The secondary school student is presented as seeing mathematics as a totally nonpractical subject due to the abstractness of certain topics. Solutions are suggested. (MP)

An example is presented that can be used to introduce the study of limits of sequences through recursive formulas yielding square roots. (MP)

A proof is given of the irrationality of the square root of 2 which depends on notions of terminating and repeating decimals. (MP)

A class's struggle with the computer solution of a nontrivial problem is related. The use of algorithms allowed a trial-and-error approach.

Topics discussed include: maximizing the volume of a box, finding different size squares on a geoboard, the angles formed by the hands of a clock, and questions related to three consecutive integers. (MP)

A brief overview is presented of the use of soap bubbles to solve minimal problems. A new class of problems that can be solved with soap film models is presented. (MP)

A description is given of an Algebra II-Chemistry I combined high school class being taught in an attempt to coordinate chemistry topics with related mathematics topics. (MP)

Instructions are given for the use of worksheets whose objectives are to challenge and develop spatial visualization through the mental folding, rotating, and intersecting of cubes. (MP)

This paper discusses the process of investigating a mathematical situation, making conjectures, formulating an equation, then using mathematical induction to show the result is valid. Several examples appropriate for secondary school level are given. (DT)

The philosophy and methodology of mathematics testing in the USSR are considered. (DT)

Properties of the cardioid, the nephroid, and the astroid curves are analyzed through a series of activities. (DT)

Activities are described in which the calculator is used for extending students' knowledge of place value and of basic arithmetic operations. (DT)

A transformation technique for graphing is described. (DT)

Conjectures about triangular arrangements of nine digits are stated and proved. (DT)

Specific procedures are outlined for teaching first-year algebra in such a way that students are given a reasonable voice in how and what they are taught and are allowed to learn at varying rates and from different materials. (DT)