Tools that assess the depth of the thinking rather than just the mathematical accuracy, encouraging students to value the process. Conclusion

What do you already think you know about this mathematical topic?

Step-by-step protocols designed specifically for mathematical inquiry (e.g., "See, Think, Wonder" adapted for geometry or data analysis).

Think-Puzzle-Explore: This routine encourages students to identify what they already know about a topic, what they are puzzled by, and what they would like to explore further. It can be used to introduce a new topic or to deepen understanding of an existing one.

: Students become more aware of their own thought processes, helping them reflect on and refine their problem-solving strategies.

Thinking routines are micro-structures—typically consisting of a few steps—that are used repeatedly in the classroom to scaffold and extend student thinking. Here are some of the most effective routines adapted specifically for the mathematics classroom. Routine 1: See, Think, Wonder

When evaluating a mathematical assertion or a peer's solution, students must:

Visible Thinking in Mathematics is a pedagogical approach—often associated with the book series by Ammiel Wan and Ang-Poh Ai Min—that shifts the focus from rote memorization to conceptual understanding by making students' internal thought processes clear and concrete. Core Components of the Approach

There are many different visible thinking routines that can be used in the mathematics classroom. Some popular examples include:

What do you think you know about this mathematical topic or problem?

Visible Thinking in Mathematics is not another task to add to the curriculum; it is a way of doing the curriculum. By making thinking visible, we empower students to be owners of their mathematical journey, transforming them from passive observers into active, critical, and creative thinkers.

Model the routines: Show your students how to use the routines by using them yourself. Explain your thinking out loud and encourage your students to do the same.

Include one-page summaries of specific thinking routines. These serve as quick-reference guides for teachers to keep on their desks during lesson planning, detailing the prompt style, time allocation, and student grouping for each routine. Formative Assessment Rubrics