Transforming the Culture of Math: Routines for Making Thinking Visible
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
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.
a deeper understanding of content
(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
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.
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.
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.
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).
Nice post it is. Many information are there with great accuracy. I would like to appreciate all your efforts, I have used many other services several times and I am very happy with it too. Finally once more thank you for this breathtaking article and I like this. custom essay writing service I hope this will be very helpful to the students to complete their educational works related with the topics.