This is the second post in a 3-part series, published on NCTM’s Teaching Children Mathematics blog.
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.
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.