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This article discusses visible thinking and its key features and practices. It also discusses the purpose and goals of visible thinking.

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This article highlights making thinking visible by creating artifacts that highlight key elements of their learning.

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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.

Gallery Walks

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. [1] 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:

Headlines

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.

References

[1] Ritchhart, R., Church, M., and Morrison, K. (2011). Making Thinking Visible: How to Promote Engagement, Understanding, and Independence for All Learners. Hoboken, NJ: John Wiley & Sons, Inc.

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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.

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http://minds-in-bloom.com/make-thinking-visible/

This is a blog from a teacher that provides great examples and techniques to use in the classroom to get students to visualize their thinking!

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Making thinking and learning visible in the classroom- Alex Lund 

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Making thinking and learning visible in the classroom- Alex Lund 

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This article discusses unique ways for visible thinking to be used in the classroom. The author of this article believes that the key to thinking visibly in the classroom is to first understand what thinking is!
http://minds-in-bloom.com/make-thinking-visible/

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This article and website overall displays a concise summarization of research and practices on visible thinking and the affect on student attitude in the classroom.

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This article discusses how using the "Think-Pair-Share" strategy in order to to encourage students to think visibly by actively reasoning and explaining their ideas.

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Encourage students to make their thinking visible by asking them to write or draw their ideas before and/or after sharing. Journals can also be useful. Student pairs can report one another's thoughts to the class and a list of ideas can be created in the classroom.

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This article talks about the importance of routines in making visible thinking and some of the different strategies that could be implemented for routines.
http://www.visiblethinkingpz.org/VisibleThinking_html_files/02_GettingStarted/02b_StartingWithRoutines.html

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This article shows how a Kindergarten teacher uses the beginning routine of the making thinking visible by the see, think, wonder strategy. See uses an image from a nature walk to let the students explain what they, see, think, and wonder about the image.

https://thecuriouskindergarten.blog/2014/10/08/see-think-wonder-developing-thinking-routines-in-the-classroom/

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This article provides multiple strategies that teachers can implement into the classroom to make learning visible.
http://minds-in-bloom.com/make-thinking-visible/

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This article clearly explains the many ways students can demonstrate visual thinking through the use of manipulatives.
https://www.hand2mind.com/pdf/learning_place/research_math_manips.pdf

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http://www.pz.harvard.edu/projects/visible-thinking

This is a video on thinking routines teachers can use in the classroom.

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This is a brief article about how making thinking visible is important in math.

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By Jancey Clark, posted October 23, 2017 - Show your thinking
As mathematics classrooms continue to shift from a focus on procedures to more conceptual understanding, students are being asked to "show their thinking." This isn't always easy. Visible Thinking routines can provide students with a structure and scaffold to support making connections, using knowledge effectively, and communicating ideas during problem solving.

In the book Making Thinking Visible: How to Promote Engagement, Understanding, and Independence for All Learners, authors Ritchhart, Church, and Morrison suggest ways to use thinking routines in all subject areas and across all grade levels. As an elementary school instructional coach, I have been excited to see how these routines can be used in the math classroom. The following routines help students see that math is about more than finding the answer.
Develop a deeper understanding of content
The Connect-Extend-Challenge (CEC) routine is perfect for introducing new concepts and skills because it encourages students to draw on prior knowledge and experience. Instead of just asking students to solve a problem, ask them how it connects with other problems they have solved. Then ask them to think about what's new to them-how the task extends their thinking further and deeper than the previous lesson. Finally, asking students to identify what challenges they are facing with the task will provide useful formative data and inform your future instruction.
Promote meaningful collaboration
As mathematicians, our students must be able to communicate a claim, make generalizations, recognize patterns, and provide evidence. The Claim-Support-Question routine guides students in doing so. Start with a claim, such as, "All multiples of nine are also multiples of three." Then ask students to work in pairs or small groups to discuss whether this claim is true or false. They must also provide support, or evidence, using manipulatives and examples. Finally, invite students to share any remaining questions that have been raised and have not yet been answered. This routine will highlight student misconceptions and disagreements, and it will keep the discussions focused on the evidence and how it supports or refutes the claim.
Scaffold students' thinking and learning abilities
To support students in uncovering patterns and developing equations, use the See-Think-Wonder routine with Visual Patterns. First, show students a pattern and ask, "What do you see?" In response, students describe patterns and talk about how they would count the objects. Then, move on to asking, "What do you think?" Instruct students to think about what the next step in the pattern would be. This will lead to the question, "What do you wonder?" Students might wonder about what the 100th step would look like and how they could find out. This discussion will lead students to a conceptual understanding of equations.
Build a culture of engaged thinkers and learners
These are just a few of the Making Thinking Visible routines that can be used in the math classroom. When used explicitly and consistently, Visible Thinking routines will promote active thinking and deep learning. In addition, students will become capable of thinking independently and communicating effectively.
Your turn
How are you transforming the culture of math teaching and learning at your school this year? Use the comment section below to share your ideas and plans for transforming the culture at your school, or join us on Twitter @TCM_at_NCTM using the hashtag #TCMblog.

Jancey Clark is an elementary school teacher and instructional coach who is passionate about personalized learning for both students and teachers. In her current role as elementary school learning coach at the American International School in Riyadh, Saudi Arabia (AIS-R), Clark facilitates professional learning through workshops, coaching cycles, and team planning. As a member of the Near East South Asia (NESA) Council of Overseas Schools Mathematics Collaborative Core, she helps develop and promote professional learning opportunities in mathematics for the NESA community. When she is not learning with colleagues at AIS-R, she enjoys sharing and reflecting on learning through Twitter (@jancey5) and her blog ( EDventures in Coaching).

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Transforming the Culture of Math: Routines for Making Thinking Visible

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By Jancey Clark, posted October 23, 2017 - Show your thinking As mathematics classrooms continue to shift from a focus on procedures to more conceptual understanding, students are being asked to "show their thinking." This isn't always easy. Visible Thinking routines can provide students with a structure and scaffold to support making connections, using knowledge effectively, and communicating ideas during problem solving.

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This website is very helpful and details the thinking routines.