"Making Thinking Visible: How to Promote Engagement, Understanding, and Independence for All Learners" Authors: Ritchhart, R., Church, M., & Morrison, K. Source: Jossey-Bass (Book) / Key Article: "Intellectual Character" (2002) or the Educational Leadership article below.
Visible thinking in mathematics is a research-based pedagogical framework that shifts the focus from rote memorization of procedures to the active externalization of reasoning processes. By using structured routines and visual tools, educators can help students move from concrete representations to abstract mathematical concepts, fostering a deeper conceptual understanding. Core Benefits of Making Thinking Visible visible thinking in mathematics pdf
| Routine | Purpose | Math Prompt Example | |---------|---------|----------------------| | | Initial exploration of a problem, graph, or pattern | See : three blue shapes, Think : maybe it’s a pattern of +2 sides, Wonder : what comes after 9 sides? | | What makes you say that? | Justifying reasoning | “I think 17 is prime.” — “What makes you say that?” | | Claim-Support-Question | Building arguments | Claim: “The sum of two odds is even.” Support: “odd+odd = (2m+1)+(2n+1)=2(m+n+1).” Question: “Does this work for negative odds?” | | Connect-Extend-Challenge | Linking new math ideas to prior knowledge | After learning integer division: Connect to sharing cookies; Extend to zero; Challenge: what does ÷ by a negative mean? | | I used to think… Now I think… | Metacognitive change | “I used to think commutative works for subtraction; now I think it doesn’t because 5–3 ≠ 3–5.” | By using structured routines and visual tools, educators
Research has shown that visible thinking in mathematics leads to numerous benefits, including: | Justifying reasoning | “I think 17 is prime
While blog posts are helpful, a structured offers unique advantages for professional development:
As mathematics educators, we strive to help our students develop a deep understanding of mathematical concepts and principles. One effective way to achieve this is by promoting visible thinking in the mathematics classroom. In this blog post, we'll explore the concept of visible thinking in mathematics, its benefits, and provide practical strategies for incorporating it into your teaching practice.