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)

Extracts from booklets providing critical reviews of and recommendations related to textbooks of the Nuffield Mathematics Project are presented. (SD)

An approach to absolute value is described which emphasizes the metric property of the absolute value function and the fact that the real number form an ordered set. (DT)

In two previous studies we investigated the non-routine problem-solving abilities of students just finishing their first year of a traditionally taught calculus sequence. This paper reports on a similar study, using the same non-routine first-year differential calculus problems, with students who had completed one and one-half years of traditional…

"Insights into Algebra 1: Teaching for Learning" is an eight-part video, print, and Web-based professional development workshop for middle and high school teachers. Participants will explore strategies to improve the way they teach 16 topics found in most Algebra 1 programs. In each session, participants will view two half-hour videos that…