Discusses the problem-solving heuristics of examining for special cases, utilizing dimensions to make sense of proposed solutions, and symmetry. Presents examples to illustrate the use of one or combinations of these heuristics. (MDH)

An exercise that gives students a chance to use the equations of state for both an ideal gas and for an adiabatic process in determining the points at which heat flow reverses direction and at which the working substance reaches its maximum temperature is demonstrated. (KR)

We report on a two-year NSF-funded project to strengthen connections among science, technology, engineering, and mathematics (STEM) disciplines. One component of this project was to produce some initial data on the effectiveness of Interdisciplinary Lively Applications Projects (ILAPs) in teaching science and engineering undergraduates. ILAPs are…

The emphasis is on so-called "best solution" problems to questions that frequently arise in practical situations, such as finding an answer for the least amount of time, greatest volume, least amount of work, maximum profit, and minimum cost. One of this module's purposes is to help users become acquainted with the types of calculations necessary…

This report discusses how a computer was used to enhance the curriculum of a college calculus course. Problems with a calculus adjunct course in computer science are detailed, along with the nature of changes in the new program. The changes moved from student use of the computer as an automatic typewriter to use as a tool with instructional…

Mathematics is considered a performing art. Examples illustrating this view are presented. Activities discussed are from the Madison Project materials and the mathematics program at University High School in Urbana, Illinois. Activities stress inventing strategies for attacking problems for elementary and secondary school mathematics. (RH)

Considers a trigonometric solution to a standard calculus minimization problem. Presents a geometric solution which can be used to solve other trigonometric or algebraic problems. (PK)

Answers and justifications for an interesting problem on the Advanced Placement Calculus AB Examination are discussed. The problem provides diverse ways in which students can gain appreciation and understanding for the subject. (MNS)

The symposium is seen to create an opportunity for students to understand the way mathematics is actually used in their own fields and to understand both their own potential as mathematics users and inherent difficulties in modeling. The symposium acts as a capstone for a two-semester, introductory calculus course. (MP)

An unusual alternative starting point for instruction in a beginning calculus course that focuses on Fixed Point Iteration (FPI) is presented. (MP)

Presents an activity for constructing and solving radical equations which can be done with or without the use of graphing calculators. Highlights one method that two students used to solve radical equations. (ASK)

Presents a project that explored student choice of a solution method for quadratic inequalities. Students were first instructed in the use of the case, critical-number, and graphical methods using the graphing calculator. The majority of students chose graphical methods of solution. (DDR)

Discussed is the tendency of students to equate the concepts of continuity and connected graphs based on their lack of an understanding of such concepts as limit points, closed sets, and connected sets. Included is a theorem with three lemmas with their proofs. (KR)

Discussed is the problem of inscribing a rectangle of maximum area in a given right triangle. Answered is whether there is an advantageous orientation and whether a corner of the rectangle of maximum area can lie on the midpoint of a leg of the triangle. (KR)

Describes a course designed by Moravian College, Pennsylvania, to integrate precalculus topics as needed into a first calculus course. The textbook developed for the course covers the concepts of functions, Cartesian coordinates, limits, continuity, infinity, and the derivative. Examples are discussed. (MDH)