Data suggests a significant decline in U.S. students' math performance exacerbated by the pandemic but rooted in pre-existing issues such as stagnant scores and superficial teaching methods. Learn how to address this issue through systemic changes in math instruction, emphasizing conceptual understanding, discovery-based learning, and project-based learning (PBL) to improve retention and application of mathematical skills in real-world contexts.

The most recent Nation’s Report Card revealed a troubling decline in students’ math performance nationwide, with fourth-grade scores dropping by five points and eighth-grade scores by eight points. As a former math teacher, this news is deeply personal and disheartening, especially for educators who have tirelessly worked to improve students’ mathematical understanding. However, these results are not solely the pandemic's fault—they reflect a long-standing trend that the pandemic exacerbated.

Even before remote learning became a necessity, math scores were stagnant or declining. Between 2017 and 2019, the average math score for U.S. fourth graders rose by just one point, while eighth-grade scores fell by the same margin. Forty states saw no significant changes during that period, and four states experienced declines. These patterns, coupled with the latest data showing scores dropping to 2003 levels, highlight the urgent need for a systemic overhaul in math instruction.

U.S. Education Secretary Miguel Cardona has called for "systemic changes" in teaching practices, and the National Council of Teachers of Mathematics (NCTM) has echoed this sentiment. NCTM emphasizes the importance of a deeper focus on students' mathematical understanding. To address these challenges, it’s time to prioritize a conceptual approach to math education, ensuring students grasp the “why” behind mathematical processes—not just the “how.”

Rethinking Math Instruction

Effective math instruction involves more than shortcuts and formulas. Students need to build a conceptual foundation that allows them to apply knowledge in new contexts and avoid common mistakes. This requires time, focus, and intentional teaching strategies. Yet, current instructional models often undermine these goals due to overly ambitious standards and tight schedules.

Teachers frequently face pressure to cover an extensive curriculum within short daily class periods. This results in rushing through topics, giving students only a superficial understanding of concepts that appear disconnected from one another. To deepen understanding, educators must shift from teacher-led demonstrations to student-driven discovery. While more time-consuming, discovery-based learning encourages students to actively engage with mathematical ideas, fostering better comprehension and long-term retention.

Rather than simply memorizing procedures, students should have opportunities to explore how math relates to their lives. This approach makes learning meaningful and increases the likelihood that key concepts will stick. For instance, during my years in education, I observed that students who engaged with math through hands-on, relevant experiences retained information better and demonstrated greater confidence in applying their knowledge.

Prioritizing Retention & Application

"Retention of math learning" refers to the ability to remember and effectively apply mathematical concepts over time, meaning a student can recall and use previously learned math skills even after a period without direct practice. This is best achieved through a deep understanding of concepts, and strategies like connecting ideas across different math topics.

Project-based learning (PBL) can improve math retention by allowing students to apply mathematical concepts to real-world scenarios, making the learning process more engaging and meaningful, which leads to a deeper understanding and better retention of the material compared to traditional learning methods. Students are more likely to remember concepts when they see their practical application, and can actively use them to solve problems within a project context. 

Key Ways PBL Enhances Math Retention

PBL integrates real-world applications into math instruction, making learning more relevant and engaging. Some of the key ways that PBL enhances retention of math content are:

• Real-world connections: Students can see how math is used in everyday life by applying concepts to projects that mimic real-world situations, like designing a room, calculating budgets, or creating a model to scale, making the learning more relevant and impactful. 
• Active engagement: PBL encourages students to actively participate in the learning process by researching, planning, and executing their projects, which leads to better comprehension and retention compared to passive listening. 
• Deeper understanding: By working through the complexities of a project, students need to not only memorize formulas but also understand the underlying principles and logic behind them, promoting a deeper conceptual grasp. 
• Problem-solving skills: PBL often involves open-ended problems that require critical thinking, collaboration, and creative solutions, which enhances problem-solving skills in a mathematical context. 
• Motivation and ownership: When students have a stake in the project outcome, they are more motivated to learn and retain the necessary math skills to complete the project successfully. 

Examples of PBL Math Tasks

Not sure where to start with PBL in the mathematics classroom? Here are a few examples by grade band. Many more PBL tasks for all grades of mathematics can be found at DefinedLearning.com.

• Early Elementary - Entrepreneur: Lemonade Stand: Students use adding and subtracting to help determine the budget for the supplies for the Lemonade Stand. They also must determine the price of glasses of lemonade and how much change a customer should receive.
• Intermediate - Mini Golf Course Designer: Students calculate area and perimeter as well as apply knowledge of geometric shapes and properties to design a few holes of a mini golf course and create a 3D model of one hole.
• Middle School - Designer: Aquatic Habitats: Students create an aquarium and construct a scale model of their design. They will also write algebraic equations to determine a cost analysis and use inequalities to help aquarium owners understand temperature and pH levels to maintain.
• High School - Smartphone Designer: Students create a scaled model of 2 smartphones and use the Pythagorean Theorem to determine the screen size of their smartphones. They also create an advertisement for their smartphones and use exponents and square roots to determine the screen resolutions.

A Path Forward

To reverse the decline in math scores, we must rethink how math is taught in schools. This means encouraging discovery-based learning and integrating real-world applications through methods like PBL. By focusing on deeper understanding and long-term retention, we can equip students with the skills they need to succeed—not just in math but in life.

About the Author:

Dr. Carolyn Marchetti is a former middle and high school math teacher.  She’s held administrative positions in math and science curriculum, assessment, and supervision at the district, county, and state levels. Carolyn is currently the Vice President of Curriculum and Professional Learning at Defined.