The examination by students of the associative property of a binary operation is used to illustrate how students can be involved in mathematical discovery. (MP)

A geoboard-related extremal problem dealing with both concave and convex polygons is discussed and a proof is given of the solution. (MP)

Two statements concerning magic squares, considered as 3x3 matrices, are discussed and their proofs given using only high school level techniques. (MP)

The reported study is an attempt to investigate possible interaction between criterion measures of learning and retention of material and figural-inductive and symbolic-deductive methods of presentation. (MN)

Ten recent results in pure mathematics are described, covering the continuum hypothesis, Diophantine equations, simple groups, resolution of singularities, Weil conjectures, Lie groups, Poincare conjecture, exotic spheres, differential equations, and the index theorem. Proofs are omitted, but references are provided. (DT)

A nontraditional approach of graphing equations using parallel axes produces some dual concepts when compared to graphing equations with the traditional perpendicular axes. (JT)

Described is the construction of a computerized test bank to generate and score tests in college algebra, trigonometry, and intermediate algebra; including a discussion of uses, advantages and disadvantages of computerized testing. (JLH)

The formula for the sum of the nth powers of the first k integers was shown by Bernonlli to be obtainable from Pascal's triangle. The derivation is reported. (SD)

Tests for divisibility of integers are derived and described. (SD)

Discusses students' uses of certain programs, in contrast to writing them. Three programs are discussed: one on nonreal roots, one on dividing polynomials by quadratic polynomials, and one on "unfactoring." (MNS)

Discusses the factoring of polynomials and Fibonacci numbers, offering several challenges teachers can give students. For example, they can give students a polynomial containing large numbers and challenge them to factor it. (JN)

The development and role of algebra in the curriculum are traced historically. The slow development over centuries is emphasized. (MNS)

Exploring the numerical nature of quadratic equations is the focus of this article. Small solutions, the general case, and a detailed analysis are each presented. (MNS)

Included in this section are brief articles on drawing altitudes of triangles, sketching parabolas, and visualizing variability. (MNS)

Discusses algebraic programing languages, availability of these languages, and programing problems. Also discusses the future of these languages in chemical research and chemical education. A program illustrating the general algebraic and algebraic matrix manipulating capabilities of the REDUCE language is included. (JN)