Michigan State University professor Kristen Vroom has received National Science Foundation (NSF) funding to develop and test new approaches to teaching calculus that encourage students to explore mathematical ideas, recognize patterns and develop their own reasoning skills. Vroom is an assistant professor of mathematics in Lyman Briggs College and is jointly appointed in the MSU Department of Mathematics through the Program in Mathematics Education (PRIME). Vroom is working on this project in collaboration with Hortensia Alzaga Elizondo, of the School of Mathematical and Statistical Sciences at the University of Texas-Rio Grande Valley.
Calculus is foundational to many fields in science, technology, engineering and mathematics. Yet students often encounter it as a set of rules and procedures to memorize. Vroom's project, “Collaborative Research: Designing for All: An Inquiry-Oriented Approach to Calculus Sequences and Series with Universal Design for Learning,” will focus on the second semester of calculus, specifically the study of sequences and series, a topic that offers opportunities for students to investigate patterns, form conjectures and discover mathematical relationships for themselves.
The project will develop classroom lessons that combine inquiry-oriented learning with Universal Design for Learning, an approach to designing instruction that anticipates students’ different learning needs and provides multiple ways to engage with material and demonstrate understanding. Rather than simply presenting established definitions and methods, the lessons will invite students to propose ideas, test their predictions and build mathematical understanding through exploration and discussion.
Over three years, Vroom and the project team will design, test and refine the lessons through multiple classroom implementations. They will study students’ work and experiences to understand how the lessons support mathematical reasoning and participation. The team will also develop online resources to help instructors adapt the lessons to their own classrooms and offer professional development workshops to support their use.
“I have been teaching with these materials in my own calculus classes, and one of my favorite moments is when students see their own conjectures written in the textbook,” said Vroom. “You can see them realize that the mathematics we build in class comes from them, and that they have a real say in it. That’s what makes me excited to work with other instructors. I want to support them in adapting these tasks in ways that build on their own strengths and fit their students and settings, so more students get to have that experience.”
The project aims to make calculus instruction more engaging and inclusive while helping instructors create opportunities for more students to contribute meaningfully to mathematical thinking. The resulting lessons and teaching resources will be freely available, allowing educators at other institutions to adapt and use them in their own courses.
By rethinking how students encounter foundational mathematical concepts, Vroom and Elizondo’s research seeks to broaden participation in mathematics and strengthen undergraduate STEM education.
The nearly $600,000 grant was awarded by the Educational Innovation & Translation Section of NSF, specifically through the Improving Undergraduate STEM Education program.