Responding to Calls to Improve Mathematics Students’ Learning and Retention: Leveraging Research on Mathematics Learning

For more than half a century, mathematics education leaders have voiced the same urgent message: precalculus and introductory calculus must be taught in ways that help students think mathematically, not just memorize formulas. Professional organizations such as the National Council of Teachers of Mathematics (NCTM), the Mathematical Association of America (MAA), and the American Mathematical Association of Two-Year Colleges (AMATYC) have all issued standards and position papers urging curriculum reform. They have called for instruction that emphasizes conceptual understanding, reasoning with functions, and the ability to model dynamically changing quantities in applied contexts.
And yet, despite these repeated calls, relatively little progress has been made in classrooms across the country. Passing rates remain stubbornly low, many students leave STEM fields after struggling in early mathematics courses, and countless instructors continue to rely on traditional, lecture-heavy approaches. For decades, precalculus and calculus have been described as “gatekeeper” courses that block students from achieving their goals rather than launching them toward success.
Against this backdrop, Dr. Marilyn P. Carlson has built her career around addressing this single, persistent challenge. A Professor of Mathematics Education at Arizona State University, Carlson has dedicated more than three decades to understanding why students struggle in precalculus and calculus, and to creating research-based solutions that make genuine improvement possible.
Carlson’s research has revealed that student struggles are not primarily the result of lack of effort or intelligence, but of instructional practices that fail to cultivate core conceptual tools. For example, many students enter calculus without a strong sense of how functions can represent relationships between quantities that change together. Without this foundation, concepts like limits, derivatives, and integrals appear abstract and inaccessible. Carlson and her collaborators have developed frameworks to analyze how students reason about functions, rate of change, and other foundational ideas, providing instructors with ways to identify and address gaps in students’ understandings.
Her most influential practical contribution is the development of the Pathways Precalculus curriculum, which emerged from a series of NSF-funded research projects. These in-depth qualitative studies informed the fine-grained scaffolding of student materials and instructor resources, with quantitative instruments providing formative data for ongoing adaptations with the student materials now in their 10th edition. Unlike traditional textbooks, Pathways does not present mathematics as a sequence of disconnected procedures. Instead, it introduces concepts through dynamic situations, contexts where students must reason about how quantities co-vary and use functions to model real-world phenomena. In classroom trials across more than 20 colleges and universities, students using Pathways have shown dramatically higher pass rates and deeper understanding compared to peers using conventional materials. In some cases, course completion rates rose by more than 40 percent.
Just as important as the curriculum itself is Carlson’s insistence on sustained professional development for instructors. In a 2024 case study, she documented how faculty learning communities supported the successful adoption of Pathways at multiple institutions. Her conclusion is clear: improving student outcomes requires not just new materials, but also new ways of teaching, grounded in ongoing faculty collaboration, reflection, and adaptation.
The impact of Carlson’s career extends far beyond any single course or program. She has trained and mentored dozens of doctoral students who now carry forward her work in research and teaching. She has contributed to national policy initiatives, including the design of placement tests for the Mathematical Association of America and the College Board’s framework for AP Precalculus. She has also authored widely used assessment instruments, such as the Calculus Concept Readiness test, which help institutions align instruction with the goal of conceptual understanding.
What makes Carlson’s career especially notable is its clarity of focus. While many researchers branch into multiple topics over time, she has remained steadfast in her commitment to one overarching problem: how to help students succeed in precalculus and calculus by engaging their mathematical thinking and building meaningful mathematical understandings. Her persistence has made her a national leader in a field where incremental progress is hard-won.
The broader implications of her work are profound. In a society increasingly reliant on data, modeling, and quantitative reasoning, the ability to learn and apply mathematics is more essential than ever. Students who leave precalculus and calculus with confidence and understanding are not only more likely to persist in STEM, but also better equipped to navigate careers and civic life in a mathematically complex world.
Dr. Marilyn Carlson’s career demonstrates what is possible when research and practice are tightly connected. By listening to decades of professional calls for reform, and by dedicating her professional life to investigating mechanisms for answering them, she has provided both the vision and the tools needed to engage students’ mathematical thinking, while improving student learning and retention. In doing so, she has generated a research-based model for others to leverage as they engage in similar efforts to make other mathematics courses more meaningful and effective. She hopes for major transformations in mathematics curriculum and instruction that lead to mathematics becoming a gateway (instead of a gatekeeper) to higher education and continued STEM learning.