Mathematics teachers need to teach students more than just a laundry list of mathematical skills. Many of us also want to train our students to use mathematical habits of mind. However, traditional grading schemes usually do not allow us to reward intellectual courage and modesty. In this paper, I report on my implementation of specifications…

An aspect of the long history of the struggle to quantify motion is briefly traced through three extended problem sets suitable for use in first year calculus courses. The sketch culminates with an application of simple mathematics to one of the most current problems in the theory of the universe. (Contains 2 figures.)

Over the past two decades, calculus reformers have called for the use of alternative pedagogical techniques to promote student learning. Some mathematics instructors have responded by developing a set of student projects intended to hone thinking skills and improve the mathematical writing skills of calculus students. Drawbacks to this strategy…