A Rubric for the Mathematical Teaching Practices

I’ve been working to develop a rubric for the mathematical teaching practices outlined in Principles to Actions. The eight practices define what I want my teaching to look like, but at times I think they can be too general to be really practical for giving myself feedback or identifying areas for growth. In addition, I have a Professional Learning Community at my new school that is composed of non-math teachers, and the language in the eight practices is, I think, too vague to present to someone outside the discipline. In addition, I think that naming two or three specific practices and their elements as focus areas to frame an observation will help make those times more useful.

Anyway, here’s my first draft. I would love to get feedback, both on the substance of this rubric, and possible alternate approaches that could be more clear or more useful.

Practice 1: Establish Mathematical Goals to Focus Learning

    • Students achieve clarity, by the end of the task or lesson, on its purpose and how it is connected to prior knowledge and future learning
    • Introductory lessons effectively motivate learning through perplexity, placing a concept in context and provision an expert model to guide student thinking, either student-generated or teacher-generated
    • Practice lessons provide opportunities to deepen understanding through deliberate practice toward clear learning goals
    • Students have opportunities to transfer learning and make explicit connections between concepts

Practice 2: Implement Tasks that Promote Reasoning and Problem Solving

    • Tasks are designed based on curricular expectations while also promoting non-routine thinking and new perspectives
    • Tasks provide opportunities for spaced and interleaved practice of concepts
    • Tasks have multiple entry points to allow both access to struggling students and challenge to high achievers

Practice 3: Use and Connect Mathematical Representations

    • Connections between representations are made explicit, by either students or the teacher, throughout learning
    • Students access concepts using multiple representations and perspectives to deepen understanding
    • Technology, manipulatives, and interactive materials are used as an aid to support understanding

Practice 4: Facilitate Meaningful Mathematical Discourse

    • Topics for discussion and discourse promote alternate approaches and disagreement that deepens understanding
    • Students communicate in writing, in pairs, in small groups, and in front of the entire class
    • Students speak both off-the-cuff and with preparation
    • Students have opportunities for formal and informal feedback on communication about math

Practice 5: Pose Purposeful Questions

    • Questions are scaffolded to provide access points at multiple levels
    • Questions provide think time, both mental and in writing, for students
    • Questions highlight key misconceptions or underlying concepts
    • Questions build toward key understandings

Practice 6: Build Procedural Fluency From Conceptual Understanding

    • Conceptual groundwork precedes practice for key skills
    • Foundational skills for which fluency is necessary are clearly identified and students have the opportunity for spaced, deliberate practice
    • Student practice is characterized by both spaced practice of key skills and reflection on where those skills fit into the larger picture

Practice 7: Support Productive Struggle in Learning Mathematics

    • All students have opportunities to be unsuccessful and work to a better understanding
    • Students are praised for effort and perseverance over intelligence or aptitude

Practice 8: Elicit and Use Evidence of Student Thinking

    • Tasks elicit genuine evidence of student understanding through varied question types and a conceptual focus
    • Teacher has the opportunity to examine evidence of student thinking objectively and without bias
    • Teacher has the opportunity to use student thinking to inform the lesson progression
    • Students have the opportunity for feedback that calibrates their work to standards of excellence
    • Students have the opportunity for feedback that allows for further mathematical thinking

Principles to Actions
Principles to Actions Executive Summary
Make It Stick
How People Learn

One thought on “A Rubric for the Mathematical Teaching Practices

  1. Joe Roicki

    Thank you for this! I, too, am working on developing a rubric for these 8 Teacher Practices. I’m trying to break it down into a progression of actions (Levels 1-4, with Level 4 being what is suggested in Principles to Actions).


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