Collaborative Research: Project CLEAR Calculus: Coherent Labs to Enhance Accessible and Rigorous Calculus Instruction

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This collaborative project is a research-based effort to make calculus conceptually accessible to more students while simultaneously increasing the coherence, rigor, and applicability of the content students are learning. Its intellectual merit rests on an ongoing program of research from which the principal investigators have conceptualized a framework for learning and teaching calculus that builds on students' intuitive reasoning about approximations and error analyses. Combining this framework with a constructivist approach, the project team is refining and disseminating lab activities that address the content of a standard course sequence in differential, integral, and multivariable calculus with supporting materials and interactive technology for students. The project is exercising broader impact through its efforts to help develop a community of practice around these ideas through a set of efforts that includes: conducting summer workshops, holding weekly video-conferences, and making available classroom video and instructor notes to support faculty professional development for implementation of the labs. Finally, a research and evaluation component is assessing the impact of the lab activities on student conceptual development of the central ideas in calculus through the use of two quantitative measures: i) a Calculus Concept Assessment (CCA) to measure shifts in students' understanding of the central concepts of calculus and ii) a Limit Models Assessment (LMA) to measure shifts in the cognitive models employed by students while reasoning with these calculus concepts. The project is further adding to the knowledge base of STEM education by studying the effectiveness of its faculty development efforts through an analysis of pilot instructors' exams using an Exam Characterization Framework (ECF) and the continuous collection of detailed feedback on all components of the project.