Curriculum Coherence: A Foundation for Teaching and Learning in Mathematics

March 2021

Although discussions have always been held about what should be taught in mathematics and how to organize it, now more than ever before (and yes it has already been more than a year since COVID-19 hit!), conversations and questions abound regarding what should be taught; in what order; which concepts, fluency, and skills are key; which are supporting, what is the best sequence . . . well, the list goes on and on. This is always an important set of questions and never more so than right now.

Last June NCTM and the National Council of Supervisors of Mathematics (NCSM) partnered in writing Moving Forward:Mathematics Learning in the Era of COVID-19 to provide guidance for teachers, school leaders, and policy makers on addressing growing challenges, including those related to mathematics curriculum as the 2020–2021 academic year began. The NCTM Back-To-SchoolTask Force also provided resources. I encourage you to revisit these documents; they include key questions, considerations, and resources to guide us as we continue to make decisions about future curriculum.

As we are approach the end of another academic year during which teachers, students, school leaders, and families have been working together through the challenges of the pandemic to engage students in powerful learning of mathematics, these curricular questions will again be at the forefront of many conversations. Individually and collectively, educators have worked to plan and implement a rich mathematics curriculum during these unprecedented times. Although we know that not all students have had equitable access to these learning opportunities, we must also acknowledge that students have experienced important learning in many different ways that include those not specifically guided by teachers, but through home, family, and community experiences. Given the wide variation in learning experiences during the past year, how do we move forward? There is no simple solution for all. One thing is certain: We must move forward by planning together with the realization that this is a long-term investment, not a quick fix. We need to confront the challenges and opportunities grounded in an understanding of the learners and their development by building on their formal and informal mathematical knowledge, strengths, and experiences and by supporting and caring for teachers and schools.

In 2010, Zalmin Usiskin shared the following in the first chapter of the 72nd NCTM Yearbook, Mathematics Curriculum: Issues, Trends, and Future Directions (p. 26): 

There are many possible roads through the world of mathematics, and despite our search for better pathways, choices still remain. Some students need to spend time on things that other students do not. Some students benefit from detours that motivate and capture their attention. Furthermore, just as there are individual differences amount students, there are individual difference among teachers, and what works for one teacher may not work for another. In designing and implementing curriculum—as in building roads—we need to have enough instructional options, enough stops along the way, enough side trips or detours so that a teacher can choose what she or he deems best for the students.

Then Usiskin raised the question, How do we decide which roads to take through this world of mathematics? And this is certainly the question we are asking today! Various students, teachers, and contexts may require different pathways, but here are a few ideas to remember as we support equitable access for each and every student. They are synthesized from the Catalyzing Change series (NCTM 2018–2020), Principles to Actions: Ensuring Mathematical Success for All (NCTM 2014), and Curriculum Focal Pointsfor Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (NCTM 2006).as we support equitable access for each and every student: 

We must focus on grade-level curriculum with effective supports in place for students and appropriate supports for teachers so that each and every student has the opportunity to learn grade-level content.

Teachers’ knowledge and understanding of the curriculum must be larger than their own grade level and must include the understanding of connections across grade levels. This supports students in seeing how the mathematics builds on their previous understanding and connects to their future learning.

To ensure coherent learning experiences for each and every student, the curriculum should address rigorous and relevant mathematics and be flexible, relevant, and responsive to current student needs, situation, and contexts.

Ensuring equitable access for all students is imperative. We must not label students or sort them into perceived ability groups that result in dead-end pathways for students in mathematics.

Attending to coherent learning progressions that support a coherent sequencing of key mathematical concepts is essential.

How do we start? I believe it is through collaboration, essential conversations, thoughtful planning, and extensive communication so all voices are heard. We must provide a consistent, coherent curriculum that is purposeful in the development of conceptual and procedural understandings and connected to rigorous and engaging mathematics instruction. To be sure, we have many guiding documents to assist in these endeavors. Each grade band of Catalyzing Change provides essential areas or domains that serve to illustrate how deep mathematical understanding might be developed across PK–12. These can provide a starting point for critical conversations in the decision-making process regarding the curriculum as we look at the upcoming year as well as curriculum over time. Curriculum Focal Points is a foundational document for this thinking within and between grade levels PK–8. Various standards documents, including the 2010 Common Core State Standards in Mathematics (National Governors Association Center for Best Practices and the Council of Chief State School Officers), and various state standards build from this effort. In addition, Pre-K-12 Guidelines for Assessment and Instruction in Statistics Education II (GAISE II): A Framework for Statistics and Data Science Education provides an in-depth look at statistics, data science, and data literacy.

Why do this? Because our teachers and our students deserve it and need it. Mathematics curriculum requires expertise in constructing a purposeful, responsive, and coherent plan for teachers and students. We need leadership and collaboration to provide this to teachers so that during the coming academic year, they can focus their energies and expertise on creating a rigorous, supportive, and engaging mathematics learning environment for every student in their class. As Zalman questioned, how do we decide among the many different paths? We decide by working together as collaborative partners so the valuable information learned informs us all.  What teachers do with students has a significant impact on their learning. We need to support teachers as they focus their efforts to develop each and every student into a confident, capable learner and doer of mathematics.

Trena Wilkerson
NCTM President
@TrenaWilkerson