Collaborative Research: Designing for All - An Inquiry-Oriented Approach to Calculus Sequences and Series with Universal Design for Learning

This project aims to serve the national interest by improving undergraduate calculus instruction so that more students experience mathematics as a creative endeavor in which they can take part. Calculus is a gateway to careers across science, technology, engineering, and mathematics, and the second-semester course carries particular importance because its final unit, on sequences and series, offers rich opportunities for creative reasoning that most instructional materials leave untapped. This Level 1 Engaged Student Learning project plans to develop classroom lessons in which students reinvent central calculus ideas for themselves by proposing definitions, noticing patterns, and forming and testing conjectures. The significance of the project lies in pairing inquiry-oriented instruction, in which the mathematics of the course grows out of students' own thinking, and Universal Design for Learning, a framework for anticipating from the outset the many different ways that students take in ideas, communicate their reasoning, and participate in a classroom. Designing lessons in this way is intended to give every student in the class a workable way to contribute to the mathematics being built, and to give instructors the flexibility to adapt the lessons to their own students and settings. Expected outcomes include instructional materials that are freely available to any interested instructor and a growing network of calculus instructors prepared to teach with them. The goals of the project are to design, test, and refine a sequence of inquiry-oriented lessons on sequences and series for second-semester calculus; to produce online instructor support materials that make the reasoning behind the lessons visible and adaptable; and to develop a professional development workshop that prepares instructors to enact the lessons in their own settings. The scope of the work spans three years and three cycles of design research, in which each round of lesson design is followed by classroom implementation, analysis, and redesign. Across these cycles the project plans eleven course and five workshop implementations. Data are expected to include classroom video; student written work, surveys, and interviews; recordings of weekly meetings between instructors and the project team; and recordings of the workshops. Through retrospective analysis of classroom episodes the project plans to examine how students can be guided to reinvent central ideas such as the tests for series convergence, while thematic analysis of student surveys and interviews plans to examine how students experience the instruction and which of its features they connect to those experiences. An additional analysis plans to examine how instructors adapt the materials to their own contexts and what features of the professional development account for those adaptations. Through this work the project anticipates advancing understanding of how Universal Design for Learning can guide the design of learning environments in undergraduate mathematics so that all students are supported while contributing to calculus reform by producing research-based lessons for sequences and series. It also anticipates advancing understanding of how inquiry-oriented materials can be designed and shared so that instructors are invited to adapt them to their own contexts rather than adopt them unchanged, a question central to the wider use of such curricula. An external evaluator plans to provide formative feedback on each version of the lessons and the workshop and a summative assessment of progress toward the project goals, and an advisory board plans to review the design work annually. Dissemination plans include freely available lessons and instructor materials, presentations at mathematics and mathematics education meetings, and publications for practitioners and researchers. The NSF IUSE: EDU Program supports research and development projects to improve the effectiveness of STEM education for all students. Through the Engaged Student Learning track, the program supports the creation, exploration, and implementation of promising practices and tools. 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.