A traveling salesman problem is used to illustrate the key idea in a general proof of a reduction technique. It is reduced to a problem in propositional calculus. (MNS)

The maximal rectangle idea is used to illustrate ways to ease students into the frame of mind required for problem solving in calculus. (MNS)

The problem "Given three planar points, find a point such that the sum of the distances from that point to the three points is a minimum" is discussed from several points of view. A solution that uses only calculus and geometry is examined in detail. (MNS)

A method of using vector analysis is presented that is an application of calculus that helps to find the best angle for tacking a boat into the wind. While the discussion is theoretical, it is seen as a good illustration of mathematical investigation of a given situation. (MP)

A method for teaching the product rule of differentiation in calculus is described. (MK)

Presents a mathematics problem involving speed of a walking student versus speed of light reflection in a high school hallway. (MKR)

Reflects on the history of the calculus reform movement and the development of course implementation projects, including use of technology in instruction. Highlights several themes permeating reform courses: reform calculus is more hands-on, students are expected to understand complex mathematical concepts in more connected ways, and new…

Focuses on students showing a lack of conceptual insight while using computer algebra systems (CAS) in the setting of an elementary calculus and linear algebra course for first year university students in social sciences. The use of a computer algebra environment has been incorporated into a more traditional course but with special attention on…

Concludes that writing about the executive processes of problem solving, difficulties encountered, alternative strategies that might have been used, and the problem solving process in general helped students in the treatment group learn to use executive processes more quickly and more effectively than students in the control group. (Author/NB)

What initially appears to be a standard maximum-minimum problem presents, with a particular independent variable, a wealth of calculus and algebraic subplots. Uses graphing calculator technology to reinforce the "pencil and paper" solution and open the problem to lower level mathematics courses. (Author/NB)

Considers examples of aspects of the infinitely small and large as they unfolded in the history of calculus from the 17th through the 20th centuries. Presents didactic observations at relevant places in the historical account. (Author/MM)

Investigated (n=61) undergraduates' ability to unpack informally written mathematical statements into the language of predicate calculus in an introduction to proofs and mathematical reasoning. Found that students were unable to construct proofs or validate them. Appendices are "A Sample Validation" and "Building a Statement Image." (MKR)

Presents a situation in which differential calculus is used with inverse trigonometric tangent functions to maximize an angle measure. A negative distance measure ultimately results, requiring a reconsideration of assumptions inherent in the initial figure. (Author/MKR)

Clarified is the assertion that the so-called complementary function is indeed the general solution of the homogeneous equation associated with a linear nth-order differential equation. Methods to obtain the particular integral, once the complementary function is determined, are illustrated for both cases of constant and of variable coefficients.…