March 2024

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Developing an equitable assessment practice is challenging even when using a high-quality standards-based curriculum such as CPM.

You have probably taught a student who had an accommodation for taking math assessments. Maybe the student leaves the room during the assessment to take the test in a different location, or maybe they have someone read every problem to them, or they have extra time. Then, despite these accommodations, the student still is unsuccessful. You may think that offering retakes seems pointless because of a belief that the student just does not seem to be able to demonstrate their true understanding on the traditional paper and pencil assessment.

In the example above, the accommodated student is unable to reach their full potential. It is important to recognize that being equitable—creating opportunities for all students to reach their full potential in mathematics—is an ongoing process that requires consistent reflection.

To be sure, using CPM as intended provides a huge first step with equitable instruction, but there are still roadblocks that may inhibit a student from reaching their full potential in a CPM classroom. One of these roadblocks might be a belief that equity is the same thing as equality, and similarly, that paper-and-pencil tests give objective measurements of what students know and can do. 

Different Students, Different Strengths

Different students have different strengths and ways of demonstrating their understanding. Knowing that there are differences, does it make sense to give traditional paper-and-pencil tests to each student? Is that equitable?

The practice of giving all students the same type of assessment may be neither equitable nor productive in motivating all students to learn. In some cases, giving a test seems to be more about compliance than identifying understanding. Yet, we continue to use this practice because we believe it is an objective measurement, making it an equal and therefore equitable practice. But there is no one-size-fits-all assessment practice that can help all students reach their full potential. We can, in fact, say that this practice is not equitable because students with accommodations frequently have to retest, take more time to test, or have other accommodations, putting more work on both the student and the teachers. This extra work highlights the shortcomings of the traditional paper-and-pencil tests. 

I will say it again: different students have different strengths and ways of demonstrating their understanding. Rather than continuing to look for the perfect pencil-and-paper test or trying to find the all-encompassing accommodation, maybe we need to change the overall paradigm of assessment—especially considering that we often use this same equality practice in a very final and summative way to justify putting certain students on an accelerated track while placing others on a remedial track.

Equality is not equity, even in assessment. Hoyun Cho, in his paper “Equity in Mathematics Assessment,” writes, “…not all students show their mathematical understanding in the same way” (Cho, p. 96). He continues, “Achieving equity in assessment implies that students have an opportunity to demonstrate an understanding of mathematical concepts in a way that is consistent with their learning styles” (p. 97). Similarly, one of CPM’s Productive Assessment Belief Statements is that “Authentic assessment means assessing in a manner that mirrors the way the students have learned, and focusing on what the students know, rather than what the students do not know.” 

Assessment that Mirrors Mathematics Learning

Core Connections Algebra Sequence Assessment. © CPM Educational Program.

One idea for equity in assessment comes from Dr. Peter Liljedahl’s book, Building Thinking Classrooms (see Ch. 14). Liljedahl uses a checkmark when knowledge has been demonstrated individually, an ‘S’ when knowledge has been demonstrated with a small mistake, an ‘H’ when it has been demonstrated with help, a ‘G’ when it was demonstrated in a group, an ‘X’ when answered incorrectly, and an ‘N’ when it was not attempted (see the figure). 

Liljedahl’s approach to assessment leverages a teacher’s ability to observe and assess students during multiple modes of instruction—such as during circulation, team challenges, or even individual work time. Because this method for assessment mirrors the way that students are learning mathematics, it may mitigate some of the frustration that accompanies traditional assessment, and it is a much more authentic assessment practice in a CPM classroom. As a data collection and scoring method, you may also consider using it in other settings such as during a team assessment, while students are working on Vertical Non-Permanent Surfaces, or on select Review & Preview problems. This practice could also provide an effective summative experience for some students, particularly those who have struggled with paper-and-pencil assessments, or even all students, in lieu of a paper-and-pencil assessment. 

Of course, in order to be equitable, Liljedahl’s assessment strategy must be grounded in documenting students’ understanding and not on compliance.

Yes, developing an equitable assessment practice is challenging. But when we are willing to engage in the process of constantly reflecting on our beliefs to identify roadblocks in our instructional practices, students will have a better chance to reach their full potential.


Cho, Hoyun. (2012). Equity in Mathematics Assessment. Journal of Mathematics Education at Teachers College, 3, 96–98.

Liljedahl, Peter. (2016). Building Thinking Classrooms in Mathematics: 14 Practices for Enhancing Mathematics Learning. Routledge.

John Hayes

John Hayes

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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.

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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.