Making a Student’s Mathematical Thinking Visible

How can we support students in making their thinking visible and how is this connected to a student’s success? As explained in Visible Thinking in the K-8 Mathematics Classroom, “True mathematical learning requires visible thinking. Research shows that, in the mathematics classroom, visible thinking is the key to mathematics learning and success. Evidence of visible thinking is apparent during mathematical discussions, explanations, demonstrations, drawing, writing, and other ways that ideas are conveyed.”

Supporting and scaffolding visible thinking in a math classroom with routines will shift student focus from procedures to conceptual understanding of the content being taught. With visual routines students learn how to organize their ideas, clarify thoughts, and frame their thinking to clearly share mathematical learning with their classmates. Providing students with tools to share their ideas strengthens problem solving skills, encourages deeper thinking, and increases equity in the learning of mathematics.

Figure 1. Table of Visible Thinking: Purposes and Effects for Students. Reprinted from Visible Thinking in the K–8 Mathematics Classroom, by Ted H. Hull, Don S. Balka and Ruth Harbin Miles, 2011, retrieved from https://us.corwin.com/sites/default/files/upm-binaries/41035_Chapter_1.pdf.

Visible Thinking, by Project Zero offers routines to develop Visible Thinking through the use of Thinking Routines in the classroom. These routines are used to promote meaningful collaboration and deepen student understanding. Below are a few examples of useful routines you can use in your math classroom.

Scaffolds such as See Think Wonder support students to show their thinking. This is a routine that gives a framework to promote student inquiry and wonder. This routine can be done whole group, small group, or independently. Students can quietly wonder in their math journals and then share their wonders whole group. A teacher documents ideas on an anchor chart to for students to reference throughout a lesson. 3 Act Math Tasks and Visual Patterns are two great resources to use with this type of routine.

Meaningful Collaboration can be supported by routines such as, Claim-Support-Question. This routine guides students in explaining or justifying their thinking. Collaboration routines are designed to help students develop, nurture, and reflect on good conversations that support learning. Being able to have conversations with their peers allows students to borrow ideas from others to make their claim/understanding stronger. This routine could be used while learning new vocabulary or mathematical concepts.

Think Pair Share and Connect Extend Challenge are two routines that support students in making connections to  prior learning and the ideas of others. A deeper understanding is fostered with intentional planning around grouping and partnering of students, facilitating  a wide range of thinking. Connect Extend Challenge also creates a space for students to think about their challenges and encourages productive struggle.

Visible thinking allows students to share and communicate their thoughts verbally and in written form. Through conversations and collaboration students are actively clarifying and extending their own ideas giving all students a voice. As you prepare for the new year, what scaffolds and visual routines will you try?