Transforming the Culture of Math: Routines for Making Thinking Visible

  • Transforming the Culture of Math: Routines for Making Thinking Visible

    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.


    2017_10_09_ClarkAuPicJancey 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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    Max 456 - 1/17/2021 1:23:24 AM

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    Shayna Engelhardt - 10/9/2020 10:15:15 PM

    Hello, my name is Shayna Engelhardt and I am a senior at Wartburg College. I am studying Secondary Mathematics Education. As a future educator I want to tranform the culture of math by using new methods of teaching math. Due to me being a student for so long I have seen that teachers get settled in the way they teach which can be good for the students who understand, but for me personally was hard. I had many teachers who teaching styles did not make sense to me and in turn made learning the things they were teaching harder. This is why I want to make sure I have a lot of different style so that hopefully I will be able to see what is best for my students.

    Gayle Allen - 4/26/2020 7:49:27 AM

    Just as we were getting into the final kindergarten stage of transforming addition thinking into subtraction, we were rudely interrupted! Thankfully, the community of educators online came to the rescue as myself and MANY others rewrote our mindsets and began the arduous task of online learning/teaching. As a kindergarten teacher, I have found the Seesaw site to be my favorite. With the wealth of lessons available and the ability to create my own and share them with others my children can still explore their thinking. Jancey, I love your terms for the thinking process and I hope you won't mind if I incorporate them into my planning. Thanks for sharing. By the way, the link to your blog does not seem to be a working link.

    jamie sumpter - 2/29/2020 6:49:39 PM

    This is a great blog. It is so important that students open up their minds. Deeper thinking can help students in so many ways. It can help them in school and also in the real world. I love the idea of visible thinking 

    Drew Howard - 2/29/2020 12:00:48 PM

    I agree with this blog. It is good that the students get to build a culture of engaged thinkers. It is also good that students are learning thinking and learning abilities.