Students transition from physical objects to drawings. They draw dots, arrays, or tape diagrams to represent the tiles they just manipulated.
In mathematics, this approach shifts the focus from "What is the answer?" to: "How did you arrive at that answer?" "What strategies did you use?" "How does this concept connect to what you already know?" Core Principles
Criteria that assess how clearly a student communicates their process, rather than just grading the correctness of their computation.
Have students work in small groups on vertical whiteboards. Standing increases engagement, and the non-permanent nature of whiteboards lowers the stakes, making students much more willing to erase mistakes and try alternative methods. visible thinking in mathematics pdf
Thinking routines are short, repeatable structures used to initiate and explore ideas. Here are the most effective routines specifically adapted for mathematical inquiry. 1. Notice and Wonder
For those looking to implement these strategies, several resources provide structured guides and downloadable materials: Core Strategies Implementation Guides Research & Theory Classroom Routines
Mathematics is often perceived as a collection of abstract rules and procedures. Many students struggle to connect these procedures to real-world applications or to understand the underlying logic. Visible thinking helps to bridge this gap by: Students transition from physical objects to drawings
A section for "Abstract Representation" (equations, variables, calculations).
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
explores how to foster a problem-rich environment where diverse solution paths are celebrated. Practical Frameworks The Institute for Arts Integration Have students work in small groups on vertical whiteboards
Teachers can facilitate visible thinking by adjusting their interaction with students:
Teachers can physically see how a student groups, divides, or builds a number, revealing their structural understanding.
When downloading or purchasing digital manuals and templates, ensure they include: