Starting the School Year with Coherence and Connections

August 2021

We are here again—the time of year when we are “returning” to school; but with the pandemic still looming over us, that return may be in person, virtual, hybrid, or even moving back and forth between formats to ensure the safety of our students and teachers. Whatever the format, returning to school, although potentially challenging, is exciting. We are ready to meet our students and colleagues; do mathematics; learn new concepts; make discoveries; make sense of our world through the lens of mathematics; and explore the wonder, joy, and beauty of mathematics. 

Recently I was reviewing Continuing the Journey: Mathematics Learning 2021 and Beyond that was developed collaboratively in July by NCTM, NCSM: Leadership in Mathematics, and the Association of State Supervisors of Mathematics (ASSM) to provide guidance in decision-making to support each and every student in learning mathematics upon returning to school in the fall. When I created a word cloud from the narrative, I noticed that student/learner was the word that occurred the most. This is as it should be. Students are the center—the reason we teach mathematics. They are our “why.” Our students bring their own experiences, interests, strengths, and brilliance to the learning of mathematics. John SanGiovanni, coordinator of elementary mathematics in the Howard County School System in Maryland, reminds us that even in the midst of this pandemic, “Kids are coming to us with strengths. They have learned things this year. We want to find those and build on that” (Adams 2021). We as teachers have the honor and opportunity of working with our students to build on what they know. But how do we do this? Although many considerations are discussed in Continuing the Journey, I want to focus on two areas, coherence and connections.

Students should see how mathematics builds on their prior knowledge and their mathematical learning experiences. Mathematical coherence occurs when concepts are connected within and across grades with strategic, intentional attention to mathematical processes and practices. We need to leverage the powerful connections among concepts, procedures, and skills to deepen student mathematical understanding. By incorporating big ideas and essential understandings of mathematics in each grade level or course, we can support student mathematical thinking to cultivate deeper understanding. When students experience mathematics as disconnected mathematical ideas, they are unable to develop a strong foundation in mathematics, that is, one that will support them in understanding mathematical structure, applying mathematics in context, and making informed decisions. As pointed out in Continuing the Journey, “When a coherent and connected approach is taken, content from previous grades that students may seem to be ‘missing’ can be taught along with grade-level content or just-in-time support” (p. 1). Creating greater coherence and focusing on connections is a matter of equity. It is a matter of each and every student seeing themselves as a thinker and doer of mathematics, building a positive mathematical identity.

In the August 2021 issue of Mathematics Teacher: Learning and Teaching PK–12, Brian Mahaffey, a middle school mathematics teacher, shared about how a rethinking of rigorous instruction on his teaching journey had transformed his classroom. He pointed out that although finding the balance among concept, procedures, and applications was challenging, doing just that was important to implement rigorous instruction that was meaningful to students. When I consider that balance, I think about the coherence and connections that are brought to bear on mathematics when we approach our teaching in a way that brings together all three to build on student knowledge and support a deeper understanding of mathematics.

I am excited to share that NCTM’s community of mathematics educators and leaders have come together to develop a collection of “grab and go” resources to help teachers design learning opportunities for students to make connections within and across grade levels, support coherency, and emphasize reasoning and sense making to ensure the highest-quality mathematics education for each and every student. Guided by the three critical focus areas outlined in Continuing the Journey, the lessons, webinars, and articles available on the NCTM website will help you promote a school structure that eliminates unproductive challenges for all students. We hope you will find these resources useful to you as you return to school to engage your students in powerful mathematical experiences. 

Trena Wilkerson
NCTM President
@TrenaWilkerson

References

Adams, Caralee. 2021. “Solutions: Zeroing In on a Handful of Strategies to Catch Kids Up in Math.” The Hechinger Report. August 25, 2021.

Mahaffey, Brian. 2021. “Teaching Is a Journey: Rigorous Instruction Transformed My Class.” Mathematics Teacher: Learning and Teaching PK–12 114, no. 8 (August): 641–42.