how their thinking has changed over time about a topic or concept.  Often students are not given time to see how their thinking on a particular topic or concept has changed from the beginning to the end of the unit.

It is important to slip activities in to help students make their thinking visible. These are a few ways you can do it. Let me know what you think, I'd love to hear.  Have a great day.