An organized series of steps designed to help students solve related rate problems often found in beginning calculus is presented. Two example problems are taken through five steps of solution. (MP)

Presented is an alternate way to derive R from Taylor's Theorem without involving the (n + 1)st derivative of f. Included is the procedure for estimating the bounds of R. (KR)

Presented are activities that help students understand the idea of a vector field. Included are definitions, flow lines, tangential and normal components along curves, flux and work, field conservation, and differential equations. (KR)

Describes an experimental test conducted with high school students to determine the effect of posting explicit goal structures on problem-solving performance in an intelligent tutoring system for calculus. Related rates word problems are discussed, and student performance in terms of speed and accuracy is analyzed. (Contains 29 references.) (LRW)

Describes an attempt to increase business calculus students' desire to learn by overcoming typical low levels of mathematical preparation and motivation utilizing a corporate structure managed by the students. Includes 10 sample problems from fictitious corporations. (JJK)

An approach that may be used to introduce the fundamental ideas of thermodynamics using a mathematical background with the knowledge of the behavior of matter is described. The physical background, conservation of energy, predicting the behavior of a system, and solving problems are topics of discussion. (KR)

Examines the point of inflection in the curve determined by the hinge of a bifold door as it opens. Determines the equation of the branch function of the curve and calculates its point of inflection. (MDH)

The United States Military Academy (USMA) has a four course core mathematics curriculum that is studied by all students. The third course is MA205, Calculus II; a multivariate calculus course filled with practical applications. During a Problem Solving Lab (PSL), students participated in a hands-on exercise with multiple vector operations,…

Recently we were presented with an interesting twist to the sliding ladder problem viewed in the related rates section of most calculus textbooks. Our problem concerning a sliding ladder that eventually hits the ground. At first, those attempting this problem fell into the calculus trap using only related rates. Previous work for this problem…

In 1945, Bronislaw Knaster proposed a procedure to divide any number of indivisible goods between a finite number of players requiring the players to place monetary values or bids on all of the goods. Often discussed in math for liberal arts courses that concentrate on contemporary applications of mathematics for non-major students, Knaster's…

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…

What is a routine question? The focus of this paper is routine questions and time (in years) since a hitherto routine question was last attempted by the solver. The data comes from undergraduate students' work on solving two calculus questions. The data was selected for reporting purposes because it is well documented and because it threw up…

We examine the behavior of the curvature function associated with most common families of functions and curves, with the focus on establishing where maximum curvature occurs. Many examples are included for student illustrations. (Contains 18 figures.)

In this paper, results of a questionnaire about continuity of functions are analysed. The tested students attend Novi Sad grammar school. The aim of this test was to check the student's theoretical and visual knowledge of continuous functions at the end of their high school education. The questions were given with and without the graphs of…

This document contains nine research papers presented at the Joint Special Session on Research in Undergraduate Mathematics Education at the annual meeting of the American Mathematical Society and the Mathematical Association of America (San Francisco, California, January 1991). Paper titles are: "The Teaching and Learning of College…