This study investigated the relationship between algebraic understanding of teachers and student achievement in algebra in one academic year. Pretests to measure teachers' understanding of modern algebra and the algebra of the real number system, student pretests to enable consideration of individual differences, and posttests to measure student…

An alternate method for factoring quadratic equations is presented as being quicker and easier to use than the trial-and-error method. (MP)

A proof is given that in the purchase price, sales tax followed by discount is the same as discount followed by sales tax. (MP)

This puzzles uses a crossword format with the entries being factors of given polynomials. (MP)

Practical decisions involving fuel economy are shown to require important skills from secondary school algebra and analysis. (MP)

Matrix examples that have been used successfully in the classroom to illustrate group concepts are given along with observations made by students in working with them. (MN)

A procedure for solving absolute value inequalities involving a distance interpretation is presented. (MN)

The author shows how changing the restriction context of "Fermat's Last Theorem" alters the statement of impossibility. (MN)

The author uses mathematical models that involve only algebra and a few basic ideas in discrete probability to describe the frequency of conception in large human societies. A number of calculations which can be done by students as exercises are given. (MN)

A system similar to the slope method of graphing a linear equation is described for graphing parabolas. (JT)

This biography of the mathematician Girolamo Cardons (1500-1576) sketches his life and discusses his mathematical works, which were controversial at the time. (SD)

Ploynomials which can be used to calculate the number of ways of coloring hexagonal patterns are presented. (SD)

The article details an instructional procedure (based on the effective instruction research) to enable learning disabled adolescents to master three types of algebraic word problems: relational problems, proportion problems, and problems with two variables and two equations. (Author/DB)

The contributions of the Persian scholar Karaji are described. Perhaps his greatest contributions were his arithmetization of algebra and the geometrical representation of algebraic operations. (MNS)

Four noncommutative groups are given, to be used by students to construct the operation tables and verify that each structure is noncommutative. (MNS)