Active Learning Materials for Critical Thinking
in a
First Course in Real Analysis

Barbara Shipman, Ph.D.
Associate Professor and Distinguished Teaching Professor

The University of Texas at Arlington

  Welcome to the website of

Active Learning Materials for Critical Thinking in a First Course in Real Analysis

Barbara A. Shipman
Associate Professor and Distinguished Teaching Professor

The University of Texas at Arlington

Supported in part by NSF grant DUE #0837810

This website contains seven chapters of materials that I have created through ten semesters of working with students in introductory real analysis. They are designed around targeted questions that guide students, in an interactive setting, to motivate, define, explain, and prove core ideas of analysis. Many are aimed at mistakes that I have observed in students’ thinking over several semesters. The 175 activities are are organized into Concept Checks and Guided Discoveries for engaging students in the classroom, Study Projects for collaborative or independent work inside or outside of class, Historical Pathways to prod students’ thinking through historical quotes, and Capstone Connections to follow ideas of analysis into in other branches of mathematics.  Below are links to the table of contents and to  an example of each type of activity from the Students’ Website.


Click here to see the table of contents.  


Click on an example.

1.1.1  Concept Check: Interpretations of "unique" 
2.1.6  Guided Discovery: More circles or more squares?

3.1.3  Historical Pathways:  Hamilton's quaternions
4.3.10  Study Project: Extending the algebra of limits
6.1.11  Capstone Connection: Notation for derivatives




"I should let you know that I tried the very first section that you gave me (on unique and one-to-one) and it did indeed create a good discussion in class. So, after that, my class was on a good track and I kept the style. I think this was a very important influence. I am sticking to this style of keeping very much in touch with the class and this is good."
Dr. Anton Betten
Department of Mathematics,
Colorado State University

"I always looked forward to the challenges that show up in class and the crazy presentations of true/false questions . . . especially the part where I search for a 'white tiger!'"  Charles Nguyen

Click here to see a white tiger.



To use the Instructors' Website, contact Barbara Shipman at 
with your name, the course you teach, your institution and contact