By NCTM President Linda M. Gojak
NCTM Summing Up, June 5, 2012

Over the last 20 years, equity has remained a burning issue in mathematics education. It is one of the foundational principles of NCTM. More president’s messages have been on equity than on any other topic. We have position statements and books on equity. Equity is also addressed as one of the six Principles inPrinciples and Standards for School Mathematics (NCTM 2000):

"All students, regardless of their personal characteristics, backgrounds, or physical challenges, must have opportunities to study—and support to learn—mathematics. This does not mean that every student should be treated the same. But all students need access each year they are in school to a coherent, challenging mathematics curriculum that is taught by competent and well-supported mathematics teachers."

As someone who has spent my entire career teaching upper elementary and middle school mathematics and working with K–12 classroom teachers, I am always thinking about how we can learn more and do more to provide every student in our classrooms with the best opportunity to learn. Teaching with a focus on equity means striving to reach each student whose life we impact as a teacher, regardless of the student’s gender, socioeconomic status, cultural background, mathematical experience, limited English knowledge, or physical challenges.

Although we have made some progress, data on achievement gaps indicate that we are still not reaching many of our students. What are some strategies that have the potential to help us make significant progress toward closing the equity gap, and what are the challenges that we face in implementing these strategies at the classroom level?

Using the Processes. Implementing the Process Standards from Principles and Standards for School Mathematics, or the Standards for Mathematical Practice in the Common Core State Standards, as an integral part of instructional practice offers us strategies to empower allstudents to become mathematical thinkers. Presenting rich mathematical tasks in meaningful contexts to students (problem solving) is highly motivational and gives students an opportunity to make connections with previously learned concepts.

This means that we need to think about the interests and experiences of our students as we plan or adapt good tasks. Encouraging students to struggle with new concepts, try ideas, ask questions, discuss with peers (communication), and use a variety of strategies and tools (representation) will help them make sense of the mathematics. We need to consider not only when it is time to intervene to help struggling students, but also how to intervene. What is confusing the student? Is it the mathematics, the language, the context, or something else? What questions should we ask to move the students forward just enough to get “unstuck” without telling them what to do?

It is through our instructional moves that we can help students realize that doing mathematics involves much more than simply arriving at the “right” answer. The challenge is thinking differently about the role of the mathematics teacher. We should encourage our students to become mathematical thinkers, while we refrain from showing and telling them mathematical procedures. They need to be engaged in making sense of the mathematics they are learning. We need to provide opportunities for them to develop conceptual understanding as well as make sense of procedural knowledge. It is time to empower our students to do the showing and telling!

Instructional Strategies. There is no doubt that teachers today are expected to do more in the classroom with fewer resources and less support while under tremendous pressure to demonstrate continued student achievement. One solution is differentiation, a term that is often used with little attention to supporting classroom teachers in adapting their instruction to meet the various needs of their students. Can differentiation lead to equity? It is one strategy that many successful teachers use to make a positive impact on student learning and understanding. At the same time, we need more practical models of effective ways to differentiate mathematics instruction—and we need to be certain that these models reach teachers at the classroom level.

Another instructional strategy to meet the needs of struggling students is a school- or district-based intervention program. In addition to receiving regular classroom instruction, struggling students are provided with extra support. An intervention program can be thought of as a cycle with three phases: diagnostic assessment, instructional actions, and follow-up assessment.

Several questions surface when we are considering intervention:

• Do the three phases of an intervention program offer a model for regular classroom instruction that can have a positive impact on the mathematics learning of all students?
• Is intervention effective if it doesn’t adjust instructional actions so that the instruction offered to students is different from regular instruction?
• Do teachers in intervention programs need to have deeper pedagogical content knowledge than classroom teachers?

All of these questions, when answered yes, pose additional challenges to successful intervention models. We need to remember that speaking more slowly or loudly has never been an effective method of intervention!

Finally, when we consider equity in mathematics education, we cannot overlook talented mathematics students. Is accelerating these students, especially in the upper elementary and middle grades, through mathematics courses the best way to develop and expand their talents and interest in mathematics? Rather, should this be a time to set up rich experiences that allow talented and highly motivated students to “mess around with mathematics” by exploring and extending their mathematical understandings in a variety of contexts and projects? Can we learn more about effective mathematics instruction for all students by affording learning opportunities other than those obtained by moving into the next book or course?

Equity must pervade all of our actions. Actions that ensure equitable mathematics education reach beyond the classroom walls. Administrators must consider issues related to equity in all aspects of instruction in their districts, schools, and classrooms. Research on effective instructional practices must reach teachers at the classroom level. Working together with families ensures that parents and guardians have strategies to support their children at home. Preservice teacher preparation must include effective instructional strategies and encourage future teachers to become lifelong learners as they work to develop instructional practices that will help them meet the needs of all their students.

NCTM Resources. As I prepared this column, I spent considerable time exploring the NCTM website to revisit our  equity resources. Although I was aware of some of the resources on the  Equity Resources webpage, others were new to me. Now that summer is here, what better time to explore the website on your own to find additional resources? If you find something that is especially interesting or helpful, share it with a colleague. Together, we can effectively enrich the successful mathematics experiences of all of our students. Happy reading!