Research Base

CPM is Built Upon Three Pillars

CPM's curriculum and professional development are grounded in decades of mathematics education research. Our Three Pillars were synthesized from NCTM standards and constructivist research — and they continue to be validated by current scholarship.

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Our Foundation

The Three Pillars

Synthesized from NCTM standards and research on constructivism in the early 1990s, CPM's Three Pillars continue to be reflected in current mathematics education research and standards — and their benefits for student learning only deepen over time.
CPM Three Pillars graphic showing Collaborative Learning, Problem-Based Learning, and Mixed Spaced Practice
Dr. Tom Sallee

CPM Co-Founder

Dr. Tom Sallee

Mathematician & Research Base Author

Dr. Tom Sallee, a mathematician and co-founder of CPM, reviewed and synthesized the research on mathematics learning in relation to each of The Three Pillars. Read CPM's research base reports below to learn more about the evidence behind CPM's instructional approach.

2024 Edition

2024 CPM Research Base Report

The full 2024 update to CPM's research base, organized by each of the Three Pillars. Download individual sections or start with the introduction.

Research Base Introduction
Overview and context for the 2024 report
Download PDF
Collaborative Learning
Executive Summary
Collaborative Learning
PDF
Full Report
Collaborative Learning
PDF
Problem-Based Learning
Executive Summary
Problem-Based Learning
PDF
Full Report
Problem-Based Learning
PDF
Mixed, Spaced Practice
Executive Summary
Mixed, Spaced Practice
PDF
Full Report
Mixed, Spaced Practice
PDF

Original Report

Original CPM Research Base Report

The foundational research synthesis authored by Dr. Tom Sallee that established CPM's Three Pillars framework — still relevant and illuminating decades later.

Full Original CPM Research Base Report
The complete original report authored by Dr. Tom Sallee
Download PDF

1 CPM originally used the term "cooperative learning" rather than "collaborative learning." As research emerged showing the powerful difference between cooperative and collaborative learning for student outcomes, CPM has shifted its language to reflect the research. For more information, please see the Cooperation v. Collaboration Research Brief (PDF).

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See the Research in Action

Explore CPM's full research hub, read independent performance reports, or learn how CPM supports student and teacher outcomes in districts nationwide.

Statistics

JAVA

Calculus
Third Edition

Precalculus
Third Edition

Precalculus
Supplement

2.3.4

Defining Concavity

4.4.1

Characteristics of Polynomial Functions

5.2.6

Semi-Log Plots

5 Closure

Closure How Can I Apply It? Activity 3

9.3.1

Transition States

9.3.2

Future and Past States

10.3.1

The Parametrization of Functions, Conics, and Their Inverses

10.3.2

Vector-Valued Functions

11.1.5

Rate of Change of Polar Functions

Matemática
Integrada I

Matemática
Integrada II

Matemática
Integrada III

Integrated I

Integrated II

Integrated III

Core Connections en español, Álgebra

Core Connections en español, Geometría

Core Connections en español, Álgebra 2

Core Connections
Algebra

Core Connections Geometry

Core Connections
Algebra 2

Core Connections 1

Core Connections 2

Core Connections 3

Core Connections en español,
Curso 1
Core Connections en español,
Curso 2
Core Connections en español,
Curso 3

Inspiring Connections
Course 1

Inspiring Connections
Course 2

Inspiring Connections
Course 3

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Algebra Tiles Blue Icon

Algebra Tiles Session

  • Used throughout CPM middle and high school courses
  • Concrete, geometric representation of algebraic concepts.
  • Two-hour virtual session,
  •  Learn how students build their conceptual understanding of simplifying algebraic expressions
  • Solving equations using these tools.  
  • Determining perimeter,
  • Combining like terms,
  • Comparing expressions,
  • Solving equations
  • Use an area model to multiply polynomials,
  • Factor quadratics and other polynomials, and
  • Complete the square.
  • Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

Foundations for Implementation

This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.

Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.

Building on Instructional Practice Series

The Building on Instructional Practice Series consists of three different events – Building on Discourse, Building on Assessment, Building on Equity – that are designed for teachers with a minimum of one year of experience teaching with CPM instructional materials and who have completed the Foundations for Implementation Series.

Building on Equity

In Building on Equity, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning. Essential questions include: How do I shift dependent learners into independent learners? How does my own math identity and cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks. Participants will develop their use of the 5 Practices for Orchestrating Meaningful Mathematical Discussions and curate strategies for supporting all students in becoming leaders of their own learning. Participants will use an equity lens to reflect on and revise their Chapter 1 lesson plans.

Building on Assessment

In Building on Assessment, participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions. On day one, participants will align assessment practices with learning progressions and the principle of mastery over time as well as write assessment items. During day two, participants will develop rubrics, explore alternate types of assessment, and plan for implementation that supports student ownership. On the third day, participants will develop strategies to monitor progress and provide evidence of proficiency with identified mathematics content and practices. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

In Building on Discourse, participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the Effective Mathematics Teaching Practices incorporated through intentional and reflective planning.