CPM Glossary


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P

Principles of Assessment

Guidance for teachers and all stakeholders regarding assessment practices and suggest teachers create their own tests, work through all assessments, only assess material students have had ample time to engage with, formatively assess as a learning experience for both students and themselves, and be flexible in grading to allow differences in reaching mastery.


Principles to Actions

Also known as PtA, strategies for teachers to engage students in mathematical thinking, reasoning, and sense making to significantly strengthen teaching and learning’ put forth by the National Council Teachers of Mathematics to offer guidance to teachers, mathematics coaches, administrators, parents, and policymakers.


Principles to Actions Executive Summary

An introduction which sets out the Mathematics Teaching Practices - consistent components research states are needed for every mathematics lesson; productive and unproductive beliefs for facing obstacles as well as suggestions for combating the issues; and a call to action to recognize the critical need in education to develop understanding in math education and confidence for all students.




Problem-Based Learning

Research says students learn ideas more usefully for other arenas when they learn by attacking problems.

Problems-Based Learning is evident in a classroom when

  • Students and teachers share math authority as they value and engage in productive struggle
  • Teachers guide without taking over the thinking.

Process Goals

Process goals are designed to build habits, stick to consistent routines, and define success as growth in one's skills and abilities.  For example, process goals might refer to how students complete their work using the Standards for Mathematical Practice.  Teachers may have particular success criteria attached to these Learning Goals that explain how and when students may demonstrate their proficiency level.


Product Goals

Product goals are project-oriented, stick to firm deadlines, and define success by the completion of great work.  For example, product goals might refer to which math problems that students should complete by the end of the day or class period. Teachers may have particular success criteria attached to these Learning Goals that explain how and when students may demonstrate their proficiency level.


Productive Struggle

One of the eight Mathematics Teaching Practices from Principles to Actions that needs to be a consistent component of every mathematics lesson. Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships.

“…productive struggle comprises the work that students do to make sense of a situation and determine a course of action when a solution strategy is not stated, implied, or immediately obvious. From an equity perspective, this implies that each and every student must have the opportunity to struggle with challenging mathematics and to receive support that encourages their persistence without removing the challenge.”

Boston, Melissa D., Fredrick Dillon, Margaret S. Smith, and Stephen Miller. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 9-12. Reston, VA: National Council of Teachers of Mathematics, 2017. [p.208]


Professional Noticing

Professional Noticing requires that the teacher be able to: identify relevant aspects of the teaching situation; use knowledge to interpret the events, and establish connections between specific aspects of teaching and learning situations and more general principles and ideas about teaching and learning. Professional noticing is a crucial component of CPM math teacher competency and requires not only knowledge and expertise with mathematics, but also knowledge of the pedagogy associated with using the curriculum as intended.


Professional Outcome 2

Establish professional relationships and learning communities that support lifelong professional growth and a commitment to mathematics education


Professional Outcome 3

Reflect on the efficacy of their instructional practices and share instructional challenges and successes with colleagues



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