Expert Viewpoint

Rethinking How We Teach Math: Three Tips for Better Long-term Retention

• By Josh Britton
• 02/01/23

In the latest version of the Nation’s Report Card, students’ math scores fell an average of five points for fourth graders and eight points for eighth graders nationwide. This historic drop in scores hits close to home for me as a former math teacher, and I recognize how disheartening it feels for educators who have worked so hard to build their students’ math knowledge over the last few decades.

It’s easy to blame the pandemic alone for these poor test results. But the truth is, U.S. students’ math scores were flat or declining even before schools and districts shifted to remote learning. The pandemic accelerated a trend that was already under way.

While the average NAEP math score in 2019 for U.S. fourth graders rose by one point, the average score for eighth graders dropped by the same amount. Between 2017 and 2019, 40 states and jurisdictions had no significant change in their average math scores—and four saw their scores fall.

When you factor in the latest NAEP results as well, it’s obvious that current approaches to math instruction just aren’t working, despite our best efforts—it’s time to rethink how we teach foundational math concepts in our classrooms.

After the release of the report, U.S. Education Secretary Miguel Cardona called for “systemic changes” in how educators teach math. According to the National Council of Teachers of Mathematics, the results “point toward the need for a greater focus and higher priority on mathematics instruction.” The fact that average NAEP math scores dropped back to 2003 levels highlights the need for “increased focus on students’ mathematical understanding,” the organization said.

NCTM is right. Our students need to learn not only math shortcuts, processes, and formulas — they also must learn the underlying concepts behind them. Students need a deeper conceptual understanding of math so they can transfer their knowledge to new contexts and are less prone to making mistakes.

But that’s not all students need. They also need more time for learning math in school and more focus on long-term retention.

With so many standards that teachers must cover, often in an unrealistic time frame (such as a 40-minute class period each day), teachers often find themselves rushing through the curriculum in order to cover the required topics. As a result, students get a brief exposure to many topics that seem siloed, instead of an in-depth understanding of math and an appreciation for how these various ideas are interconnected.

This same drive to cover all the standards in such a limited amount of time leads to an overreliance on teacher-demonstrated processes, rather than student discovery facilitated by the teacher. The latter takes more time but is a much more powerful instructional approach, deepening students’ understanding and motivation through doing.

Rather than simply memorizing procedures and steps, student discovery encourages students to apply math to their lives — increasing the likelihood important concepts and lessons stick.

The pressure that teachers feel to push forward into new math content also prevents many of us from devoting any class time to ensuring retention. During my 18 years in the classroom, I had students who struggled with long-term retention of key concepts.

I realized that if students aren’t retaining these concepts, they’re unable to build the strong foundation they need to learn new, more difficult material. So much of new math learning builds upon students’ prior understanding. If students don’t retain this information, they’re likely to encounter problems down the road.

Carving out more time within the school day for students to learn math helps. Based on my own teaching experience, here are three additional strategies I’ve found to be effective in improving long-term math retention for all students.

Three Key Ways to Improve Student Math Retention

1) Allocate time for daily spiral review.

The key to enhancing students’ long-term math retention is to mix in a review of earlier content as students are learning new concepts. This doesn’t have to take time away from instruction: Teachers can give students practice problems that focus not only on the latest skill or concept, but also concepts from previous units.

This practice is called spiral review, and it can be quite effective in reinforcing key concepts. It can also deepen students’ understanding of math: By revisiting and reviewing material over time, students are able to build on their understanding and see the connections between different ideas.

2) Use cumulative assessments to track students’ progress and determine areas of need.

Just as teachers should have students regularly review prior content, they should also include concepts that students learned earlier in the school year on tests and quizzes. Making every test a cumulative assessment of students’ knowledge provides valuable insight into the gaps in understanding that could stand in the way of students’ further progress, allowing teachers to give students highly targeted practice on those skills.

3) Implement tools to save teachers’ time and make instruction more efficient.

With class time at a premium, teachers need tools that can help them make the most of this time, such as software that combines math practice and assessment by quickly identifying the skills students need to practice further and delivering problems that target those skills. Automating these processes means that every student can receive highly personalized math practice and assessment, while freeing up teachers to work one-on-one with students as needed.

There’s no question that COVID had a tremendous impact on education, and we see those effects in the latest iteration of the Nation’s Report Card. The pandemic was tough on everyone, but a small silver lining is that it has allowed us to take a step back, determine what’s best for our students and try new things.

As schools move forward, now is the time to rethink how we teach foundational math concepts to position students for success by implementing strategies we know are effective — and focusing on students’ long-term math retention. Techniques such as spiral review and cumulative assessments are an important aspect of these efforts.