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We describe some classic experiments on the Möbius strip, the projective plane band, and the Klein bottle band. We present our experience with freshmen college students, college teachers, high school students, and Mathematics Education graduate students. These experiments are designed to encourage readers to learn more about the properties of the Möbius strip and provide visual proofs of these properties using exploration techniques. The experiments include constructing the objects, observing their properties, and explaining via experiments that altering the objects by cutting them does not preserve their hereditary properties. [ABSTRACT FROM AUTHOR]

In this article, we share some experiences about working with students on research projects. Instead of giving them problems from our own projects to work, we use open problems from journals. Using these resources we have worked with several undergraduate and some graduate students giving them a taste of their first research experience. Here we describe how these projects were conducted and the various criteria we thought about when we found the right problems for the students to work on. We also give a list of problems that our students worked on and the books and articles the students may read in order to get ready for the projects. [ABSTRACT FROM AUTHOR]