Through interacting with students over eight semesters of introductory real analysis from 2006 – 2009 and attending to their thinking during classroom debates, I have created textbook-independent learning materials for critical thinking in real analysis designed to place the students in the position of the mathematician, prompting them to develop core concepts, definitions, results, and proofs in an interactive, discovery-based setting. The preparation of these materials for other instructors and students to use and its review and evaluation by students and faculty, together with a study of students’ learning in conjunction with the materials, is supported in part by the National Science Foundation, through NSF grant DUE #0837810 (2009 – 2011). The project involves feedback from fifteen faculty consultants from eight institutions in five states in various capacities and stages; it has funded three workshops centered on implementation of the materials, which appear on the website www.uta.edu/faculty/shipman/analysis (B.A. Shipman, Active Learning Materials for Critical Thinking in a First Course in Real Analysis, 2009).

On each course exam, I have included a set of true/false questions designed to target misconceptions that the materials address. Statistical analysis of students' performance on these diagnostic questions has yielded interesting observations that are analyzed in forthcoming publications.

The 178 activities on the website are organized into five components, each with a specific purpose. The Concept Checks are short, focused true/false or multiple choice questions that target one misconception or concept at a time, to be debated by the students in class. These prepare students for the Guided Discoveries, which are longer sequences of questions that lead the class in creating their own definitions, hypotheses, and proofs.For engaging work between class meetings, the Study Projects are multi-layered exploratory problems for students to investigate either on their own or in teams. These are designed to provide rich material for written homework and oral presentations. The Historical Pathways are thought-provoking activities centered on quotes from mathematicians decades and centuries back as they worked to formulate foundational concepts and express them rigorously. Capstone Connections provide a broader perspective on ideas met in analysis that run across different fields of mathematics, highlighting relationships among various courses in the undergraduate curriculum.