CAREER- The Dynamic Variables Project - Developing STEM Undergraduate Students' Dynamic Meanings for Variables

Variable literacy, the ability to comprehend and use mathematical symbols, is a foundational mathematical underpinning of our world’s scientific and technological advances, yet research has shown that students struggle with using variables meaningfully. For example, students may switch variables or have difficulty interpreting symbols as representing varying values. This latter meaning is crucial at the precalculus level and beyond when symbols often represent dynamic quantities. Thus, the need to support students’ variable literacy is shared by researchers, educators, and curricula developers. The Dynamic Variables Project seeks to serve the variable literacy needs of the nation’s undergraduate student population by developing a learning progression to support students’ meanings for variables through contexts that are relevant to today’s STEM careers. To develop this targeted and systematic framework detailing how students develop variable literacy, the project team will document the ways in which undergraduate precalculus students think about symbols and test and refine tasks for instruction. These tasks will be informed by STEM professionals and include students’ use of dynamic interactive digital tools. Beyond the theoretical contribution of the learning progression, this project will design and test instructional and training materials for undergraduate precalculus instructors and provide STEM instructors with clear guidance and supporting tasks on the professional variable literacy needs of their students. Drawing from existing research on students’ representational activity, the Dynamic Variables Project will develop a student-centered theoretical framework to inform mathematics instruction of variables via a design-based research study with undergraduate precalculus students and instructors. Specifically, the team will draw on existing frameworks for students’ reasoning about dynamic quantities changing together and teacher decision making to develop tasks and instructional materials that consider the cognitive strategies students use when interpreting and constructing symbols to represent dynamic quantities. The project team will map how variable literacy develops to construct a learning progression. The resulting framework will include a pool of STEM-relevant variable tasks for research and instruction. To accomplish these objectives, the team will conduct several rounds of single- and multi-session task-based clinical interviews with undergraduate precalculus students to determine their cognitive strategies and conduct focus groups with STEM professionals to identify their variable literacy needs and inform task design. The project team will analyze these data to develop the learning progression that the team will then translate to instructional materials to test with precalculus students and graduate student instructors (GSIs). Instructional materials for precalculus students will include a pool of STEM-relevant variable tasks with detailed implementation suggestions for instructors and a video library illustrating student thinking. Instructional materials for GSIs will be designed to inform GSIs about students’ variable literacy needs and identify tasks they can use to support their students. The success of the project will be assessed via feedback on instructional materials from students and instructors, including assessing students’ learning progression throughout the sequence of instructional materials. We will disseminate research findings and tasks via publications, curricular materials, and guidance for STEM undergraduate educators on the variable literacy needs of STEM professionals. Overall, this project has the potential to grow and adapt to the everchanging needs of our STEM students by designing a framework that is both specific enough to detail the cognitive steps STEM undergraduate students need to take to develop variable literacy but also general enough to enable future adaptations to STEM contexts. The Faculty Early Career Development (CAREER) program is a National Science Foundation (NSF)-wide activity that supports early-career faculty who have the potential to serve as academic role models in research and education. This CAREER project is supported by NSF’s Improving Undergraduate STEM Education (IUSE: EDU) program. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.