March 2024

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.

**References**

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

johnhayes@cpm.org