Motivational classroom materials that provide direct instruction on problem-solving skills are given. The activity highlights and provides opportunities for practice with two problem-solving skills, make a drawing and work backward. (MNS)

Comments on the history of negative numbers, some methods that can be used to introduce the multiplication of negative numbers to students, and an explanation of why the product of two negative numbers is a positive number are included. (MNS)

Some techniques for managing the classroom and teaching programing that have worked well are described. Hardware placement and use, classroom management, instructional recommendations, and programing ideas are each discussed. (MNS)

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

Focusing on why the elliptical form in architecture is found only in the baroque period, discusses the development of the conic section and interactions in the baroque period with art, astronomy, and mathematics. An experimental approach to the topic carried out with high school seniors is reported. (Author/JN)

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)

Three computer programs are listed for finding binomial probabilities. Other applications and variations are discussed. (MNS)

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)

A problem-solving approach involving systematic experimentation, one of the most-used problem-solving strategies, is advocated since it is useful beyond mathematics problems. Examples of its use are given, with two problems explored and four others noted. (MNS)

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)

The author's conclusions about teaching proof are presented. Four types of mathematical proof are described and an approach to begin to teach direct proof in Year Eight is presented, with the idea of implication in logic gradually inculcated through the use of sentences. (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)

A function-graphing program is given, plus a series of experiments that students can carry out using the program. (MNS)