Describes ways to help preservice teachers become good classroom instructors of problem solving. It is felt it is impossible to teach problem solving if teachers themselves are not adequate problem solvers. In all cases, preservice teachers should have opportunities to solve problems and identify strategies used. (MP)

A discussion of a contest between the German mathematician Adam Riese and a draftsman involving the construction of as many perpendicular lines as possible in one minute leads to a review of some interesting constructions involving circles. It is suggested teachers challenge their students with the historic contest question. (MP)

Certain properties of lenses provide a physical model of the mathematical concepts of multiplication of integral numbers and of similarity transformations in geometry. Further, they can provide a realistic concrete representation for rules governing multiplication of signed numbers. Suggestions for problems and classroom demonstrations involving…

The creation of "false laws" of mathematics by many pupils as they attempt to rephrase new ideas and make them understandable and useful is discussed. The reasons for these mistakes and some ways teachers can help students adopt correct rules are reviewed. (MP)

Calculators are used to compute tables of values in solving problems of maximizing areas. Reproducable worksheets are included. (MP)

Seven activities designed to lead students to the idea that the ratio of the perimeter of a square and its diagonal is a fixed number for all squares are presented. The activities are groundwork for preparing students for the ratio between the circumference and diameter of a circle. (MP)

Increasing the amount of problem-solving training in the preservice education of mathematics teachers is promoted. Such problems should be designed to help preservice teachers acquire an "open search" frame of mind, according to the authors. (MP)

A simple enumeration problem from some research on problem solving is used to illustrate the contention that conjecture and proof have a central place in mathematics teaching. (Author/TG)

Multiple examples of the mathematics involved in photography are given. (MP)

The use of mathematical modelling as a systematic framework for solving word problems is presented. Applications for typical elementary algebra and calculus problems are featured. (MP)

An unusual alternative starting point for instruction in a beginning calculus course that focuses on Fixed Point Iteration (FPI) is presented. (MP)

"Pure" geometry is promoted as instructional material suitable for enriching the education of the mathematically gifted student. Examples of mathematical and logical concepts that can be highlighted with geometric presentations are given. (MP)

Three differences between the mathematics training of students from Spanish-speaking countries and that typical for pupils in the United States are discussed. (MP)

This discussion concerns itself with difficulties encountered by students in multiplication and concludes that when children understand a problem they can usually solve it. (MP)

Summarizes solutions submitted for a problem posed in a previous issue of Mathematics Teaching in the Middle School. The problem pertains to making a fraction equivalent to one-third that uses all the numbers, zero through nine, exactly once. Includes actual student solutions. (DDR)