Making Thinking Visible
When you are establishing student ownership of their learning, a first step is to have students prepare artifacts that will be displayed for peer observation followed by whole-class or small group dialogue about their artifacts. Those student-created artifacts may be on chart paper, newsprint paper, or construction paper, written on a smart board or whiteboard, or displayed with a document camera. In some CMP classes, students share their work through videos. When students know that their peers are going to be viewing their work while making specific comments, they put forth greater effort to communicate more effectively. Asking students to select various artifacts that will be displayed on the class memory wall will also encourage students to make their thinking visible to others.
Groups display their work on poster paper. You can then use some or all of these in the Summarize. Students can move around from poster to poster, leaving a comment or question. You can provide the groups with a question to ask as they view the posters.
Promoting Visible Thinking
Making Thinking Visible is a book by Ron Ritchhart, Mark Church, and Karin Morrison.  The book provides rationale for having students’ thinking made visible and also shares multiple thinking routines that foster visible thinking. In addition there are “Pictures of Practice” to provide specific examples to show student work from classrooms. Some of the specific Pictures of Practice are work from CMP teachers and their students.
The following routines from the book are useful for introducing and exploring Big Idea concepts at the beginning of a CMP Unit:
- See, Think, Wonder: Unit Introduction “As you preview the Unit, what do you see? What do you think you will be learning? What do you wonder about this Unit?”
- Think, Puzzle Explore: Launching a Problem “What do think may occur here? What are you puzzling about? How can you explore to confirm or counter what you’re thinking?”
- Chalk Talk: Vocabulary Sense-making Post each essential vocabulary term in the middle of a sheet of chart paper. Each student has a marker and rotates from term to term adding his or her definition or comment about that term. Students may not talk. Your “chalk,” in this case a “marker,” does the talking. You could also use this format for Mathematical Reflections by posting each question on a different sheet of chart paper around the classroom. Students could add their understandings, specific examples, and clarifying questions.
The following list of routines is helpful for delving deeper in big idea concepts throughout a Unit:
- What makes you say that? This routine is effective in daily discourse during which students initially engage in the whole-class conversation. When students make a prediction, you can follow up by asking “What makes you say that?” to clarify what reasoning they used to make that prediction. When students make a claim about a situation, you can pose the question “What makes you say that?” to see what evidence they used to come up with that claim.
- Claim, Support, Question This routine is effective to use as students are conducting a gallery walk while quietly (no talking) observing each other’s visual displays of learning around a key exploration. Students are asked to make a claim or conjecture while providing support or evidence for that claim. The teacher follows up the claims with questions such as, “What questions do you still have about these claims?” or “What additional questions did your classmates’ visual displays of learning bring up for you?” Crafting the Summarize phase around students’ challenging each other’s conjectures will deepen student understanding of key mathematical ideas.
These routines are useful for synthesizing and organizing ideas at the close of an Investigation or a Unit:
For this routine, students are asked to capture their new learning from a Unit or an Investigation by composing a headline—a catchy phrase or sentence similar to those seen in newspapers. Students write their headlines on strips of paper that can be posted on the memory wall. It is especially informative when you ask students to explain their headline on the back of their paper strips.
Connect, Extend, Challenge
This routine can be used effectively when comparing student strategies for drawing conclusions about a situation. For example, the Orange Juice Problem, in the seventh-grade Unit Comparing and Scaling, is likely to have multiple student-selected strategies for determining which orange juice mixture is the most flavorful or the least flavorful. As students display their problem-solving techniques and conclusions, you can begin the Summarize by posing questions such as: “What connections do you see among each other’s strategies? How does a strategy that is different from yours extend your thinking or reasoning? How would a different strategy challenge your thinking? Do you have a challenge to pose about a strategy or conclusion that is displayed?” Students may write their responses to these questions prior to engaging in small-group or whole-group discussions. The teacher may circulate during this writing phase to get a sense of which ideas to bring out in the whole- class discussion.
I used to think . . . Now I think . . .
This routine provides teachers and students with an opportunity to formally recognize a change in their thinking from the beginning of an Investigation to the end or from the start of a Problem to its conclusion. Students confront their original thinking about a concept and reflect on what has changed about that thinking. Acknowledging a change in thinking is powerful for all learners. This is easily done with sticky notes.