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Focuses mainly on a common example in technology-rich mathematics curricula, namely the line of best fit, followed by a discussion of two additional examples, interpolating polynomials and complete graphs. (ASK)

Describes the development of an Interactive Teaching and Learning Environment for Graph Sketching (ITALEGS) of polynomial graphs at the college level. Highlights include hypermedia examples, the design of questionnaires for evaluation, and enhancing effectiveness by incorporating pedagogical content knowledge in computer-assisted instruction. (Author/LRW)

Computational environments that provide integrated numeric, symbolic, and graphical capabilities provide new opportunities for laboratories in Numerical Analysis. Hermite interpolation is one topic that can benefit from such an environment. Describes a laboratory session using Mathematica that allows students to actively experience Hermite interpolation. (Author)

This article provides pedagogical techniques that require active student participation in the use of computer spreadsheets while determining recursive numerical solutions to equations. Included are several computer screen displays which illustrate the various advantages in using spreadsheets specific to synthetic division, the bisection method, and Newton's method. (JJK)

Discussed is the classroom suitability of an open learning computer microworld centered around families of quadratic equations that provides a framework for exploring questions about parabolas to establish the link between the graphical and the algebraic representations of quadratic equations. (JJK)

Described is an instructional method that makes use of an electronic spreadsheet for the numerical and graphical introduction of the fundamentals of Taylor polynomials. Included is a demonstration spreadsheet using the expansion polynomial to evaluate the cosine function. (JJK)

The first idea concerns a board game similar to tic-tac-toe in which the strategy involves the knowledge of the factorization of quadratic polynomials. The second game uses the calculation of the surface areas of solid figures applying the specific examples of cigar boxes and cylindrical tin cans. (JJK)

Presented is a method for factoring quadratic equations that helps the teacher demonstrate how to eliminate guessing through establishment of the connection between multiplication and factoring. Included are examples that allow the student to understand the link between the algebraic and the pictorial representations of quadratic equations. (JJK)

The sign-chart method is often used to solve polynomial inequalities involving products or quotients. Presented are examples that extend this method to solve higher-degree polynomial, radical, exponential, logarithmic, absolute-value, and trigonometric inequalities and whose graphic representations lead to intuitive discussions of continuity. (MDH)

Presented are two ideas to improve instruction. The first celebrates the Christmas birthday of Isaac Newton with an essay assignment related to Newton and a party. The second suggests a more appropriate moment to introduce the technique of completing the square to promote greater flexibility in factoring problems. (MDH)

Following a short introduction on the rationale and purpose for using algorithmic structures in the teaching of algebra, two topics from elementary algebra are presented in relation to control structures from computer programing, specifically: the multiplication of polynomials defined in terms of nested loops, and the distributive property described in terms of tree diagrams. (JJK)

The complexity of the proof of the Fundamental Theorem of Algebra makes it inaccessible to lower level students. Described are more understandable attempts of proving the theorem and a historical account of Euler's efforts that relates the progression of the mathematical process used and indicates some of the pitfalls encountered. (MDH)

Introduced are the basic ideas of interpolation and approximation theory through a combination of theory and exercises written for extramural education at the university level. Topics treated are spline methods, Lagrange interpolation, trigonometric approximation, Fourier series, and polynomial approximation. (MDH)

The phenomenon of 2 x 2 x 2 arrays having nonmaximal rank with positive probability, pointed out by J. Kruskal (1989), is generalized to 2 x "n" x "n" arrays. It is concluded that a pair of asymmetric square matrices can be diagonalized simultaneously with positive probability. (SLD)

Presented are five short articles which describe innovations in mathematics teaching. Included are "Polar Summation,""The Age of the Solar System,""Forward Homework--A Motivational Tool,""Trigonometric Identities through Calculus," and "Algorithms for Evaluation of Polynomials." (CW)

Illustrated is the use of computer algebra software to assist in both a computational and theoretical way to develop the underlying theory of polynomials and the partial fraction decomposition of a rational function. Background information and a discussion of theoretical considerations are provided. (KR)

Described is an approach to the derivation of numerical integration formulas. Students develop their own formulas using polynomial interpolation and determine error estimates. The Newton-Cotes formulas and error analysis are reviewed. (KR)

Elementary error estimation in the approximation of functions by polynomials as a computational assignment, error-bounding functions and error bounds, and the choice of interpolation points are discussed. Precalculus and computer instruction are used on some of the calculations. (KR)

Presented are 44 examples in which students are invited to guess what pattern of numbers is emerging and to decide whether the pattern will persist. Topics of examples include Pascal's triangle, integers, vertices, Fibonacci numbers, power series, partition functions, and Euler's theorem. The answers to all problems are included. (KR)

Illustrates how Lagrange's approach applies to the differential calculus of polynomial functions when approximations are obtained. Discusses how to obtain polynomial approximations in other cases. (YP)

Described is a decomposition theory from which the Cayley-Hamilton theorem, the diagonalizability of complex square matrices, and functional calculus can be developed. The theory and its applications are based on elementary polynomial algebra. (KR)

Discussed is how a separable field extension can play a major role in many treatments of Galois theory. The technique of diagonalizing matrices is used. Included are the introduction, the proofs, theorems, and corollaries. (KR)

Discusses a method of cubic splines to determine a curve through a series of points and a second method for obtaining parametric equations for a smooth curve that passes through a sequence of points. Procedures for determining the curves and results of each of the methods are compared. (YP)

Discussed is the use of a program called MathCAD which allows students to solve higher order polynomial equations and geometry problems. The use of cooperative learning is emphasized. Included are graphs and part of a printout generated while solving problems with MathCAD. (KR)

Demonstrates how the uniqueness and anonymity of a student's Social Security number can be utilized to create individualized polynomial equations that students can investigate using computers or graphing calculators. Students write reports of their efforts to find and classify all real roots of their equation. (MDH)