A simple in-class demonstration of integral Calculus for first-time students is described for straightforward whole number area magnitudes, for ease of understanding. Following the Second Fundamental Theorem of the Calculus, macroscopic differences in ordinal values of several integrals, [delta]"F"(x), are compared to the regions of area…

In this article, the authors share activities designed to help students make a connection between the complex roots of X[superscript 2] - 2x + 5 = 0 and the graph of y = X[superscript 2] - 2x + 5. We piloted these activities in three precalculus classes. The activities involved both concrete and technological representations of the mathematical…

Calculus has frequently been called one the greatest intellectual achievements of humankind. As a key transitional course to college mathematics, it combines such elementary ideas as rate with new abstract ideas--such as infinity, instantaneous change, and limit--to formulate the derivative and the integral. Most calculus texts begin with the…

Like many mathematics teachers, the authors often find that students who struggle with a difficult concept may be assisted by the use of a well-chosen graph or other visual representation. While one should not rely solely on such tools, they can suggest possible theorems which then might be proved with the proper rigor. Even when a picture…

Many popular mathematical software products including Maple, Mathematica, Derive, Mathcad, Matlab, and some of the TI calculators produce incorrect graphs because they use complex arithmetic instead of "real" arithmetic. This article expounds on this issue, provides possible remedies for instructors to share with their students, and demonstrates…

Gives an example of one danger of using graphing software without an accompanying mathematical analysis by illustrating what might happen if a student were capable of dealing with the drawing of the complete graph of a function only by using a technological tool. (MKR)

Pre- and posttests and interviews concerning misconceptions and alternate conceptions of rates of change were administered to (n=42) students in first-semester calculus using a conceptually-motivated curriculum. Suggests that an emphasis on visual representations through construction and interpretation in conjunction with teacher-student analysis…

Provides examples in which graphs are used in the statements of problems or in their solutions as a means of testing understanding of mathematical concepts. Examples (appropriate for a beginning course in calculus and analytic geometry) include slopes of lines and curves, quadratic formula, properties of the definite integral, and others. (JN)

Uses parametric equations and a graphing calculator to investigate the connections among the algebraic, numerical, and graphical representations of functions. (MKR)

This booklet contains a representative sample of the efforts of colleagues at 11 institutions to use graphing calculators to enhance the teaching of calculus and precalculus. The first section contains examples of graphs for teachers to choose from for presentations, including: simple examples to illustrate some standard ideas in precalculus,…

Illustrates exploration of composition of functions, translations, and inverse functions on a graphing calculator. Includes reproducible student worksheets. (MKR)

Presents a strategy for graphing conic sections on the polar plane without using a table of values by beginning with information gained from the graphs of circular functions. (MKR)

Attempts to answer and generalize the question: When is the numerical derivative obtained on the graphing calculator greater than the actual derivative, and when is it smaller? Discusses symmetric difference. (MKR)

Three activities with Knuth functions are discussed and illustrated, with sample computer programs listed. (MNS)

Demonstrates how microcomputers can be used in teaching differential calculus, iteration, integral calculus, graphs, and statistics. Several ideas for putting this information into practice are outlined. Sample computer programs are included for the discussions on differential calculus, integral calculus, and iteration. (JN)