Activities that provide opportunities for students to investigate solving linear equations using both a physical and a pictorial model are given. Students should discover a method that will permit them to solve such equations at the symbolic level. (MNS)

The role of sentential logic traditionally taught in high school geometry is challenged. A rationale for shifting that content to algebra and replacing it with inferential logic, which directly affects proof making, is given. (MNS)

Reviews two science computer software packages (on time and seasons and on maps) and three mathematics packages (on solving equations and inequalities, an algebraic coordinate game, and statistics). In addition to descriptions of the contents of each, comments indicate weaknesses and strengths. (MNS)

Examples for determining the equation of a line through two points or a quadratic function that contains three noncollinear points are presented. (MNS)

High school students in algebra classes were presented lessons on direct variation and then tested on comprehension. The lessons were analyzed according to low-inference teacher behaviors. Findings show that lesson structure and categories of teacher vagueness were related significantly to student achievement. (Author/MT)

Four experiments involving 180 undergraduates evaluated the effectiveness of computer graphics in improving estimates for algebra word problems. Variations in the simulation resulted in successful and unsuccessful programs as measured by the frequency with which students improved their estimates. Quality of feedback to students while learning is…

Discusses computer solutions for factoring problems. Includes listing for (1) a program that multiplies two user-chosen factors (X-R times X-S) and allows subsequent multiplications by more linear factors and (2) a program which computes P(X)/(AX plus B), where P(X) is a user-chosen polynomial and AX plus B is a user-chosen divisor. (JN)

Shows a direct solution for factoring trinomials, without trial and error, using a calculator. When a calculator is not available, the mathematical chore is eased somewhat using reference tables, as shown in two noncalculator methods (determining nonfactorability and factorability). (JN)

Shows how to solve the Diophantine equation (x-squared plus y-squared equals z-cubed) with only one literal symbol. Listings of computer programs used in the solution are included. (JN)

Included in this department are brief articles on generating primitive Pythagorean triples with a computer program; using pictographs or pictures on graph paper to teach general graphing concepts; a method for factoring trinomials; and summing the harmonic series. (MNS)

This section contains brief articles on triangular differences, when one is not equal to one, using calculators to check solutions of quadratic equations, and a county agents' problem. (MNS)

An efficient division algorithm is developed, using a computer program, to convert any positive fraction to its decimal representation. The computer program listing is included. (MNS)

Sometimes the immediate use of an algebraic approach to solve a problem can obscure what is actually happening. The solution to one problem is described both algebraically and through a numerical approach. (MNS)

After six weeks of testing college algebra students (n=84) either on recall or recognition tests, the test modes were changed without warning. Results showed that performance suffered when the test mode was changed for students anticipating a recognition test. Students anticipating a recall test did equally well in both test modes. (Author/PN)

Uses of the historical approach to the teaching of mathematics throughout the last century are discussed. Examples from turn-of-the-century tests are provided, and the place of history in Mathematics teaching today is explored. (SD)