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

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