How do I know what my students know, can do, and understand?


  • develop my professional knowledge of mathematical concepts in order to support student learning through examining learning continua, trajectories, and progressions
  • give students opportunities to make their mathematical thinking visible through multiple communication formats:
    • constructing with materials and building models
    • dialogue and discussion
    • drawing diagrams, pictures, charts
    • using symbols
    • photos and descriptive captions
    • creating narratives
    • writing
    • use technology tools to capture student learning
  • recognize and embrace "mistakes" as part of deep learning and productive struggle
  • use evidence of student learning to inform and guide planning for next steps with students
  • assess in a variety of ways: product, observation, conversation


Professional Books

This book provides strategies for maximizing student's comprehension by integrating visual thinking into the classroom.

Hull, Ted 2011

This resource helps teachers direct student thinking and structure classroom discussion. Good for all grade levels.

Ritchart, Ron 2011

This book identifies the critical learning phases children go through as they develop their mathematical understanding that is essential to building a solid foundation of numerical reasoning.

To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like to get there.

Hattie, John 2016

The authors offer an alternative assessment method by examining a wide variety of assessment tools and match the student evidence with a description of achievement.


The following resources provide teachers with information about formative assessment, including ways to make thinking visible.

The resources below help teachers understand the learning progression for students as they learn and understand mathematical concepts.


These resources can support teachers with their own mathematical understanding.


Video: What is Visible Learning for Mathematics