Encouraging students to share and compare solution methods is a key component of reform efforts in mathematics, and comparison is emerging as a fundamental learning mechanism. To experimentally evaluate the effects of comparison for mathematics learning, the authors randomly assigned 70 seventh-grade students to learn about algebra equation…

"C[squared] = Creative Coordinates" is an engaging group of tasks that fosters the integration of mathematics and art to create meaningful understanding. The project lets students illustrate of find an image, then plot points to map their design on a grid. The project usually takes about a week to complete. When it is finished, students who are…

At their final exam in linear algebra students at the author's university were given the possibility to choose between two types of proofs to be done. They could either prove two short statements by themselves or they could explain four steps in a given proof. This paper reports on investigations of students' responses to the choice option…

It is in the field of numerical analysis that this "easy-looking" function, also known as the Runge function, exhibits a behavior so idiosyncratic that it is mentioned even in most undergraduate textbooks. In spite of the fact that the function is infinitely differentiable, the common procedure of (uniformly) interpolating it with polynomials that…

The addition and subtraction of integers is the first major avenue, and roadblock, to student success in learning algebra. This article describes a hands-on activity using a regular deck of playing cards that facilitates class discussion and helps students overcome this initial roadblock. (Contains 14 figures.)

This book is a collection of activities designed to complement an Algebra I program that features cooperative learning. The activity descriptions contain learning outcomes, the National Council of Teachers of Mathematics (NCTM) standards addressed in the activity, a suggested time frame for the activity, assessment opportunities, materials…

This course of study guide is designed to help teachers establish a continuity within the scope and sequence of their elementary school mathematics curriculum and to assist those teachers in formulating some realistic goals for themselves and their students. This guide delineates content requirements needed to satisfy K-8 proficiency expectations…

Similarities and differences in the univariate and multivariate analysis of repeated measures designs are discussed, using a hypothetical data set studying the effects of practice on the algebra performance of four students to illustrate both methods. When data are analyzed through the univariate approach and the homogeneity assumption is…

Solutions to systems of linear equations with coefficients related to each other by an arithmetic progression are discussed. (SD)

The author illustrates many problems in which drawing graphs of functions involving absolute values assists in the solution of algebraic equations and inequalities. (SD)

Euler's famous formula, e to the (i, pi) power equals -1, is developed by a purely algebraic method that avoids the use of both trigonometry and calculus. A heuristic outline is given followed by the rigorous theory. Pedagogical considerations for classroom presentation are suggested. (LS)

This textbook aims to present the mathematical sciences in clear, everyday language for apprentices, students and mechanics--willing, industrious, anxious to study at home, yet unable to give time or money for professional teaching. It is trusted that this effort to place before English-speaking students a treatise on arithmetic and algebra, freed…