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)

An alternative approach is described for presenting the idea of the derivative through the use of chords of a graph. (MP)

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)

Curve stitching activities can be used to motivate calculus students. The problem described here involves showing that a given envelope of a curve is parabolic. (SD)

An examination of a student question concerning a calculus problem leads to a discussion of some of the symmetric properties of a specific set of polynomials. (MP)

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)

This paper describes student difficulties in first-year calculus classes and suggests some instructional strategies to address these difficulties. Participants in this study were 200 low socio-economic background freshmen majoring in business in Brazil. Results show that the main difficulties are related to lack of understanding of algebraic…

Describes how the computer algebra system Mathematica can be used to enhance the teaching of the topics of sequences and series. Examines its capabilities to find exact, approximate, and graphically generated approximate solutions to problems from these topics and to understand proofs about sequences. (MDH)