Suggests that, for some classes of functions, an algebraic method is available that provides a nonstandard application of the discriminant conditions as well as an exact method of optimization for precalculus students. Examples are given, and students should compare these methods with others regarding generality, ease, and efficiency. (AIM)

Examines how components of the concept of function (variable, domain, and range) and the process-object duality in its nature emerge as highly relevant to student learning in various mathematical contexts related to linear and abstract algebra. (Contains 22 references.) (ASK)

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…

Discusses four computer-assisted-instruction programs used in a college-level mathematics course to introduce computer literacy and improve mathematical skills. The BASIC programs include polynomial functions, trigonometric functions, matrix algebra, and differential calculus. Each program discusses mathematics theory and introduces programming…

This document is concerned with developing an understanding of problem solving by providing tasks to help students with their problem solving strategies. These tasks were used by Vermont teachers during the pilot years of the High School Mathematics Assessment and were selected by attendees of the June, 1995 Research Scoring meeting. Tasks are…

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 a simple cooling experiment that can be conducted in class at the college algebra, precalculus, calculus, or differential equations level whose aim is to determine the best exponential function to fit the experimental data. (Author/ASK)

Describes a game used in precalculus that builds interest and confidence in the uses of inverse functions. The game is preceded by a worksheet that enables students to discover that f(x) and f-1(x) are mirror images of the line y=x. (DDR)

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…

Describes three teaching activities for secondary school mathematics classroom: designing a house; guessing the slope function in a calculus course; and solving the six problems of bisymmetric matrices. (YP)

Describes a Calculus I project in which students discover the formula for the derivative of an exponential function. The project includes two targeted writing assignments and leads to several additional problems. Together these tasks provide a basis for an algebraic approach to the exponential function. (AIM)

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)

This report examines mathematical graphing utilities or function plotters for use in introductory algebra classes of more advanced courses. Each product selected for inclusion in this report is able to construct the graph of a given equation on the screen and serves as a utility which may be used by the student for an open-ended exploration of a…

This conference proceedings contains three plenary session reports, 12 working group and 79 research reports, 35 short oral reports, 60 poster session reports, and two discussion group reports. The titles of all papers (excluding "short orals", "posters", and brief discussion group reports) are: (1) "On Relationships…