Inspiring exercises are used to guide students at all levels to rediscover the essential meaning of various individual pieces of mathematics. Presents five sets of examples including Abel's identity, Hensel's lemma, finitely generated Abelian groups, Baire's category theorem, and the Weierstrass preparation theorem. (Author/ASK)

Integrates different geometries and blends several topics that have important applications in both higher mathematics and other disciplines. Aims to make these topics more attractive and understandable to high school students in a way that reinforces logical thinking with visual understanding obtained through computer usage. Contains 28…

Describes a process for creating a more diverse set of experiences for undergraduate students in mathematics by focusing on linear algebra. Emphasizes that the diversity of the activities is generated in part through the use of a taxonomy that addresses the nature of the activities rather than a hierarchy of levels of difficulty. Contains 13…

Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)

Presents examples of mathematical experiences and investigations for preservice teachers. Discusses potential benefits of the suggested mathematical experiences for the personal and professional growth of teachers. Contains 21 references. (Author/ASK)