How can we teach inquiry? In this paper, I offer practical techniques for teaching inquiry effectively using activities built from routine textbook exercises with minimal advanced preparation, including rephrasing exercises as questions, creating activities that inspire students to make conjectures, and asking for counterexamples to reasonable,…

In many post-secondary, introductory mathematics courses failure and withdrawal rates are reaching as high as 50% and average GPA is steadily decreasing. This is a problem that has been witnessed across the globe. With widespread reforms taking place in K-12 mathematics education, many innovative teaching strategies have been created, implemented,…

Described is an instructional method that makes use of an electronic spreadsheet for the numerical and graphical introduction of the fundamentals of Taylor polynomials. Included is a demonstration spreadsheet using the expansion polynomial to evaluate the cosine function. (JJK)

Described is a programing application of the software, Mathematica, which allows students to explore the various cases involved in minimizing the sum of squares for the best fit of a regression line. Several examples are included with appropriate software commands. (JJK)

Presented are classroom-tested examples of instructional materials (courseware) for ordinary differential equations using the software package PHASER. All of the examples include in-class demonstration techniques and commentaries for instructor use, student homework and laboratory exercises, and suggestions for in-class examination questions. (JJK)

Described are some of the visualization techniques employed in the computer-animated videotapes generated through the blending of commentary, animated imagery, music, and special effects. Instructions for procurement are included for these tapes, which are produced by Project MATHEMATICS! at the California Institute of Technology. (JJK)