Reports on a study of students' responses to two types of questions on final examinations in calculus. Concludes that the two kinds of understanding--pointwise and across time--are clearly distinguishable. Discusses the differences between these two types of understanding. (ASK)

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

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

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

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…

Presented is a simple method which may be used to determine points of intersection in graphs of functions if they do exist. Several examples are given with illustrations of the functions. (CW)

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)

Demonstrates that the functions known as the witch of Agnesi and the normal distribution are not identical by comparing the areas under the curves and the slopes of the lines tangent to the curves of the two functions. Suggests follow-up activities to the investigation. (MDH)

Computer algebra systems (such as MACSYMA and muMath) can carry out many of the operations of calculus, linear algebra, and differential equations. Use of them with sketching graphs of rational functions and with other topics is discussed. (MNS)

Describes an approach to the design of learning environments around a computer algebra kernel. Presents two environments to help students learn precalculus. Provides students with symbolic, graphic, and numeric tools as well as functionalities to help them build proofs. (Author/KHR)

Describes an experimental study in which two sections of calculus were taught using the same materials, except one section was enhanced with the computer algebra system Mathematica. Results indicated that the students in the technology group had advantages to understanding certain key topics in calculus such as limits, derivatives, and curve…

Describes five college and two high school students' understandings of function and limit in a graphics calculator-based environment and identifies instances where students' understanding seems to have been influenced by the availability of a graphing calculator. (27 references) (MKR)

The advent of calculators for graphing and function plotters is changing the way college algebra and calculus are taught. This paper illustrates how the machines are used for teaching the following: (1) domain and range; (2) product and quotient inequalities; and (3) the solving of equations. Instructional hints are provided for each topic with…

Discussed are several activities suitable for students from middle school through high school designed to furnish concrete experiences with the concepts of rate of change and slope and approximating areas, the central themes of differential and integral calculus. The implementation of national curriculum standards is stressed. (CW)

Discusses research findings related to students' ability to make connections between analytical (symbolic) and graphical representations of functions in calculus. Describes graphing tasks and typical student interpretations. Implications for teaching are suggested. (Contains 17 references.) (MKR)